/// <summary>
/// １次線要素を作成する（固有値問題用）
/// </summary>
/// <param name="nodes"></param>
/// <param name="EdgeToElementNoH"></param>
/// <param name="Elements"></param>
/// <param name="elements"></param>
public static void MkElements(
IList <int> nodes,
Dictionary <string, IList <int> > EdgeToElementNoH,
IList <FemElement> Elements,
ref IList <FemLineElement> elements)
{
// 要素内節点数
const int nno = Constants.LineNodeCnt_FirstOrder; //2; // 1次線要素
// 要素リスト作成
int elemCnt = (nodes.Count - 1); // 1次線要素
for (int elemIndex = 0; elemIndex < elemCnt; elemIndex++)
{
// 線要素の要素内節点
// 節点番号はポート上の1D節点番号(1起点の番号)
// 1 2
// +---+
FemLineElement element = new FemLineElement();
element.No = elemIndex + 1;
element.NodeNumbers = new int[nno];
element.NodeNumbers[0] = elemIndex + 1;
element.NodeNumbers[1] = elemIndex + 1 + 1;
element.MediaIndex = 0;
elements.Add(element);
}
// 要素を１辺とする2D領域の要素番号を取得
for (int elemIndex = 0; elemIndex < elements.Count; elemIndex++)
{
FemElement element = elements[elemIndex];
int[] nodeNumbers = element.NodeNumbers;
// 1辺だけ調べればよい(1-2をチェック)
int stNodeNumber = nodes[nodeNumbers[0] - 1];
int edNodeNumber = nodes[nodeNumbers[1] - 1];
string edgeKey = "";
if (stNodeNumber < edNodeNumber)
{
edgeKey = string.Format("{0}_{1}", stNodeNumber, edNodeNumber);
}
else
{
edgeKey = string.Format("{0}_{1}", edNodeNumber, stNodeNumber);
}
if (!EdgeToElementNoH.ContainsKey(edgeKey))
{
System.Diagnostics.Debug.WriteLine("logical error: Not find edge {0}", edgeKey);
}
else
{
// 隣接する2Dの要素を1つ取得する
int elemNo2d = EdgeToElementNoH[edgeKey][0];
FemElement element2d = Elements[elemNo2d - 1];
// 媒質インデックスをセット
element.MediaIndex = element2d.MediaIndex;
}
}
}
/// <summary>
/// コピー
/// </summary>
/// <param name="src"></param>
public override void CP(FemElement src)
{
if (src == this)
{
return;
}
// 基本クラスのコピー
base.CP(src);
}
/// <summary>
/// コピー
/// </summary>
/// <param name="src"></param>
public override void CP(FemElement src)
{
if (src == this)
{
return;
}
// 基本クラスのコピー
base.CP(src);
}
/// <summary>
/// 要素の節点数から該当するFemElementインスタンスを作成する
/// </summary>
/// <param name="eNodeCnt"></param>
/// <returns></returns>
public static FemElement CreateFemElementByElementNodeCnt(int eNodeCnt)
{
FemElement femElement = null;
Constants.FemElementShapeDV elemShapeDv;
int order;
int vertexCnt;
GetElementShapeDvAndOrderByElemNodeCnt(eNodeCnt, out elemShapeDv, out order, out vertexCnt);
if (vertexCnt == Constants.TriVertexCnt)
{
femElement = new FemTriElement();
}
else if (vertexCnt == Constants.QuadVertexCnt)
{
femElement = new FemQuadElement();
}
else
{
femElement = new FemElement();
}
return femElement;
}
/// <summary>
/// コピー
/// </summary>
/// <param name="src"></param>
public virtual void CP(FemElement src)
{
if (src == this)
{
return;
}
No = src.No;
NodeNumbers = null;
if (src.NodeNumbers != null)
{
NodeNumbers = new int[src.NodeNumbers.Length];
for (int i = 0; i < src.NodeNumbers.Length; i++)
{
NodeNumbers[i] = src.NodeNumbers[i];
}
}
MediaIndex = src.MediaIndex;
LineColor = src.LineColor;
BackColor = src.BackColor;
// 内部使用のフィールドはコピーしない
_Nodes = null;
_FValues = null;
_RotXFValues = null;
_RotYFValues = null;
_PoyntingXFValues = null;
_PoyntingYFValues = null;
_FactorForRot = 1.0;
_media_Q = new double[, ]
{
{ 1.0, 0.0, 0.0 },
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 },
};
_WaveModeDv = FemSolver.WaveModeDV.TE;
_WGStructureDv = FemSolver.WGStructureDV.HPlane2D;
IsCoarseFieldMesh = false;
}
/// <summary>
/// Fem入力データをファイルから読み込み
/// </summary>
/// <param name="filename">ファイル名(*.fem)</param>
/// <param name="nodes">節点リスト</param>
/// <param name="elements">要素リスト</param>
/// <param name="ports">ポートの節点番号リストのリスト</param>
/// <param name="forceBCNodes">強制境界節点番号リスト</param>
/// <param name="incidentPortNo">入射ポート番号</param>
/// <param name="medias">媒質情報リスト</param>
/// <param name="firstWaveLength">計算開始波長</param>
/// <param name="lastWaveLength">計算終了波長</param>
/// <param name="calcCnt">計算件数</param>
/// <param name="wgStructureDv">導波路構造区分</param>
/// <param name="waveModeDv">波のモード区分</param>
/// <param name="lsEqnSoverDv">線形方程式解法区分</param>
/// <param name="waveguideWidthForEPlane">導波管幅(E面解析用)</param>
/// <returns></returns>
public static bool LoadFromFile(
string filename,
out IList <FemNode> nodes,
out IList <FemElement> elements,
out IList <IList <int> > ports,
out IList <int> forceBCNodes,
out int incidentPortNo,
out MediaInfo[] medias,
out double firstWaveLength,
out double lastWaveLength,
out int calcCnt,
out FemSolver.WGStructureDV wgStructureDv,
out FemSolver.WaveModeDV waveModeDv,
out FemSolver.LinearSystemEqnSoverDV lsEqnSoverDv,
out double waveguideWidthForEPlane
)
{
int eNodeCnt = 0;
nodes = new List <FemNode>();
elements = new List <FemElement>();
ports = new List <IList <int> >();
forceBCNodes = new List <int>();
incidentPortNo = 1;
medias = new MediaInfo[Constants.MaxMediaCount];
for (int i = 0; i < medias.Length; i++)
{
MediaInfo media = new MediaInfo();
media.BackColor = CadLogic.MediaBackColors[i];
medias[i] = media;
}
firstWaveLength = 0.0;
lastWaveLength = 0.0;
calcCnt = 0;
wgStructureDv = Constants.DefWGStructureDv;
waveModeDv = Constants.DefWaveModeDv;
lsEqnSoverDv = Constants.DefLsEqnSolverDv;
waveguideWidthForEPlane = 0;
if (!File.Exists(filename))
{
return(false);
}
// 入力データ読み込み
try
{
using (StreamReader sr = new StreamReader(filename))
{
const char delimiter = ',';
string line;
string[] tokens;
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "Nodes")
{
MessageBox.Show("節点情報がありません", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int nodeCnt = int.Parse(tokens[1]);
for (int i = 0; i < nodeCnt; i++)
{
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 3)
{
MessageBox.Show("節点情報が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int no = int.Parse(tokens[0]);
if (no != i + 1)
{
MessageBox.Show("節点番号が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
FemNode femNode = new FemNode();
femNode.No = no;
femNode.Coord = new double[2];
femNode.Coord[0] = double.Parse(tokens[1]);
femNode.Coord[1] = double.Parse(tokens[2]);
nodes.Add(femNode);
}
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "Elements")
{
MessageBox.Show("要素情報がありません", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int elementCnt = int.Parse(tokens[1]);
for (int i = 0; i < elementCnt; i++)
{
line = sr.ReadLine();
tokens = line.Split(delimiter);
if ((tokens.Length != 1 + Constants.TriNodeCnt_SecondOrder) &&
(tokens.Length != 2 + Constants.TriNodeCnt_SecondOrder) && // ver1.1.0.0で媒質インデックスを番号の後に挿入
(tokens.Length != 2 + Constants.QuadNodeCnt_SecondOrder_Type2) &&
(tokens.Length != 2 + Constants.TriNodeCnt_FirstOrder) &&
(tokens.Length != 2 + Constants.QuadNodeCnt_FirstOrder)
)
{
MessageBox.Show("要素情報が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int elemNo = int.Parse(tokens[0]);
int mediaIndex = 0;
int indexOffset = 1; // ver1.0.0.0
int workENodeCnt = Constants.TriNodeCnt_SecondOrder;
if (tokens.Length == 1 + Constants.TriNodeCnt_SecondOrder)
{
// 媒質インデックスのない古い形式(ver1.0.0.0)
}
else
{
// ver1.1.0.0で媒質インデックスを追加
mediaIndex = int.Parse(tokens[1]);
indexOffset = 2;
workENodeCnt = tokens.Length - 2;
}
if (workENodeCnt <= 0)
{
MessageBox.Show("要素節点数が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
if (eNodeCnt == 0)
{
// 最初の要素の節点数を格納（チェックに利用)
eNodeCnt = workENodeCnt;
}
else
{
// 要素の節点数が変わった？
if (workENodeCnt != eNodeCnt)
{
MessageBox.Show("要素節点数が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
}
//FemElement femElement = new FemElement();
FemElement femElement = FemMeshLogic.CreateFemElementByElementNodeCnt(eNodeCnt);
femElement.No = elemNo;
femElement.MediaIndex = mediaIndex;
femElement.NodeNumbers = new int[eNodeCnt];
for (int n = 0; n < femElement.NodeNumbers.Length; n++)
{
femElement.NodeNumbers[n] = int.Parse(tokens[n + indexOffset]);
}
elements.Add(femElement);
}
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "Ports")
{
MessageBox.Show("入出力ポート情報がありません", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int portCnt = int.Parse(tokens[1]);
for (int i = 0; i < portCnt; i++)
{
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 2)
{
MessageBox.Show("入出力ポート情報が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int portNo = int.Parse(tokens[0]);
int portNodeCnt = int.Parse(tokens[1]);
if (portNo != i + 1)
{
MessageBox.Show("ポート番号が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
IList <int> portNodes = new List <int>();
for (int n = 0; n < portNodeCnt; n++)
{
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 2)
{
MessageBox.Show("ポートの節点情報が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int portNodeNumber = int.Parse(tokens[0]);
int nodeNumber = int.Parse(tokens[1]);
if (portNodeNumber != n + 1)
{
MessageBox.Show("ポートの節点番号が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
portNodes.Add(nodeNumber);
}
ports.Add(portNodes);
}
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "Force")
{
MessageBox.Show("強制境界情報がありません", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
int forceNodeCnt = int.Parse(tokens[1]);
for (int i = 0; i < forceNodeCnt; i++)
{
line = sr.ReadLine();
int nodeNumber = int.Parse(line);
forceBCNodes.Add(nodeNumber);
}
line = sr.ReadLine();
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "IncidentPortNo")
{
MessageBox.Show("入射ポート番号がありません", "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
incidentPortNo = int.Parse(tokens[1]);
//////////////////////////////////////////
//// Ver1.1.0.0からの追加情報
//////////////////////////////////////////
line = sr.ReadLine();
if (line == null || line.Length == 0)
{
// 媒質情報なし
// ver1.0.0.0
}
else
{
// 媒質情報？
// ver1.1.0.0
tokens = line.Split(delimiter);
if (tokens[0] != "Medias")
{
MessageBox.Show("媒質情報がありません");
return(false);
}
int cnt = int.Parse(tokens[1]);
if (cnt > Constants.MaxMediaCount)
{
MessageBox.Show("媒質情報の個数が不正です");
return(false);
}
for (int i = 0; i < cnt; i++)
{
line = sr.ReadLine();
if (line.Length == 0)
{
MessageBox.Show("媒質情報が不正です");
return(false);
}
tokens = line.Split(delimiter);
if (tokens.Length != 1 + 9 + 9)
{
MessageBox.Show("媒質情報が不正です");
return(false);
}
int mediaIndex = int.Parse(tokens[0]);
System.Diagnostics.Debug.Assert(mediaIndex == i);
double[,] p = new double[3, 3];
for (int m = 0; m < p.GetLength(0); m++)
{
for (int n = 0; n < p.GetLength(1); n++)
{
p[m, n] = double.Parse(tokens[1 + m * p.GetLength(1) + n]);
}
}
medias[i].SetP(p);
double[,] q = new double[3, 3];
for (int m = 0; m < q.GetLength(0); m++)
{
for (int n = 0; n < q.GetLength(1); n++)
{
q[m, n] = double.Parse(tokens[1 + 9 + m * q.GetLength(1) + n]);
}
}
medias[i].SetQ(q);
}
}
line = sr.ReadLine();
if (line == null || line.Length == 0)
{
}
else
{
tokens = line.Split(delimiter);
if (tokens.Length != 4 || tokens[0] != "WaveLengthRange")
{
MessageBox.Show("計算対象周波数情報がありません");
return(false);
}
firstWaveLength = double.Parse(tokens[1]);
lastWaveLength = double.Parse(tokens[2]);
calcCnt = int.Parse(tokens[3]);
}
line = sr.ReadLine();
if (line == null || line.Length == 0)
{
}
else
{
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "LsEqnSolverDv")
{
MessageBox.Show("線形方程式解法区分情報がありません");
return(false);
}
string value = tokens[1];
lsEqnSoverDv = FemSolver.StrToLinearSystemEqnSolverDV(value);
}
line = sr.ReadLine();
if (line == null || line.Length == 0)
{
}
else
{
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "WaveModeDv")
{
MessageBox.Show("計算対象モード区分情報がありません");
return(false);
}
if (tokens[1] == "TE")
{
waveModeDv = FemSolver.WaveModeDV.TE;
}
else if (tokens[1] == "TM")
{
waveModeDv = FemSolver.WaveModeDV.TM;
}
else
{
MessageBox.Show("計算対象モード区分情報が不正です");
return(false);
}
}
line = sr.ReadLine();
if (line == null || line.Length == 0)
{
}
else
{
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "WGStructureDv")
{
MessageBox.Show("計算対象導波路構造区分情報がありません");
return(false);
}
wgStructureDv = FemSolver.StrToWGStructureDV(tokens[1]);
}
line = sr.ReadLine();
if (line == null || line.Length == 0)
{
}
else
{
tokens = line.Split(delimiter);
if (tokens.Length != 2 || tokens[0] != "WaveguideWidthForEPlane")
{
MessageBox.Show("E面解析用導波路幅がありません");
return(false);
}
waveguideWidthForEPlane = double.Parse(tokens[1]);
}
}
}
catch (Exception exception)
{
System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace);
MessageBox.Show(exception.Message, "", MessageBoxButtons.OK, MessageBoxIcon.Error);
return(false);
}
return(true);
}
/// <summary>
/// ヘルムホルツ方程式に対する有限要素マトリクス作成
/// </summary>
/// <param name="waveLength">波長</param>
/// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
/// <param name="element">有限要素</param>
/// <param name="Nodes">節点リスト</param>
/// <param name="Medias">媒質リスト</param>
/// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
/// <param name="WGStructureDv">導波路構造区分</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param>
/// <param name="mat">マージされる全体行列</param>
public static void AddElementMat(double waveLength,
Dictionary<int, int> toSorted,
FemElement element,
IList<FemNode> Nodes,
MediaInfo[] Medias,
Dictionary<int, bool> ForceNodeNumberH,
FemSolver.WGStructureDV WGStructureDv,
FemSolver.WaveModeDV WaveModeDv,
double waveguideWidthForEPlane,
ref MyComplexMatrix mat)
{
// 定数
const double pi = Constants.pi;
const double c0 = Constants.c0;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 要素頂点数
const int vertexCnt = Constants.TriVertexCnt; //3;
// 要素内節点数
const int nno = Constants.TriNodeCnt_SecondOrder; //6; // 2次三角形要素
// 座標次元数
const int ndim = Constants.CoordDim2D; //2;
int[] nodeNumbers = element.NodeNumbers;
int[] no_c = new int[nno];
MediaInfo media = Medias[element.MediaIndex]; // ver1.1.0.0 媒質情報の取得
double[,] media_P = null;
double[,] media_Q = null;
// ヘルムホルツ方程式のパラメータP,Qを取得する
FemSolver.GetHelmholtzMediaPQ(
k0,
media,
WGStructureDv,
WaveModeDv,
waveguideWidthForEPlane,
out media_P,
out media_Q);
// 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
double[][] pp = new double[nno][];
for (int ino = 0; ino < nno; ino++)
{
int nodeNumber = nodeNumbers[ino];
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
no_c[ino] = nodeNumber;
pp[ino] = new double[ndim];
for (int n = 0; n < ndim; n++)
{
pp[ino][n] = node.Coord[n];
}
}
// 面積を求める
double area = KerEMatTri.TriArea(pp[0], pp[1], pp[2]);
//System.Diagnostics.Debug.WriteLine("Elem No {0} area: {1}", element.No, area);
System.Diagnostics.Debug.Assert(area >= 0.0);
// 面積座標の微分を求める
// dldx[k, n] k面積座標Lkのn方向微分
double[,] dldx = null;
double[] const_term = null;
KerEMatTri.TriDlDx(out dldx, out const_term, pp[0], pp[1], pp[2]);
// 形状関数の微分の係数を求める
// dndxC[ino,n,k] ino節点のn方向微分のLk(k面積座標)の係数
// dNino/dn = dndxC[ino, n, 0] * L0 + dndxC[ino, n, 1] * L1 + dndxC[ino, n, 2] * L2 + dndxC[ino, n, 3]
double[, ,] dndxC = new double[nno, ndim, vertexCnt + 1]
{
{
{4.0 * dldx[0, 0], 0.0, 0.0, -1.0 * dldx[0, 0]},
{4.0 * dldx[0, 1], 0.0, 0.0, -1.0 * dldx[0, 1]},
},
{
{0.0, 4.0 * dldx[1, 0], 0.0, -1.0 * dldx[1, 0]},
{0.0, 4.0 * dldx[1, 1], 0.0, -1.0 * dldx[1, 1]},
},
{
{0.0, 0.0, 4.0 * dldx[2, 0], -1.0 * dldx[2, 0]},
{0.0, 0.0, 4.0 * dldx[2, 1], -1.0 * dldx[2, 1]},
},
{
{4.0 * dldx[1, 0], 4.0 * dldx[0, 0], 0.0, 0.0},
{4.0 * dldx[1, 1], 4.0 * dldx[0, 1], 0.0, 0.0},
},
{
{0.0, 4.0 * dldx[2, 0], 4.0 * dldx[1, 0], 0.0},
{0.0, 4.0 * dldx[2, 1], 4.0 * dldx[1, 1], 0.0},
},
{
{4.0 * dldx[2, 0], 0.0, 4.0 * dldx[0, 0], 0.0},
{4.0 * dldx[2, 1], 0.0, 4.0 * dldx[0, 1], 0.0},
},
};
// ∫dN/dndN/dn dxdy
// integralDNDX[n, ino, jno] n = 0 --> ∫dN/dxdN/dx dxdy
// n = 1 --> ∫dN/dydN/dy dxdy
double[, ,] integralDNDX = new double[ndim, nno, nno];
for (int n = 0; n < ndim; n++)
{
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralDNDX[n, ino, jno]
= area / 6.0 * (dndxC[ino, n, 0] * dndxC[jno, n, 0] + dndxC[ino, n, 1] * dndxC[jno, n, 1] + dndxC[ino, n, 2] * dndxC[jno, n, 2])
+ area / 12.0 * (dndxC[ino, n, 0] * dndxC[jno, n, 1] + dndxC[ino, n, 0] * dndxC[jno, n, 2]
+ dndxC[ino, n, 1] * dndxC[jno, n, 0] + dndxC[ino, n, 1] * dndxC[jno, n, 2]
+ dndxC[ino, n, 2] * dndxC[jno, n, 0] + dndxC[ino, n, 2] * dndxC[jno, n, 1])
+ area / 3.0 * (dndxC[ino, n, 0] * dndxC[jno, n, 3] + dndxC[ino, n, 1] * dndxC[jno, n, 3]
+ dndxC[ino, n, 2] * dndxC[jno, n, 3]
+ dndxC[ino, n, 3] * dndxC[jno, n, 0] + dndxC[ino, n, 3] * dndxC[jno, n, 1]
+ dndxC[ino, n, 3] * dndxC[jno, n, 2])
+ area * dndxC[ino, n, 3] * dndxC[jno, n, 3];
}
}
}
// ∫N N dxdy
double[,] integralN = new double[nno, nno]
{
{ 6.0 * area / 180.0, -1.0 * area / 180.0, -1.0 * area / 180.0, 0.0, -4.0 * area / 180.0, 0.0},
{ -1.0 * area / 180.0, 6.0 * area / 180.0, -1.0 * area / 180.0, 0.0, 0.0, -4.0 * area / 180.0},
{ -1.0 * area / 180.0, -1.0 * area / 180.0, 6.0 * area / 180.0, -4.0 * area / 180.0, 0.0, 0.0},
{ 0.0, 0.0, -4.0 * area / 180.0, 32.0 * area / 180.0, 16.0 * area / 180.0, 16.0 * area / 180.0},
{ -4.0 * area / 180.0, 0.0, 0.0, 16.0 * area / 180.0, 32.0 * area / 180.0, 16.0 * area / 180.0},
{ 0.0, -4.0 * area / 180.0, 0.0, 16.0 * area / 180.0, 16.0 * area / 180.0, 32.0 * area / 180.0},
};
// 要素剛性行列を作る
double[,] emat = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
emat[ino, jno] = media_P[0, 0] * integralDNDX[1, ino, jno] + media_P[1, 1] * integralDNDX[0, ino, jno]
- k0 * k0 * media_Q[2, 2] * integralN[ino, jno];
}
}
// 要素剛性行列にマージする
for (int ino = 0; ino < nno; ino++)
{
int iNodeNumber = no_c[ino];
if (ForceNodeNumberH.ContainsKey(iNodeNumber)) continue;
int inoGlobal = toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
int jNodeNumber = no_c[jno];
if (ForceNodeNumberH.ContainsKey(jNodeNumber)) continue;
int jnoGlobal = toSorted[jNodeNumber];
//mat[inoGlobal, jnoGlobal] += emat[ino, jno];
//mat._body[inoGlobal + jnoGlobal * mat.RowSize] += emat[ino, jno];
// 実数部に加算する
//mat._body[inoGlobal + jnoGlobal * mat.RowSize].Real += emat[ino, jno];
// バンドマトリクス対応
mat._body[mat.GetBufferIndex(inoGlobal, jnoGlobal)].Real += emat[ino, jno];
}
}
}
/// <summary>
/// 三角形要素：点が要素内に含まれる？
/// </summary>
/// <param name="element">要素</param>
/// <param name="test_pp">テストする点</param>
/// <param name="Nodes">節点リスト（要素は座標を持たないので節点リストが必要）</param>
/// <returns></returns>
public static bool TriElement_IsPointInElement(FemElement element, double[] test_pp, IList<FemNode> nodes)
{
bool hit = false;
// 三角形の頂点数
const int vertexCnt = Constants.TriVertexCnt;
double[][] pps = new double[vertexCnt][];
// 2次三角形要素の最初の３点＝頂点の座標を取得
for (int ino = 0; ino < vertexCnt; ino++)
{
int nodeNumber = element.NodeNumbers[ino];
FemNode node = nodes[nodeNumber - 1];
System.Diagnostics.Debug.Assert(node.No == nodeNumber);
pps[ino] = node.Coord;
}
// バウンディングボックス取得
double minX = double.MaxValue;
double maxX = double.MinValue;
double minY = double.MaxValue;
double maxY = double.MinValue;
foreach (double[] pp in pps)
{
double xx = pp[0];
double yy = pp[1];
if (minX > xx)
{
minX = xx;
}
if (maxX < xx)
{
maxX = xx;
}
if (minY > yy)
{
minY = yy;
}
if (maxY < yy)
{
maxY = yy;
}
}
// バウンディングボックスでチェック
if (test_pp[0] < minX || test_pp[0] > maxX)
{
return hit;
}
if (test_pp[1] < minY || test_pp[1] > maxY)
{
return hit;
}
// 頂点？
foreach (double[] pp in pps)
{
if (Math.Abs(pp[0] - test_pp[0]) < Constants.PrecisionLowerLimit && Math.Abs(pp[1] - test_pp[1]) < Constants.PrecisionLowerLimit)
{
hit = true;
break;
}
}
if (!hit)
{
// 面積から内部判定する
double area = KerEMatTri.TriArea(pps[0], pps[1], pps[2]);
double sumOfSubArea = 0.0;
for (int ino = 0; ino < vertexCnt; ino++)
{
double[][] subArea_pp = new double[vertexCnt][];
subArea_pp[0] = pps[ino];
subArea_pp[1] = pps[(ino + 1) % vertexCnt];
subArea_pp[2] = test_pp;
//foreach (double[] work_pp in subArea_pp)
//{
// System.Diagnostics.Debug.Write("{0},{1} ", work_pp[0], work_pp[1]);
//}
double subArea = KerEMatTri.TriArea(subArea_pp[0], subArea_pp[1], subArea_pp[2]);
//System.Diagnostics.Debug.Write(" subArea = {0}", subArea);
//System.Diagnostics.Debug.WriteLine();
//BUGFIX
//if (subArea <= 0.0)
// 丁度辺上の場合は、サブエリアの１つが０になるのでこれは許可しないといけない
if (subArea < -1.0 * Constants.PrecisionLowerLimit) // 0未満
{
sumOfSubArea = 0.0;
break;
// 外側？
}
sumOfSubArea += Math.Abs(subArea);
}
if (Math.Abs(area - sumOfSubArea) < Constants.PrecisionLowerLimit)
{
hit = true;
}
}
return hit;
}
/// <summary>
/// コピー
/// </summary>
/// <param name="src"></param>
public virtual void CP(FemElement src)
{
if (src == this)
{
return;
}
No = src.No;
NodeNumbers = null;
if (src.NodeNumbers != null)
{
NodeNumbers = new int[src.NodeNumbers.Length];
for (int i = 0; i < src.NodeNumbers.Length; i++)
{
NodeNumbers[i] = src.NodeNumbers[i];
}
}
MediaIndex = src.MediaIndex;
LineColor = src.LineColor;
BackColor = src.BackColor;
// 内部使用のフィールドはコピーしない
_Nodes = null;
_FValues = null;
_RotXFValues = null;
_RotYFValues = null;
_PoyntingXFValues = null;
_PoyntingYFValues = null;
_FactorForRot = 1.0;
_media_Q = new double[,]
{
{1.0, 0.0, 0.0},
{0.0, 1.0, 0.0},
{0.0, 0.0, 1.0},
};
_WaveModeDv = FemSolver.WaveModeDV.TE;
_WGStructureDv = FemSolver.WGStructureDV.HPlane2D;
IsCoarseFieldMesh = false;
}
/// <summary>
/// フィールド値等高線図描画
/// </summary>
/// <param name="g"></param>
/// <param name="panel"></param>
public void DrawFieldEx(Graphics g, Panel panel, Rectangle clientRectangle, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv)
{
if (!isInputDataReady())
{
return;
}
if (!isOutputDataReady())
{
return;
}
Size delta;
Size ofs;
Size regionSize;
//getFitDrawRegion(panel, out delta, out ofs, out regionSize);
getFitDrawRegion(clientRectangle.Width, clientRectangle.Height, out delta, out ofs, out regionSize);
ofs.Width += clientRectangle.Left;
ofs.Height += clientRectangle.Top;
double min = 0.0;
double max = 1.0;
if (fieldDv == FemElement.FieldDV.Field)
{
min = MinFValue;
max = MaxFValue;
}
else if (fieldDv == FemElement.FieldDV.RotX || fieldDv == FemElement.FieldDV.RotY)
{
min = MinRotFValue;
max = MaxRotFValue;
}
else
{
return;
}
// カラーマップに最小、最大を設定
if (valueDv == FemElement.ValueDV.Real || valueDv == FemElement.ValueDV.Imaginary)
{
FValueColorMap.Min = -max;
FValueColorMap.Max = max;
}
else
{
// 既定値は絶対値で処理する
//FValueColorMap.Min = min;
FValueColorMap.Min = 0.0;
FValueColorMap.Max = max;
}
foreach (FemElement element in Elements)
{
// 等高線描画
element.DrawField(g, ofs, delta, regionSize, fieldDv, valueDv, FValueColorMap);
}
}
/// <summary>
/// ヘルムホルツ方程式に対する有限要素マトリクス作成
/// </summary>
/// <param name="waveLength">波長</param>
/// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
/// <param name="element">有限要素</param>
/// <param name="Nodes">節点リスト</param>
/// <param name="Medias">媒質リスト</param>
/// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
/// <param name="WGStructureDv">導波路構造区分</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param>
/// <param name="mat">マージされる全体行列</param>
public static void AddElementMat(double waveLength,
Dictionary <int, int> toSorted,
FemElement element,
IList <FemNode> Nodes,
MediaInfo[] Medias,
Dictionary <int, bool> ForceNodeNumberH,
FemSolver.WGStructureDV WGStructureDv,
FemSolver.WaveModeDV WaveModeDv,
double waveguideWidthForEPlane,
ref MyComplexMatrix mat)
{
// 定数
const double pi = Constants.pi;
const double c0 = Constants.c0;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 要素頂点数
const int vertexCnt = Constants.TriVertexCnt; //3;
// 要素内節点数
const int nno = Constants.TriNodeCnt_SecondOrder; //6; // 2次三角形要素
// 座標次元数
const int ndim = Constants.CoordDim2D; //2;
int[] nodeNumbers = element.NodeNumbers;
int[] no_c = new int[nno];
MediaInfo media = Medias[element.MediaIndex]; // ver1.1.0.0 媒質情報の取得
double[,] media_P = null;
double[,] media_Q = null;
// ヘルムホルツ方程式のパラメータP,Qを取得する
FemSolver.GetHelmholtzMediaPQ(
k0,
media,
WGStructureDv,
WaveModeDv,
waveguideWidthForEPlane,
out media_P,
out media_Q);
// 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
double[][] pp = new double[nno][];
for (int ino = 0; ino < nno; ino++)
{
int nodeNumber = nodeNumbers[ino];
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
no_c[ino] = nodeNumber;
pp[ino] = new double[ndim];
for (int n = 0; n < ndim; n++)
{
pp[ino][n] = node.Coord[n];
}
}
// 面積を求める
double area = KerEMatTri.TriArea(pp[0], pp[1], pp[2]);
//System.Diagnostics.Debug.WriteLine("Elem No {0} area: {1}", element.No, area);
System.Diagnostics.Debug.Assert(area >= 0.0);
// 面積座標の微分を求める
// dldx[k, n] k面積座標Lkのn方向微分
double[,] dldx = null;
double[] const_term = null;
KerEMatTri.TriDlDx(out dldx, out const_term, pp[0], pp[1], pp[2]);
// 形状関数の微分の係数を求める
// dndxC[ino,n,k] ino節点のn方向微分のLk(k面積座標)の係数
// dNino/dn = dndxC[ino, n, 0] * L0 + dndxC[ino, n, 1] * L1 + dndxC[ino, n, 2] * L2 + dndxC[ino, n, 3]
double[, ,] dndxC = new double[nno, ndim, vertexCnt + 1]
{
{
{ 4.0 * dldx[0, 0], 0.0, 0.0, -1.0 * dldx[0, 0] },
{ 4.0 * dldx[0, 1], 0.0, 0.0, -1.0 * dldx[0, 1] },
},
{
{ 0.0, 4.0 * dldx[1, 0], 0.0, -1.0 * dldx[1, 0] },
{ 0.0, 4.0 * dldx[1, 1], 0.0, -1.0 * dldx[1, 1] },
},
{
{ 0.0, 0.0, 4.0 * dldx[2, 0], -1.0 * dldx[2, 0] },
{ 0.0, 0.0, 4.0 * dldx[2, 1], -1.0 * dldx[2, 1] },
},
{
{ 4.0 * dldx[1, 0], 4.0 * dldx[0, 0], 0.0, 0.0 },
{ 4.0 * dldx[1, 1], 4.0 * dldx[0, 1], 0.0, 0.0 },
},
{
{ 0.0, 4.0 * dldx[2, 0], 4.0 * dldx[1, 0], 0.0 },
{ 0.0, 4.0 * dldx[2, 1], 4.0 * dldx[1, 1], 0.0 },
},
{
{ 4.0 * dldx[2, 0], 0.0, 4.0 * dldx[0, 0], 0.0 },
{ 4.0 * dldx[2, 1], 0.0, 4.0 * dldx[0, 1], 0.0 },
},
};
// ∫dN/dndN/dn dxdy
// integralDNDX[n, ino, jno] n = 0 --> ∫dN/dxdN/dx dxdy
// n = 1 --> ∫dN/dydN/dy dxdy
double[, ,] integralDNDX = new double[ndim, nno, nno];
for (int n = 0; n < ndim; n++)
{
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralDNDX[n, ino, jno]
= area / 6.0 * (dndxC[ino, n, 0] * dndxC[jno, n, 0] + dndxC[ino, n, 1] * dndxC[jno, n, 1] + dndxC[ino, n, 2] * dndxC[jno, n, 2])
+ area / 12.0 * (dndxC[ino, n, 0] * dndxC[jno, n, 1] + dndxC[ino, n, 0] * dndxC[jno, n, 2]
+ dndxC[ino, n, 1] * dndxC[jno, n, 0] + dndxC[ino, n, 1] * dndxC[jno, n, 2]
+ dndxC[ino, n, 2] * dndxC[jno, n, 0] + dndxC[ino, n, 2] * dndxC[jno, n, 1])
+ area / 3.0 * (dndxC[ino, n, 0] * dndxC[jno, n, 3] + dndxC[ino, n, 1] * dndxC[jno, n, 3]
+ dndxC[ino, n, 2] * dndxC[jno, n, 3]
+ dndxC[ino, n, 3] * dndxC[jno, n, 0] + dndxC[ino, n, 3] * dndxC[jno, n, 1]
+ dndxC[ino, n, 3] * dndxC[jno, n, 2])
+ area * dndxC[ino, n, 3] * dndxC[jno, n, 3];
}
}
}
// ∫N N dxdy
double[,] integralN = new double[nno, nno]
{
{ 6.0 * area / 180.0, -1.0 * area / 180.0, -1.0 * area / 180.0, 0.0, -4.0 * area / 180.0, 0.0 },
{ -1.0 * area / 180.0, 6.0 * area / 180.0, -1.0 * area / 180.0, 0.0, 0.0, -4.0 * area / 180.0 },
{ -1.0 * area / 180.0, -1.0 * area / 180.0, 6.0 * area / 180.0, -4.0 * area / 180.0, 0.0, 0.0 },
{ 0.0, 0.0, -4.0 * area / 180.0, 32.0 * area / 180.0, 16.0 * area / 180.0, 16.0 * area / 180.0 },
{ -4.0 * area / 180.0, 0.0, 0.0, 16.0 * area / 180.0, 32.0 * area / 180.0, 16.0 * area / 180.0 },
{ 0.0, -4.0 * area / 180.0, 0.0, 16.0 * area / 180.0, 16.0 * area / 180.0, 32.0 * area / 180.0 },
};
// 要素剛性行列を作る
double[,] emat = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
emat[ino, jno] = media_P[0, 0] * integralDNDX[1, ino, jno] + media_P[1, 1] * integralDNDX[0, ino, jno]
- k0 * k0 * media_Q[2, 2] * integralN[ino, jno];
}
}
// 要素剛性行列にマージする
for (int ino = 0; ino < nno; ino++)
{
int iNodeNumber = no_c[ino];
if (ForceNodeNumberH.ContainsKey(iNodeNumber))
{
continue;
}
int inoGlobal = toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
int jNodeNumber = no_c[jno];
if (ForceNodeNumberH.ContainsKey(jNodeNumber))
{
continue;
}
int jnoGlobal = toSorted[jNodeNumber];
//mat[inoGlobal, jnoGlobal] += emat[ino, jno];
//mat._body[inoGlobal + jnoGlobal * mat.RowSize] += emat[ino, jno];
// 実数部に加算する
//mat._body[inoGlobal + jnoGlobal * mat.RowSize].Real += emat[ino, jno];
// バンドマトリクス対応
mat._body[mat.GetBufferIndex(inoGlobal, jnoGlobal)].Real += emat[ino, jno];
}
}
}
/// <summary>
/// フィールド値の回転を描画する
/// </summary>
/// <param name="g"></param>
/// <param name="ofs"></param>
/// <param name="delta"></param>
/// <param name="regionSize"></param>
/// <param name="drawColor"></param>
/// <param name="fieldDv"></param>
/// <param name="minRotFValue"></param>
/// <param name="maxRotFValue"></param>
public override void DrawRotField(Graphics g, Size ofs, Size delta, Size regionSize, Color drawColor, FemElement.FieldDV fieldDv, double minRotFValue, double maxRotFValue)
{
if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null)
{
return;
}
Complex[] tagtXValues = null;
Complex[] tagtYValues = null;
if (fieldDv == FemElement.FieldDV.PoyntingXY)
{
tagtXValues = _PoyntingXFValues;
tagtYValues = _PoyntingYFValues;
}
else if (fieldDv == FemElement.FieldDV.RotXY)
{
tagtXValues = _RotXFValues;
tagtYValues = _RotYFValues;
}
else
{
return;
}
const int ndim = Constants.CoordDim2D; //2; // 座標の次元数
//const int vertexCnt = Constants.QuadVertexCnt; //4; // 四角形形の頂点の数(2次要素でも同じ)
//const int nodeCnt = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 四角形形2次要素
int nodeCnt = NodeNumbers.Length;
if (nodeCnt != Constants.QuadNodeCnt_SecondOrder_Type2 && nodeCnt != Constants.QuadNodeCnt_FirstOrder)
{
return;
}
// 四角形の節点座標を取得
double[][] pp = new double[nodeCnt][];
for (int ino = 0; ino < pp.GetLength(0); ino++)
{
FemNode node = _Nodes[ino];
System.Diagnostics.Debug.Assert(node.Coord.Length == ndim);
pp[ino] = new double[ndim];
pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width;
pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height;
}
// 四角形内部を四角形で分割
// 要素節点座標( 局所r,s成分 )
// s
// |
// 3+ 6 +2
// | | |
// ---7---+---5-->r
// | | |
// 0+ 4 +1
// |
//
double[][] n_pts =
{
// r, s
new double[] {-1.0, -1.0}, //0
new double[] { 1.0, -1.0}, //1
new double[] { 1.0, 1.0}, //2
new double[] {-1.0, 1.0}, //3
new double[] { 0, -1.0}, //4
new double[] { 1.0, 0}, //5
new double[] { 0, 1.0}, //6
new double[] {-1.0, 0}, //7
};
// 節点上のrot(Ez)を求める
int nno = nodeCnt;
{
double r = 0;
double s = 0;
// 形状関数
double[] N = new double[nno];
if (nodeCnt == Constants.QuadNodeCnt_SecondOrder_Type2)
{
// 節点0～3 : 四角形の頂点
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s) * (ri * r + si * s - 1.0);
}
// 節点4,6 : r方向辺上中点
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
N[i] = 0.5 * (1.0 - r * r) * (1.0 + si * s);
}
// 節点5,7 : s方向辺上中点
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
N[i] = 0.5 * (1.0 + ri * r) * (1.0 - s * s);
}
}
else if (nodeCnt == Constants.QuadNodeCnt_FirstOrder)
{
// 節点0～3 : 四角形の頂点
for (int i = 0; i < nno; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s);
}
}
// 表示する位置
double showPosX = 0;
double showPosY = 0;
for (int k = 0; k < nodeCnt; k++)
{
showPosX += pp[k][0] * N[k];
showPosY += pp[k][1] * N[k];
}
Complex cvalueX = new Complex(0, 0);
Complex cvalueY = new Complex(0, 0);
for (int k = 0; k < nodeCnt; k++)
{
cvalueX += tagtXValues[k] * N[k];
cvalueY += tagtYValues[k] * N[k];
}
try
{
double showScale = ((double)regionSize.Width / DefPanelWidth) * ArrowLength;
// 実数部のベクトル表示
int lenX = (int)((double)(cvalueX.Real / maxRotFValue) * showScale);
int lenY = (int)((double)(cvalueY.Real / maxRotFValue) * showScale);
if (lenX != 0 || lenY != 0)
{
// Y方向は表示上逆になる
lenY = -lenY;
using (Pen pen = new Pen(drawColor, 1))
{
//pen.DashStyle = System.Drawing.Drawing2D.DashStyle.Dot;
//pen.StartCap = System.Drawing.Drawing2D.LineCap.Round;
pen.EndCap = System.Drawing.Drawing2D.LineCap.ArrowAnchor;
//pen.CustomEndCap = new System.Drawing.Drawing2D.AdjustableArrowCap(3, 3, false); // 重い
g.DrawLine(pen, (int)showPosX, (int)showPosY, (int)(showPosX + lenX), (int)(showPosY + lenY));
}
}
}
catch (Exception exception)
{
System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace);
}
}
}
/* 数値積分版
/// <summary>
/// ヘルムホルツ方程式に対する有限要素マトリクス作成
/// </summary>
/// <param name="waveLength">波長</param>
/// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
/// <param name="element">有限要素</param>
/// <param name="Nodes">節点リスト</param>
/// <param name="Medias">媒質リスト</param>
/// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="mat">マージされる全体行列</param>
public static void AddElementMat(double waveLength,
Dictionary<int, int> toSorted,
FemElement element,
IList<FemNode> Nodes,
MediaInfo[] Medias,
Dictionary<int, bool> ForceNodeNumberH,
FemSolver.WaveModeDv WaveModeDv,
ref MyComplexMatrix mat)
{
// 定数
const double pi = Constants.pi;
const double c0 = Constants.c0;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 要素頂点数
const int vertexCnt = Constants.QuadVertexCnt; //4;
// 要素内節点数
const int nno = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 2次セレンディピティ
// 座標次元数
const int ndim = Constants.CoordDim2D; //2;
int[] nodeNumbers = element.NodeNumbers;
int[] no_c = new int[nno];
MediaInfo media = Medias[element.MediaIndex];
double[,] media_P = null;
double[,] media_Q = null;
if (WaveModeDv == FemSolver.WaveModeDv.TE)
{
media_P = media.P;
media_Q = media.Q;
}
else if (WaveModeDv == FemSolver.WaveModeDv.TM)
{
media_P = media.Q;
media_Q = media.P;
}
else
{
System.Diagnostics.Debug.Assert(false);
}
// [p]は逆数をとる
media_P = MyMatrixUtil.matrix_Inverse(media_P);
// 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
double[][] pp = new double[nno][];
for (int ino = 0; ino < nno; ino++)
{
int nodeNumber = nodeNumbers[ino];
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
no_c[ino] = nodeNumber;
pp[ino] = new double[ndim];
for (int n = 0; n < ndim; n++)
{
pp[ino][n] = node.Coord[n];
}
}
//// 四角形の辺の長さを求める
//double[] le = new double[4];
//le[0] = FemMeshLogic.GetDistance(pp[0], pp[1]);
//le[1] = FemMeshLogic.GetDistance(pp[1], pp[2]);
//le[2] = FemMeshLogic.GetDistance(pp[2], pp[3]);
//le[3] = FemMeshLogic.GetDistance(pp[3], pp[0]);
// 要素節点座標( 局所r,s成分 )
// s
// |
// 3+ 6 +2
// | | |
// ---7---+---5-->r
// | | |
// 0+ 4 +1
// |
//
double[][] n_pts =
{
// r, s
new double[] {-1.0, -1.0}, //0
new double[] { 1.0, -1.0}, //1
new double[] { 1.0, 1.0}, //2
new double[] {-1.0, 1.0}, //3
new double[] { 0, -1.0}, //4
new double[] { 1.0, 0}, //5
new double[] { 0, 1.0}, //6
new double[] {-1.0, 0}, //7
};
// ガウスルジャンドルの積分公式
double[][] g_pts = new double[5][]
{
// ポイント(ξ: [-1 +1]区間)、重み
new double[] { -0.90617985, 0.23692689},
new double[] { -0.53846931, 0.47862867},
new double[] {0.0, 0.56888889},
new double[] {0.53846931, 0.47862867},
new double[] {0.90617985, 0.23692689}
};
// 要素剛性行列を作る
double[,] emat = new Complex[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
emat[ino, jno] = 0.0;
double detjsum = 0; //check
foreach (double[] s_g_pt in g_pts)
{
foreach (double[] r_g_pt in g_pts)
{
// 積分点
double r = r_g_pt[0];
double s = s_g_pt[0];
// 重み(2次元)
double weight = r_g_pt[1] * s_g_pt[1];
// 形状関数
double[] N = new double[nno];
// 形状関数のr, s方向微分
double[] dNdr = new double[nno];
double[] dNds = new double[nno];
// 節点0～3 : 四角形の頂点
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s) * (ri* r + si * s - 1.0);
// 形状関数のr方向微分
dNdr[i] = 0.25 * ri * (1.0 + si * s) * (2.0 * ri * r + si * s);
// 形状関数のs方向微分
dNds[i] = 0.25 * si * (1.0 + ri * r) * (ri * r + 2.0 * si * s);
}
// 節点4,6 : r方向辺上中点
foreach (int i in new int[]{ 4, 6})
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
N[i] = 0.5 * (1.0 - r * r) * (1.0 + si * s);
// 形状関数のr方向微分
dNdr[i] = -1.0 * r * (1.0 + si * s);
// 形状関数のs方向微分
dNds[i] = 0.5 * si * (1.0 - r * r);
}
// 節点5,7 : s方向辺上中点
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
N[i] = 0.5 * (1.0 + ri * r) * (1.0 - s * s);
// 形状関数のr方向微分
dNdr[i] = 0.5 * ri * (1.0 - s * s);
// 形状関数のs方向微分
dNds[i] = -1.0 * s * (1.0 + ri * r);
}
// ヤコビアン行列
double j11;
double j12;
double j21;
double j22;
j11 = 0;
j12 = 0;
j21 = 0;
j22 = 0;
//for (int i = 0; i < vertexCnt; i++)
//{
// // 頂点の座標の微分
// // 座標の形状関数は一次四角形のものを使用する
// // 節点の局所座標
// double ri = n_pts[i][0];
// double si = n_pts[i][1];
// double dNdr_1stOrder = 0.25 * ri * (1.0 + si * s);
// double dNds_1stOrder = 0.25 * (1.0 + ri * r) * si;
// j11 += dNdr_1stOrder * pp[i][0];
// j12 += dNdr_1stOrder * pp[i][1];
// j21 += dNds_1stOrder * pp[i][0];
// j22 += dNds_1stOrder * pp[i][1];
//}
for (int i = 0; i < nno; i++)
{
j11 += dNdr[i] * pp[i][0];
j12 += dNdr[i] * pp[i][1];
j21 += dNds[i] * pp[i][0];
j22 += dNds[i] * pp[i][1];
}
// ヤコビアン
double detj = j11 * j22 - j12 * j21;
detjsum += detj * weight;
//System.Diagnostics.Debug.WriteLine("det:{0}", detj);
// gradr[0] : gradrのx成分 grad[1] : gradrのy成分
// grads[0] : gradsのx成分 grads[1] : gradsのy成分
double[] gradr = new double[2];
double[] grads = new double[2];
gradr[0] = j22 / detj;
gradr[1] = - j21 / detj;
grads[0] = - j12 / detj;
grads[1] = j11 / detj;
// 形状関数のx, y方向微分
double[,] dNdX = new double[ndim, nno];
for (int i = 0; i < nno; i++)
{
for (int direction = 0; direction < ndim; direction++)
{
dNdX[direction, i] = dNdr[i] * gradr[direction] + dNds[i] * grads[direction];
}
}
// 汎関数
double functional = media_P[0, 0] * dNdX[1, ino] * dNdX[1, jno] + media_P[1, 1] * dNdX[0, ino] * dNdX[0, jno]
- k0 * k0 * media_Q[2, 2] * N[ino] * N[jno];
emat[ino, jno] += detj * weight * functional;
}
}
//System.Diagnostics.Debug.WriteLine("detsum: {0}", detjsum);
}
}
// 要素剛性行列にマージする
for (int ino = 0; ino < nno; ino++)
{
int iNodeNumber = no_c[ino];
if (ForceNodeNumberH.ContainsKey(iNodeNumber)) continue;
int inoGlobal = toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
int jNodeNumber = no_c[jno];
if (ForceNodeNumberH.ContainsKey(jNodeNumber)) continue;
int jnoGlobal = toSorted[jNodeNumber];
mat[inoGlobal, jnoGlobal] += emat[ino, jno];
}
}
}
*/
/// <summary>
/// ヘルムホルツ方程式に対する有限要素マトリクス作成
/// </summary>
/// <param name="waveLength">波長</param>
/// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
/// <param name="element">有限要素</param>
/// <param name="Nodes">節点リスト</param>
/// <param name="Medias">媒質リスト</param>
/// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
/// <param name="WGStructureDv">導波路構造区分</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param>
/// <param name="mat">マージされる全体行列</param>
public static void AddElementMat(double waveLength,
Dictionary<int, int> toSorted,
FemElement element,
IList<FemNode> Nodes,
MediaInfo[] Medias,
Dictionary<int, bool> ForceNodeNumberH,
FemSolver.WGStructureDV WGStructureDv,
FemSolver.WaveModeDV WaveModeDv,
double waveguideWidthForEPlane,
ref MyComplexMatrix mat)
{
// 定数
const double pi = Constants.pi;
const double c0 = Constants.c0;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 要素頂点数
//const int vertexCnt = Constants.QuadVertexCnt; //4;
// 要素内節点数
const int nno = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 2次セレンディピティ
// 座標次元数
const int ndim = Constants.CoordDim2D; //2;
int[] nodeNumbers = element.NodeNumbers;
int[] no_c = new int[nno];
MediaInfo media = Medias[element.MediaIndex];
double[,] media_P = null;
double[,] media_Q = null;
// ヘルムホルツ方程式のパラメータP,Qを取得する
FemSolver.GetHelmholtzMediaPQ(
k0,
media,
WGStructureDv,
WaveModeDv,
waveguideWidthForEPlane,
out media_P,
out media_Q);
// 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
double[][] pp = new double[nno][];
for (int ino = 0; ino < nno; ino++)
{
int nodeNumber = nodeNumbers[ino];
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
no_c[ino] = nodeNumber;
pp[ino] = new double[ndim];
for (int n = 0; n < ndim; n++)
{
pp[ino][n] = node.Coord[n];
}
}
// 四角形の辺の長さを求める
double[] le = new double[4];
le[0] = FemMeshLogic.GetDistance(pp[0], pp[1]);
le[1] = FemMeshLogic.GetDistance(pp[1], pp[2]);
le[2] = FemMeshLogic.GetDistance(pp[2], pp[3]);
le[3] = FemMeshLogic.GetDistance(pp[3], pp[0]);
System.Diagnostics.Debug.Assert(Math.Abs(le[0] - le[2]) < Constants.PrecisionLowerLimit);
System.Diagnostics.Debug.Assert(Math.Abs(le[1] - le[3]) < Constants.PrecisionLowerLimit);
double lx = le[0];
double ly = le[1];
// 要素節点座標( 局所r,s成分 )
// s
// |
// 3+ 6 +2
// | | |
// ---7---+---5-->r
// | | |
// 0+ 4 +1
// |
//
double[][] n_pts =
{
// r, s
new double[] {-1.0, -1.0}, //0
new double[] { 1.0, -1.0}, //1
new double[] { 1.0, 1.0}, //2
new double[] {-1.0, 1.0}, //3
new double[] { 0, -1.0}, //4
new double[] { 1.0, 0}, //5
new double[] { 0, 1.0}, //6
new double[] {-1.0, 0}, //7
};
// Ni = a0(r^2*s) + a1(r^2) + a2(r) + a3(rs) + a4(rs^2) + a5(s^2) + a6(s) + a7
double[,] Ni_a = new double[nno, 8];
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
Ni_a[i, 0] = 0.25 * ri * ri * si;
Ni_a[i, 1] = 0.25 * ri * ri;
Ni_a[i, 2] = 0.0;
Ni_a[i, 3] = 0.25 * ri * si;
Ni_a[i, 4] = 0.25 * ri * si * si;
Ni_a[i, 5] = 0.25 * si * si;
Ni_a[i, 6] = 0.0;
Ni_a[i, 7] = -0.25;
}
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
Ni_a[i, 0] = -0.5 * si;
Ni_a[i, 1] = -0.5;
Ni_a[i, 2] = 0.0;
Ni_a[i, 3] = 0.0;
Ni_a[i, 4] = 0.0;
Ni_a[i, 5] = 0.0;
Ni_a[i, 6] = 0.5 * si;
Ni_a[i, 7] = 0.5;
}
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
Ni_a[i, 0] = 0.0;
Ni_a[i, 1] = 0.0;
Ni_a[i, 2] = 0.5 * ri;
Ni_a[i, 3] = 0.0;
Ni_a[i, 4] = -0.5 * ri;
Ni_a[i, 5] = -0.5;
Ni_a[i, 6] = 0.0;
Ni_a[i, 7] = 0.5;
}
// dNidr = a0(r^2*s) + a1(r^2) + a2(r) + a3(rs) + a4(rs^2) + a5(s^2) + a6(s) + a7
double[,] dNidr_a = new double[nno, 8];
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNidr_a[i, 0] = 0.0;
dNidr_a[i, 1] = 0.0; // r^2
dNidr_a[i, 2] = 0.25 * 2.0 * ri * ri; // r
dNidr_a[i, 3] = 0.25 * 2.0 * ri * ri * si; // rs
dNidr_a[i, 4] = 0.0;
dNidr_a[i, 5] = 0.25 * ri * si * si; // s^2
dNidr_a[i, 6] = 0.25 * ri * si; // s
dNidr_a[i, 7] = 0.0; //1
}
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNidr_a[i, 0] = 0.0;
dNidr_a[i, 1] = 0.0; // r^2
dNidr_a[i, 2] = -1.0; // r
dNidr_a[i, 3] = -si; // rs
dNidr_a[i, 4] = 0.0;
dNidr_a[i, 5] = 0.0; // s^2
dNidr_a[i, 6] = 0.0; // s
dNidr_a[i, 7] = 0.0; // 1
}
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNidr_a[i, 0] = 0.0;
dNidr_a[i, 1] = 0.0; // r^2
dNidr_a[i, 2] = 0.0; // r
dNidr_a[i, 3] = 0.0; // rs
dNidr_a[i, 4] = 0.0;
dNidr_a[i, 5] = -0.5 * ri; // s^2
dNidr_a[i, 6] = 0.0; // s
dNidr_a[i, 7] = 0.5 * ri; // 1
}
// dNids = a0(r^2*s) + a1(r^2) + a2(r) + a3(rs) + a4(rs^2) + a5(s^2) + a6(s) + a7
double[,] dNids_a = new double[nno, 8];
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNids_a[i, 0] = 0.0;
dNids_a[i, 1] = 0.25 * ri * ri * si; // r^2
dNids_a[i, 2] = 0.25 * ri * si; // r
dNids_a[i, 3] = 0.25 * 2.0 * ri * si * si; // rs
dNids_a[i, 4] = 0.0;
dNids_a[i, 5] = 0.0; // s^2
dNids_a[i, 6] = 0.25 * 2.0 * si * si; // s
dNids_a[i, 7] = 0.0; //1
}
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNids_a[i, 0] = 0.0;
dNids_a[i, 1] = -0.5 * si; // r^2
dNids_a[i, 2] = 0.0; // r
dNids_a[i, 3] = 0.0; // rs
dNids_a[i, 4] = 0.0;
dNids_a[i, 5] = 0.0; // s^2
dNids_a[i, 6] = 0.0; // s
dNids_a[i, 7] = 0.5 * si; //1
}
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNids_a[i, 0] = 0.0;
dNids_a[i, 1] = 0.0; // r^2
dNids_a[i, 2] = 0.0; // r
dNids_a[i, 3] = -ri; // rs
dNids_a[i, 4] = 0.0;
dNids_a[i, 5] = 0.0; // s^2
dNids_a[i, 6] = -1.0; // s
dNids_a[i, 7] = 0.0; //1
}
// ∫dN/dndN/dn dxdy
// integralDNDX[n, ino, jno] n = 0 --> ∫dN/dxdN/dx dxdy
// n = 1 --> ∫dN/dydN/dy dxdy
double[, ,] integralDNDX = new double[ndim, nno, nno];
// ∫N N dxdy
double[,] integralN = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralN[ino, jno] = lx * ly / 4.0 *
(
// r^4s^2
4.0 / 15.0 * Ni_a[ino, 0] * Ni_a[jno, 0]
// r^2s^2
+ 4.0 / 9.0 * (Ni_a[ino, 6] * Ni_a[jno, 0] + Ni_a[ino, 5] * Ni_a[jno, 1] + Ni_a[ino, 4] * Ni_a[jno, 2] + Ni_a[ino, 3] * Ni_a[jno, 3]
+ Ni_a[ino, 2] * Ni_a[jno, 4] + Ni_a[ino, 1] * Ni_a[jno, 5] + Ni_a[ino, 0] * Ni_a[jno, 6])
// r^4
+ 4.0 / 5.0 * Ni_a[ino, 1] * Ni_a[jno, 1]
// r^2
+ 4.0 / 3.0 * (Ni_a[ino, 7] * Ni_a[jno, 1] + Ni_a[ino, 2] * Ni_a[jno, 2] + Ni_a[ino, 1] * Ni_a[jno, 7])
// r^2s^4
+ 4.0 / 15.0 * Ni_a[ino, 4] * Ni_a[jno, 4]
// s^4
+ 4.0 / 5.0 * Ni_a[ino, 5] * Ni_a[jno, 5]
// s^2
+ 4.0 / 3.0 * (Ni_a[ino, 7] * Ni_a[jno, 5] + Ni_a[ino, 6] * Ni_a[jno, 6] + Ni_a[ino, 5] * Ni_a[jno, 7])
// 1
+ 4.0 * Ni_a[ino, 7] * Ni_a[jno, 7]
);
integralDNDX[0, ino, jno] = ly / lx *
(
// r^4s^2
4.0 / 15.0 * dNidr_a[ino, 0] * dNidr_a[jno, 0]
// r^2s^2
+ 4.0 / 9.0 * (dNidr_a[ino, 6] * dNidr_a[jno, 0] + dNidr_a[ino, 5] * dNidr_a[jno, 1] + dNidr_a[ino, 4] * dNidr_a[jno, 2]
+ dNidr_a[ino, 3] * dNidr_a[jno, 3]
+ dNidr_a[ino, 2] * dNidr_a[jno, 4] + dNidr_a[ino, 1] * dNidr_a[jno, 5] + dNidr_a[ino, 0] * dNidr_a[jno, 6])
// r^4
+ 4.0 / 5.0 * dNidr_a[ino, 1] * dNidr_a[jno, 1]
// r^2
+ 4.0 / 3.0 * (dNidr_a[ino, 7] * dNidr_a[jno, 1] + dNidr_a[ino, 2] * dNidr_a[jno, 2] + dNidr_a[ino, 1] * dNidr_a[jno, 7])
// r^2s^4
+ 4.0 / 15.0 * dNidr_a[ino, 4] * dNidr_a[jno, 4]
// s^4
+ 4.0 / 5.0 * dNidr_a[ino, 5] * dNidr_a[jno, 5]
// s^2
+ 4.0 / 3.0 * (dNidr_a[ino, 7] * dNidr_a[jno, 5] + dNidr_a[ino, 6] * dNidr_a[jno, 6] + dNidr_a[ino, 5] * dNidr_a[jno, 7])
// 1
+ 4.0 * dNidr_a[ino, 7] * dNidr_a[jno, 7]
);
integralDNDX[1, ino, jno] = lx / ly *
(
// r^4s^2
4.0 / 15.0 * dNids_a[ino, 0] * dNids_a[jno, 0]
// r^2s^2
+ 4.0 / 9.0 * (dNids_a[ino, 6] * dNids_a[jno, 0] + dNids_a[ino, 5] * dNids_a[jno, 1] + dNids_a[ino, 4] * dNids_a[jno, 2]
+ dNids_a[ino, 3] * dNids_a[jno, 3]
+ dNids_a[ino, 2] * dNids_a[jno, 4] + dNids_a[ino, 1] * dNids_a[jno, 5] + dNids_a[ino, 0] * dNids_a[jno, 6])
// r^4
+ 4.0 / 5.0 * dNids_a[ino, 1] * dNids_a[jno, 1]
// r^2
+ 4.0 / 3.0 * (dNids_a[ino, 7] * dNids_a[jno, 1] + dNids_a[ino, 2] * dNids_a[jno, 2] + dNids_a[ino, 1] * dNids_a[jno, 7])
// r^2s^4
+ 4.0 / 15.0 * dNids_a[ino, 4] * dNids_a[jno, 4]
// s^4
+ 4.0 / 5.0 * dNids_a[ino, 5] * dNids_a[jno, 5]
// s^2
+ 4.0 / 3.0 * (dNids_a[ino, 7] * dNids_a[jno, 5] + dNids_a[ino, 6] * dNids_a[jno, 6] + dNids_a[ino, 5] * dNids_a[jno, 7])
// 1
+ 4.0 * dNids_a[ino, 7] * dNids_a[jno, 7]
);
}
}
// 要素剛性行列を作る
double[,] emat = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
emat[ino, jno] = media_P[0, 0] * integralDNDX[1, ino, jno] + media_P[1, 1] * integralDNDX[0, ino, jno]
- k0 * k0 * media_Q[2, 2] * integralN[ino, jno];
}
}
// 要素剛性行列にマージする
for (int ino = 0; ino < nno; ino++)
{
int iNodeNumber = no_c[ino];
if (ForceNodeNumberH.ContainsKey(iNodeNumber)) continue;
int inoGlobal = toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
int jNodeNumber = no_c[jno];
if (ForceNodeNumberH.ContainsKey(jNodeNumber)) continue;
int jnoGlobal = toSorted[jNodeNumber];
//mat[inoGlobal, jnoGlobal] += emat[ino, jno];
//mat._body[inoGlobal + jnoGlobal * mat.RowSize] += emat[ino, jno];
// 実数部に加算する
//mat._body[inoGlobal + jnoGlobal * mat.RowSize].Real += emat[ino, jno];
// バンドマトリクス対応
mat._body[mat.GetBufferIndex(inoGlobal, jnoGlobal)].Real += emat[ino, jno];
}
}
}
/// <summary>
/// フィールド値の回転を描画する
/// </summary>
/// <param name="g"></param>
/// <param name="ofs"></param>
/// <param name="delta"></param>
/// <param name="regionSize"></param>
/// <param name="drawColor"></param>
/// <param name="fieldDv"></param>
/// <param name="minRotFValue"></param>
/// <param name="maxRotFValue"></param>
public override void DrawRotField(Graphics g, Size ofs, Size delta, Size regionSize, Color drawColor, FemElement.FieldDV fieldDv, double minRotFValue, double maxRotFValue)
{
if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null)
{
return;
}
Complex[] tagtXValues = null;
Complex[] tagtYValues = null;
if (fieldDv == FemElement.FieldDV.PoyntingXY)
{
tagtXValues = _PoyntingXFValues;
tagtYValues = _PoyntingYFValues;
}
else if (fieldDv == FemElement.FieldDV.RotXY)
{
tagtXValues = _RotXFValues;
tagtYValues = _RotYFValues;
}
else
{
return;
}
const int ndim = Constants.CoordDim2D; //2; // 座標の次元数
const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ)
//const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素
int nodeCnt = NodeNumbers.Length;
if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder)
{
return;
}
// 三角形の節点座標を取得
double[][] pp = new double[nodeCnt][];
for (int ino = 0; ino < pp.GetLength(0); ino++)
{
FemNode node = _Nodes[ino];
System.Diagnostics.Debug.Assert(node.Coord.Length == ndim);
pp[ino] = new double[ndim];
pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width;
pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height;
}
// 表示する位置の面積座標
double[] Li = new double[vertexCnt]
{
1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0
};
// 表示する位置の形状関数
double[] vNi = null;
if (nodeCnt == Constants.TriNodeCnt_FirstOrder)
{
vNi = new double[]
{
Li[0],
Li[1],
Li[2]
};
}
else
{
vNi = new double[]
{
Li[0] * (2.0 * Li[0] - 1.0),
Li[1] * (2.0 * Li[1] - 1.0),
Li[2] * (2.0 * Li[2] - 1.0),
4.0 * Li[0] * Li[1],
4.0 * Li[1] * Li[2],
4.0 * Li[2] * Li[0],
};
}
// 表示する位置
double showPosX = 0;
double showPosY = 0;
for (int k = 0; k < nodeCnt; k++)
{
showPosX += pp[k][0] * vNi[k];
showPosY += pp[k][1] * vNi[k];
}
Complex cvalueX = new Complex(0, 0);
Complex cvalueY = new Complex(0, 0);
for (int k = 0; k < nodeCnt; k++)
{
cvalueX += tagtXValues[k] * vNi[k];
cvalueY += tagtYValues[k] * vNi[k];
}
try
{
double showScale = ((double)regionSize.Width / DefPanelWidth) * ArrowLength;
// 実数部のベクトル表示
int lenX = 0;
int lenY = 0;
if (Math.Abs(maxRotFValue) >= Constants.PrecisionLowerLimit)
{
lenX = (int)((double)(cvalueX.Real / maxRotFValue) * showScale);
lenY = (int)((double)(cvalueY.Real / maxRotFValue) * showScale);
}
if (lenX != 0 || lenY != 0)
{
// Y方向は表示上逆になる
lenY = -lenY;
using (Pen pen = new Pen(drawColor, 1))
{
//pen.DashStyle = System.Drawing.Drawing2D.DashStyle.Dot;
//pen.StartCap = System.Drawing.Drawing2D.LineCap.Round;
pen.EndCap = System.Drawing.Drawing2D.LineCap.ArrowAnchor;
//pen.CustomEndCap = new System.Drawing.Drawing2D.AdjustableArrowCap(3, 3, false); // 重い
g.DrawLine(pen, (int)showPosX, (int)showPosY, (int)(showPosX + lenX), (int)(showPosY + lenY));
}
}
}
catch (Exception exception)
{
System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace);
}
}
/// <summary>
/// フィールド値を描画する
/// </summary>
/// <param name="g"></param>
/// <param name="ofs"></param>
/// <param name="delta"></param>
/// <param name="regionSize"></param>
/// <param name="fieldDv"></param>
/// <param name="valueDv"></param>
/// <param name="colorMap"></param>
/*
public override void DrawField(Graphics g, Size ofs, Size delta, Size regionSize, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv, ColorMap colorMap)
{
//base.DrawField(g, ofs, delta, regionSize, colorMap);
if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null)
{
return;
}
Complex[] tagtValues = null;
if (fieldDv == FemElement.FieldDV.Field)
{
tagtValues = _FValues;
}
else if (fieldDv == FemElement.FieldDV.RotX)
{
tagtValues = _RotXFValues;
}
else if (fieldDv == FemElement.FieldDV.RotY)
{
tagtValues = _RotYFValues;
}
else
{
return;
}
const int ndim = Constants.CoordDim2D; //2; // 座標の次元数
const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ)
//const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素
int nodeCnt = NodeNumbers.Length;
if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder)
{
return;
}
// 三角形の節点座標を取得
double[][] pp = new double[nodeCnt][];
for (int ino = 0; ino < pp.GetLength(0); ino++)
{
FemNode node = _Nodes[ino];
System.Diagnostics.Debug.Assert(node.Coord.Length == ndim);
pp[ino] = new double[ndim];
pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width;
pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height;
}
// 下記分割ロジックの原点となる頂点
// 頂点0固定で計算していたが、原点の内角が直角のとき長方形メッシュになるので原点を2（頂点を0,1,2としたとき）にする
int orginVertexNo = 2;
// 内角が最大の頂点を取得し、その頂点を原点とする(後のロジックは原点が頂点を0,1,2としたとき、2になっている
{
double minCosth = double.MaxValue;
int minCosthVertexNo = 0;
for (int ino = 0; ino < vertexCnt; ino++)
{
const int vecCnt = 2;
double[][] vec = new double[vecCnt][] { new double[ndim]{0, 0}, new double[ndim]{0, 0} };
double[] len = new double[vecCnt];
double costh;
{
int n1 = ino;
int n2 = (ino + 1) % 3;
int n3 = (ino + 2) % 3;
vec[0][0] = pp[n2][0] - pp[n1][0];
vec[0][1] = pp[n2][1] - pp[n1][1];
vec[1][0] = pp[n3][0] - pp[n1][0];
vec[1][1] = pp[n3][1] - pp[n1][1];
len[0] = FemMeshLogic.GetDistance(pp[n1], pp[n2]);
len[1] = FemMeshLogic.GetDistance(pp[n1], pp[n3]);
costh = (vec[0][0] * vec[1][0] + vec[0][1] * vec[1][1]) / (len[0] * len[1]);
if (costh < minCosth)
{
minCosth = costh;
minCosthVertexNo = ino;
}
}
}
orginVertexNo = (minCosthVertexNo + 2) % 3;
}
// 三角形内部を四角形で分割
// 面積座標L1方向分割数
//int ndiv = 4;
int ndiv = Constants.TriDrawFieldMshDivCnt;
double defdL1 = 1.0 / (double)ndiv;
double defdL2 = defdL1;
for (int i1 = 0; i1 < ndiv; i1++)
{
double vL1 = i1 * defdL1;
double vL1Next = (i1 + 1) * defdL1;
if (i1 == ndiv - 1)
{
vL1Next = 1.0;
}
double vL2max = 1.0 - vL1;
if (vL2max < 0.0)
{
// ERROR
System.Diagnostics.Debug.WriteLine("logic error vL2max = {0}", vL2max);
continue;
}
double fdiv2 = (double)ndiv * vL2max;
int ndiv2 = (int)fdiv2;
if (fdiv2 - (double)ndiv2 > Constants.PrecisionLowerLimit)
{
ndiv2++;
}
for (int i2 = 0; i2 < ndiv2; i2++)
{
double vL2 = i2 * defdL2;
double vL2Next = (i2 + 1) * defdL2;
if (i2 == ndiv2 - 1)
{
vL2Next = vL2max;
}
double vL3 = 1.0 - vL1 - vL2;
if (vL3 < 0.0)
{
// ERROR
System.Diagnostics.Debug.WriteLine("logic error vL3 = {0}", vL3);
continue;
}
// 四角形の頂点
const int rectVCnt = 4;
double[][] rectLi = new double[rectVCnt][]
{
new double[]{vL1 , vL2 , 0},
new double[]{vL1Next, vL2 , 0},
new double[]{vL1Next, vL2Next, 0},
new double[]{vL1 , vL2Next, 0}
};
if ((i1 == ndiv - 1) || (i2 == ndiv2 - 1))
{
for (int k = 0; k < 3; k++)
{
rectLi[2][k] = rectLi[3][k];
}
}
double[][] rectpp = new double[rectVCnt][];
for (int ino = 0; ino < rectVCnt; ino++)
{
if (rectLi[ino][0] < 0.0)
{
rectLi[ino][0] = 0.0;
System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][0] = {1}", ino, rectLi[ino][0]);
}
if (rectLi[ino][0] > 1.0)
{
rectLi[ino][0] = 1.0;
System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][0] = {1}", ino, rectLi[ino][0]);
}
if (rectLi[ino][1] < 0.0)
{
rectLi[ino][1] = 0.0;
System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][1] = {1}", ino, rectLi[ino][1]);
}
if (rectLi[ino][1] > (1.0 - rectLi[ino][0])) // L2最大値(1 - L1)チェック
{
rectLi[ino][1] = 1.0 - rectLi[ino][0];
}
rectLi[ino][2] = 1.0 - rectLi[ino][0] - rectLi[ino][1];
if (rectLi[ino][2] < 0.0)
{
System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][2] = {1}", ino, rectLi[ino][2]);
}
}
for (int ino = 0; ino < rectVCnt; ino++)
{
double[] vLpp = rectLi[ino];
double xx = 0.0;
double yy = 0.0;
for (int k = 0; k < vertexCnt; k++)
{
xx += pp[k][0] * vLpp[(k + orginVertexNo) % vertexCnt];
yy += pp[k][1] * vLpp[(k + orginVertexNo) % vertexCnt];
}
rectpp[ino] = new double[] { xx, yy };
}
// 表示する位置
double[] vLi = new double[] { (rectLi[0][0] + rectLi[1][0]) * 0.5, (rectLi[0][1] + rectLi[3][1]) * 0.5, 0 };
if (vLi[0] < 0.0)
{
vLi[0] = 0.0;
}
if (vLi[0] > 1.0)
{
vLi[0] = 1.0;
}
if (vLi[1] < 0.0)
{
vLi[1] = 0.0;
}
if (vLi[1] > (1.0 - vLi[0]))
{
vLi[1] = (1.0 - vLi[0]);
}
vLi[2] = 1.0 - vLi[0] - vLi[1];
if (vLi[2] < 0.0)
{
System.Diagnostics.Debug.WriteLine("logic error vLi[2] = {0}", vLi[2]);
}
// 表示する値
Complex cvalue = new Complex(0.0, 0.0);
// 表示する位置の形状関数値
double[] vNi = null;
double[] shiftedLi = new double[vertexCnt];
for (int i = 0; i < vertexCnt; i++)
{
shiftedLi[i] = vLi[(i + orginVertexNo) % vertexCnt];
}
if (nodeCnt == Constants.TriNodeCnt_FirstOrder)
{
vNi = new double[]
{
shiftedLi[0],
shiftedLi[1],
shiftedLi[2]
};
}
else
{
vNi = new double[]
{
shiftedLi[0] * (2.0 * shiftedLi[0] - 1.0),
shiftedLi[1] * (2.0 * shiftedLi[1] - 1.0),
shiftedLi[2] * (2.0 * shiftedLi[2] - 1.0),
4.0 * shiftedLi[0] * shiftedLi[1],
4.0 * shiftedLi[1] * shiftedLi[2],
4.0 * shiftedLi[2] * shiftedLi[0],
};
}
for (int k = 0; k < nodeCnt; k++)
{
cvalue += tagtValues[k] * vNi[k];
}
// 四角形の頂点（描画用）
Point[] rectp = new Point[rectVCnt];
for (int ino = 0; ino < rectVCnt; ino++)
{
rectp[ino] = new Point((int)rectpp[ino][0], (int)rectpp[ino][1]);
}
try
{
// 表示する値
double showValue = 0.0;
if (valueDv == ValueDV.Real)
{
showValue = cvalue.Real;
}
else if (valueDv == ValueDV.Imaginary)
{
showValue = cvalue.Imaginary;
}
else
{
// 既定値は絶対値
showValue = Complex.Abs(cvalue);
}
// 塗りつぶし色の取得
Color fillColor = colorMap.GetColor(showValue);
// 塗りつぶし
using (Brush brush = new SolidBrush(fillColor))
{
g.FillPolygon(brush, rectp);
}
}
catch (Exception exception)
{
System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace);
}
}
}
}
*/
public override void DrawField(Graphics g, Size ofs, Size delta, Size regionSize, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv, ColorMap colorMap)
{
//base.DrawField(g, ofs, delta, regionSize, colorMap);
if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null)
{
return;
}
Complex[] tagtValues = null;
if (fieldDv == FemElement.FieldDV.Field)
{
tagtValues = _FValues;
}
else if (fieldDv == FemElement.FieldDV.RotX)
{
tagtValues = _RotXFValues;
}
else if (fieldDv == FemElement.FieldDV.RotY)
{
tagtValues = _RotYFValues;
}
else
{
return;
}
const int ndim = Constants.CoordDim2D; //2; // 座標の次元数
const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ)
//const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素
int nodeCnt = NodeNumbers.Length;
if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder)
{
return;
}
// 三角形の節点座標を取得
double[][] pp = new double[nodeCnt][];
for (int ino = 0; ino < pp.GetLength(0); ino++)
{
FemNode node = _Nodes[ino];
System.Diagnostics.Debug.Assert(node.Coord.Length == ndim);
pp[ino] = new double[ndim];
pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width;
pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height;
}
// 長方形描画領域のリスト
IList<double[][]> rectLiList = _RectLiList;
// 描画ロジック上の原点となる頂点
int orginVertexNo = _OrginVertexNo;
// 四角形の頂点
const int rectVCnt = 4;
foreach (double[][] rectLi in rectLiList)
{
double[][] rectpp = new double[rectVCnt][];
for (int ino = 0; ino < rectVCnt; ino++)
{
double[] vLpp = rectLi[ino];
double xx = 0.0;
double yy = 0.0;
for (int k = 0; k < vertexCnt; k++)
{
xx += pp[k][0] * vLpp[(k + orginVertexNo) % vertexCnt];
yy += pp[k][1] * vLpp[(k + orginVertexNo) % vertexCnt];
}
rectpp[ino] = new double[] { xx, yy };
}
// 表示する位置
double[] vLi = new double[] { (rectLi[0][0] + rectLi[1][0]) * 0.5, (rectLi[0][1] + rectLi[3][1]) * 0.5, 0 };
if (vLi[0] < 0.0)
{
vLi[0] = 0.0;
}
if (vLi[0] > 1.0)
{
vLi[0] = 1.0;
}
if (vLi[1] < 0.0)
{
vLi[1] = 0.0;
}
if (vLi[1] > (1.0 - vLi[0]))
{
vLi[1] = (1.0 - vLi[0]);
}
vLi[2] = 1.0 - vLi[0] - vLi[1];
if (vLi[2] < 0.0)
{
System.Diagnostics.Debug.WriteLine("logic error vLi[2] = {0}", vLi[2]);
}
// 表示する値
Complex cvalue = new Complex(0.0, 0.0);
// 表示する位置の形状関数値
double[] vNi = null;
double[] shiftedLi = new double[vertexCnt];
for (int i = 0; i < vertexCnt; i++)
{
shiftedLi[i] = vLi[(i + orginVertexNo) % vertexCnt];
}
if (nodeCnt == Constants.TriNodeCnt_FirstOrder)
{
vNi = new double[]
{
shiftedLi[0],
shiftedLi[1],
shiftedLi[2]
};
}
else
{
vNi = new double[]
{
shiftedLi[0] * (2.0 * shiftedLi[0] - 1.0),
shiftedLi[1] * (2.0 * shiftedLi[1] - 1.0),
shiftedLi[2] * (2.0 * shiftedLi[2] - 1.0),
4.0 * shiftedLi[0] * shiftedLi[1],
4.0 * shiftedLi[1] * shiftedLi[2],
4.0 * shiftedLi[2] * shiftedLi[0],
};
}
for (int k = 0; k < nodeCnt; k++)
{
cvalue += tagtValues[k] * vNi[k];
}
// 四角形の頂点（描画用）
Point[] rectp = new Point[rectVCnt];
for (int ino = 0; ino < rectVCnt; ino++)
{
rectp[ino] = new Point((int)rectpp[ino][0], (int)rectpp[ino][1]);
}
try
{
// 表示する値
double showValue = 0.0;
if (valueDv == ValueDV.Real)
{
showValue = cvalue.Real;
}
else if (valueDv == ValueDV.Imaginary)
{
showValue = cvalue.Imaginary;
}
else
{
// 既定値は絶対値
showValue = Complex.Abs(cvalue);
}
// 塗りつぶし色の取得
Color fillColor = colorMap.GetColor(showValue);
// 塗りつぶし
using (Brush brush = new SolidBrush(fillColor))
{
g.FillPolygon(brush, rectp);
}
}
catch (Exception exception)
{
System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace);
}
}
}
/// <summary>
/// フィールド値の回転を描画する
/// </summary>
/// <param name="g"></param>
/// <param name="ofs"></param>
/// <param name="delta"></param>
/// <param name="regionSize"></param>
/// <param name="drawColor"></param>
/// <param name="fieldDv"></param>
/// <param name="minRotFValue"></param>
/// <param name="maxRotFValue"></param>
public virtual void DrawRotField(Graphics g, Size ofs, Size delta, Size regionSize, Color drawColor, FemElement.FieldDV fieldDv, double minRotFValue, double maxRotFValue)
{
}
/// <summary>
/// フィールド値を描画する
/// </summary>
/// <param name="g"></param>
/// <param name="ofs"></param>
/// <param name="delta"></param>
/// <param name="regionSize"></param>
/// <param name="fieldDv"></param>
/// <param name="valueDv"></param>
/// <param name="colorMap"></param>
public virtual void DrawField(Graphics g, Size ofs, Size delta, Size regionSize, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv, ColorMap colorMap)
{
}
/// <summary>
/// フィールド値を描画する
/// </summary>
/// <param name="g"></param>
/// <param name="ofs"></param>
/// <param name="delta"></param>
/// <param name="regionSize"></param>
/// <param name="colorMap"></param>
/// <param name="valueDv"></param>
public override void DrawField(Graphics g, Size ofs, Size delta, Size regionSize, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv, ColorMap colorMap)
{
//base.DrawField(g, ofs, delta, regionSize, colorMap);
if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null)
{
return;
}
Complex[] tagtValues = null;
if (fieldDv == FemElement.FieldDV.Field)
{
tagtValues = _FValues;
}
else if (fieldDv == FemElement.FieldDV.RotX)
{
tagtValues = _RotXFValues;
}
else if (fieldDv == FemElement.FieldDV.RotY)
{
tagtValues = _RotYFValues;
}
else
{
return;
}
const int ndim = Constants.CoordDim2D; //2; // 座標の次元数
const int vertexCnt = Constants.QuadVertexCnt; //3; // 四角形形の頂点の数(2次要素でも同じ)
//const int nodeCnt = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 四角形2次要素
int nodeCnt = NodeNumbers.Length;
if (nodeCnt != Constants.QuadNodeCnt_SecondOrder_Type2 && nodeCnt != Constants.QuadNodeCnt_FirstOrder)
{
return;
}
// 四角形節点座標を取得
double[][] pp = new double[nodeCnt][];
for (int ino = 0; ino < pp.GetLength(0); ino++)
{
FemNode node = _Nodes[ino];
System.Diagnostics.Debug.Assert(node.Coord.Length == ndim);
pp[ino] = new double[ndim];
pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width;
pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height;
}
// 四角形内部を四角形で分割
// 要素節点座標( 局所r,s成分 )
// s
// |
// 3+ 6 +2
// | | |
// ---7---+---5-->r
// | | |
// 0+ 4 +1
// |
//
double[][] n_pts =
{
// r, s
new double[] {-1.0, -1.0}, //0
new double[] { 1.0, -1.0}, //1
new double[] { 1.0, 1.0}, //2
new double[] {-1.0, 1.0}, //3
new double[] { 0, -1.0}, //4
new double[] { 1.0, 0}, //5
new double[] { 0, 1.0}, //6
new double[] {-1.0, 0}, //7
};
int ndiv = this.IsCoarseFieldMesh ? (Constants.TriDrawFieldMshDivCnt / 2) : Constants.TriDrawFieldMshDivCnt;
double defdr = 2.0 / (double)ndiv;
double defds = defdr;
for (int i1 = 0; i1 < ndiv; i1++)
{
double r = - 1.0 + i1 * defdr;
double rNext = r + defdr;
for (int i2 = 0; i2 < ndiv; i2++)
{
double s = -1.0 + i2 * defds;
double sNext = s + defds;
// 四角形の頂点
const int rectVCnt = 4;
double[][] rect_local_p = new double[rectVCnt][]
{
new double[]{r , s },
new double[]{rNext, s },
new double[]{rNext, sNext},
new double[]{r , sNext}
};
double[][] rectpp = new double[rectVCnt][];
for (int ino = 0; ino < rectVCnt; ino++)
{
double work_r = rect_local_p[ino][0];
double work_s = rect_local_p[ino][1];
double xx = 0.0;
double yy = 0.0;
for (int k = 0; k < vertexCnt; k++)
{
double ri = n_pts[k][0];
double si = n_pts[k][1];
xx += pp[k][0] * 0.25 * (1 + ri * work_r) * (1 + si * work_s);
yy += pp[k][1] * 0.25 * (1 + ri * work_r) * (1 + si * work_s);
}
rectpp[ino] = new double[] { xx, yy };
}
// 表示する位置
double[] disp_p = new double[] { (rect_local_p[0][0] + rect_local_p[1][0]) * 0.5, (rect_local_p[0][1] + rect_local_p[3][1]) * 0.5 };
// 表示する値
Complex cvalue = new Complex(0.0, 0.0);
// 表示する位置の形状関数値
double[] workN = new double[nodeCnt];
if (nodeCnt == Constants.QuadNodeCnt_FirstOrder)
{
double work_r = disp_p[0];
double work_s = disp_p[1];
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
workN[i] = 0.25 * (1.0 + ri * work_r) * (1.0 + si * work_s);
}
}
else
{
double work_r = disp_p[0];
double work_s = disp_p[1];
// 節点0～3 : 四角形の頂点
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
workN[i] = 0.25 * (1.0 + ri * work_r) * (1.0 + si * work_s) * (ri * work_r + si * work_s - 1.0);
}
// 節点4,6 : r方向辺上中点
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
workN[i] = 0.5 * (1.0 - work_r * work_r) * (1.0 + si * work_s);
}
// 節点5,7 : s方向辺上中点
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
// 形状関数N
workN[i] = 0.5 * (1.0 + ri * work_r) * (1.0 - work_s * work_s);
}
}
for (int k = 0; k < nodeCnt; k++)
{
cvalue += tagtValues[k] * workN[k];
}
// 四角形の頂点（描画用）
Point[] rectp = new Point[rectVCnt];
for (int ino = 0; ino < rectVCnt; ino++)
{
rectp[ino] = new Point((int)rectpp[ino][0], (int)rectpp[ino][1]);
}
try
{
// 表示する値
double showValue = 0.0;
if (valueDv == ValueDV.Real)
{
showValue = cvalue.Real;
}
else if (valueDv == ValueDV.Imaginary)
{
showValue = cvalue.Imaginary;
}
else
{
// 既定値は絶対値
showValue = Complex.Abs(cvalue);
}
// 塗りつぶし色の取得
Color fillColor = colorMap.GetColor(showValue);
// 塗りつぶし
using (Brush brush = new SolidBrush(fillColor))
{
g.FillPolygon(brush, rectp);
}
}
catch (Exception exception)
{
System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace);
}
}
}
}
/* 数値積分版
* /// <summary>
* /// ヘルムホルツ方程式に対する有限要素マトリクス作成
* /// </summary>
* /// <param name="waveLength">波長</param>
* /// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
* /// <param name="element">有限要素</param>
* /// <param name="Nodes">節点リスト</param>
* /// <param name="Medias">媒質リスト</param>
* /// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
* /// <param name="WaveModeDv">計算する波のモード区分</param>
* /// <param name="mat">マージされる全体行列</param>
* public static void AddElementMat(double waveLength,
* Dictionary<int, int> toSorted,
* FemElement element,
* IList<FemNode> Nodes,
* MediaInfo[] Medias,
* Dictionary<int, bool> ForceNodeNumberH,
* FemSolver.WaveModeDv WaveModeDv,
* ref MyComplexMatrix mat)
* {
* // 定数
* const double pi = Constants.pi;
* const double c0 = Constants.c0;
* // 波数
* double k0 = 2.0 * pi / waveLength;
* // 角周波数
* double omega = k0 * c0;
*
* // 要素頂点数
* const int vertexCnt = Constants.QuadVertexCnt; //4;
* // 要素内節点数
* const int nno = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 2次セレンディピティ
* // 座標次元数
* const int ndim = Constants.CoordDim2D; //2;
*
* int[] nodeNumbers = element.NodeNumbers;
* int[] no_c = new int[nno];
* MediaInfo media = Medias[element.MediaIndex];
* double[,] media_P = null;
* double[,] media_Q = null;
* if (WaveModeDv == FemSolver.WaveModeDv.TE)
* {
* media_P = media.P;
* media_Q = media.Q;
* }
* else if (WaveModeDv == FemSolver.WaveModeDv.TM)
* {
* media_P = media.Q;
* media_Q = media.P;
* }
* else
* {
* System.Diagnostics.Debug.Assert(false);
* }
* // [p]は逆数をとる
* media_P = MyMatrixUtil.matrix_Inverse(media_P);
*
* // 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
* double[][] pp = new double[nno][];
* for (int ino = 0; ino < nno; ino++)
* {
* int nodeNumber = nodeNumbers[ino];
* int nodeIndex = nodeNumber - 1;
* FemNode node = Nodes[nodeIndex];
*
* no_c[ino] = nodeNumber;
* pp[ino] = new double[ndim];
* for (int n = 0; n < ndim; n++)
* {
* pp[ino][n] = node.Coord[n];
* }
* }
*
* //// 四角形の辺の長さを求める
* //double[] le = new double[4];
* //le[0] = FemMeshLogic.GetDistance(pp[0], pp[1]);
* //le[1] = FemMeshLogic.GetDistance(pp[1], pp[2]);
* //le[2] = FemMeshLogic.GetDistance(pp[2], pp[3]);
* //le[3] = FemMeshLogic.GetDistance(pp[3], pp[0]);
*
* // 要素節点座標( 局所r,s成分 )
* // s
* // |
* // 3+ 6 +2
* // | | |
* // ---7---+---5-->r
* // | | |
* // 0+ 4 +1
* // |
* //
* double[][] n_pts =
* {
* // r, s
* new double[] {-1.0, -1.0}, //0
* new double[] { 1.0, -1.0}, //1
* new double[] { 1.0, 1.0}, //2
* new double[] {-1.0, 1.0}, //3
* new double[] { 0, -1.0}, //4
* new double[] { 1.0, 0}, //5
* new double[] { 0, 1.0}, //6
* new double[] {-1.0, 0}, //7
* };
*
*
* // ガウスルジャンドルの積分公式
* double[][] g_pts = new double[5][]
* {
* // ポイント(ξ: [-1 +1]区間)、重み
* new double[] { -0.90617985, 0.23692689},
* new double[] { -0.53846931, 0.47862867},
* new double[] {0.0, 0.56888889},
* new double[] {0.53846931, 0.47862867},
* new double[] {0.90617985, 0.23692689}
* };
*
* // 要素剛性行列を作る
* double[,] emat = new Complex[nno, nno];
* for (int ino = 0; ino < nno; ino++)
* {
* for (int jno = 0; jno < nno; jno++)
* {
* emat[ino, jno] = 0.0;
* double detjsum = 0; //check
* foreach (double[] s_g_pt in g_pts)
* {
* foreach (double[] r_g_pt in g_pts)
* {
* // 積分点
* double r = r_g_pt[0];
* double s = s_g_pt[0];
* // 重み(2次元)
* double weight = r_g_pt[1] * s_g_pt[1];
* // 形状関数
* double[] N = new double[nno];
* // 形状関数のr, s方向微分
* double[] dNdr = new double[nno];
* double[] dNds = new double[nno];
* // 節点0～3 : 四角形の頂点
* for (int i = 0; i < 4; i++)
* {
* // 節点の局所座標
* double ri = n_pts[i][0];
* double si = n_pts[i][1];
* // 形状関数N
* N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s) * (ri* r + si * s - 1.0);
* // 形状関数のr方向微分
* dNdr[i] = 0.25 * ri * (1.0 + si * s) * (2.0 * ri * r + si * s);
* // 形状関数のs方向微分
* dNds[i] = 0.25 * si * (1.0 + ri * r) * (ri * r + 2.0 * si * s);
* }
* // 節点4,6 : r方向辺上中点
* foreach (int i in new int[]{ 4, 6})
* {
* // 節点の局所座標
* double ri = n_pts[i][0];
* double si = n_pts[i][1];
* // 形状関数N
* N[i] = 0.5 * (1.0 - r * r) * (1.0 + si * s);
* // 形状関数のr方向微分
* dNdr[i] = -1.0 * r * (1.0 + si * s);
* // 形状関数のs方向微分
* dNds[i] = 0.5 * si * (1.0 - r * r);
* }
* // 節点5,7 : s方向辺上中点
* foreach (int i in new int[] { 5, 7 })
* {
* // 節点の局所座標
* double ri = n_pts[i][0];
* double si = n_pts[i][1];
* // 形状関数N
* N[i] = 0.5 * (1.0 + ri * r) * (1.0 - s * s);
* // 形状関数のr方向微分
* dNdr[i] = 0.5 * ri * (1.0 - s * s);
* // 形状関数のs方向微分
* dNds[i] = -1.0 * s * (1.0 + ri * r);
* }
*
* // ヤコビアン行列
* double j11;
* double j12;
* double j21;
* double j22;
* j11 = 0;
* j12 = 0;
* j21 = 0;
* j22 = 0;
*
* //for (int i = 0; i < vertexCnt; i++)
* //{
* // // 頂点の座標の微分
* // // 座標の形状関数は一次四角形のものを使用する
* // // 節点の局所座標
* // double ri = n_pts[i][0];
* // double si = n_pts[i][1];
* // double dNdr_1stOrder = 0.25 * ri * (1.0 + si * s);
* // double dNds_1stOrder = 0.25 * (1.0 + ri * r) * si;
* // j11 += dNdr_1stOrder * pp[i][0];
* // j12 += dNdr_1stOrder * pp[i][1];
* // j21 += dNds_1stOrder * pp[i][0];
* // j22 += dNds_1stOrder * pp[i][1];
* //}
*
* for (int i = 0; i < nno; i++)
* {
* j11 += dNdr[i] * pp[i][0];
* j12 += dNdr[i] * pp[i][1];
* j21 += dNds[i] * pp[i][0];
* j22 += dNds[i] * pp[i][1];
* }
* // ヤコビアン
* double detj = j11 * j22 - j12 * j21;
* detjsum += detj * weight;
* //System.Diagnostics.Debug.WriteLine("det:{0}", detj);
*
* // gradr[0] : gradrのx成分 grad[1] : gradrのy成分
* // grads[0] : gradsのx成分 grads[1] : gradsのy成分
* double[] gradr = new double[2];
* double[] grads = new double[2];
* gradr[0] = j22 / detj;
* gradr[1] = - j21 / detj;
* grads[0] = - j12 / detj;
* grads[1] = j11 / detj;
*
* // 形状関数のx, y方向微分
* double[,] dNdX = new double[ndim, nno];
* for (int i = 0; i < nno; i++)
* {
* for (int direction = 0; direction < ndim; direction++)
* {
* dNdX[direction, i] = dNdr[i] * gradr[direction] + dNds[i] * grads[direction];
* }
* }
*
* // 汎関数
* double functional = media_P[0, 0] * dNdX[1, ino] * dNdX[1, jno] + media_P[1, 1] * dNdX[0, ino] * dNdX[0, jno]
* - k0 * k0 * media_Q[2, 2] * N[ino] * N[jno];
* emat[ino, jno] += detj * weight * functional;
* }
* }
* //System.Diagnostics.Debug.WriteLine("detsum: {0}", detjsum);
* }
* }
*
* // 要素剛性行列にマージする
* for (int ino = 0; ino < nno; ino++)
* {
* int iNodeNumber = no_c[ino];
* if (ForceNodeNumberH.ContainsKey(iNodeNumber)) continue;
* int inoGlobal = toSorted[iNodeNumber];
* for (int jno = 0; jno < nno; jno++)
* {
* int jNodeNumber = no_c[jno];
* if (ForceNodeNumberH.ContainsKey(jNodeNumber)) continue;
* int jnoGlobal = toSorted[jNodeNumber];
*
* mat[inoGlobal, jnoGlobal] += emat[ino, jno];
* }
* }
* }
*/
/// <summary>
/// ヘルムホルツ方程式に対する有限要素マトリクス作成
/// </summary>
/// <param name="waveLength">波長</param>
/// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
/// <param name="element">有限要素</param>
/// <param name="Nodes">節点リスト</param>
/// <param name="Medias">媒質リスト</param>
/// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
/// <param name="WGStructureDv">導波路構造区分</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param>
/// <param name="mat">マージされる全体行列</param>
public static void AddElementMat(double waveLength,
Dictionary <int, int> toSorted,
FemElement element,
IList <FemNode> Nodes,
MediaInfo[] Medias,
Dictionary <int, bool> ForceNodeNumberH,
FemSolver.WGStructureDV WGStructureDv,
FemSolver.WaveModeDV WaveModeDv,
double waveguideWidthForEPlane,
ref MyComplexMatrix mat)
{
// 定数
const double pi = Constants.pi;
const double c0 = Constants.c0;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 要素頂点数
//const int vertexCnt = Constants.QuadVertexCnt; //4;
// 要素内節点数
const int nno = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 2次セレンディピティ
// 座標次元数
const int ndim = Constants.CoordDim2D; //2;
int[] nodeNumbers = element.NodeNumbers;
int[] no_c = new int[nno];
MediaInfo media = Medias[element.MediaIndex];
double[,] media_P = null;
double[,] media_Q = null;
// ヘルムホルツ方程式のパラメータP,Qを取得する
FemSolver.GetHelmholtzMediaPQ(
k0,
media,
WGStructureDv,
WaveModeDv,
waveguideWidthForEPlane,
out media_P,
out media_Q);
// 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
double[][] pp = new double[nno][];
for (int ino = 0; ino < nno; ino++)
{
int nodeNumber = nodeNumbers[ino];
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
no_c[ino] = nodeNumber;
pp[ino] = new double[ndim];
for (int n = 0; n < ndim; n++)
{
pp[ino][n] = node.Coord[n];
}
}
// 四角形の辺の長さを求める
double[] le = new double[4];
le[0] = FemMeshLogic.GetDistance(pp[0], pp[1]);
le[1] = FemMeshLogic.GetDistance(pp[1], pp[2]);
le[2] = FemMeshLogic.GetDistance(pp[2], pp[3]);
le[3] = FemMeshLogic.GetDistance(pp[3], pp[0]);
System.Diagnostics.Debug.Assert(Math.Abs(le[0] - le[2]) < Constants.PrecisionLowerLimit);
System.Diagnostics.Debug.Assert(Math.Abs(le[1] - le[3]) < Constants.PrecisionLowerLimit);
double lx = le[0];
double ly = le[1];
// 要素節点座標( 局所r,s成分 )
// s
// |
// 3+ 6 +2
// | | |
// ---7---+---5-->r
// | | |
// 0+ 4 +1
// |
//
double[][] n_pts =
{
// r, s
new double[] { -1.0, -1.0 }, //0
new double[] { 1.0, -1.0 }, //1
new double[] { 1.0, 1.0 }, //2
new double[] { -1.0, 1.0 }, //3
new double[] { 0, -1.0 }, //4
new double[] { 1.0, 0 }, //5
new double[] { 0, 1.0 }, //6
new double[] { -1.0, 0 }, //7
};
// Ni = a0(r^2*s) + a1(r^2) + a2(r) + a3(rs) + a4(rs^2) + a5(s^2) + a6(s) + a7
double[,] Ni_a = new double[nno, 8];
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
Ni_a[i, 0] = 0.25 * ri * ri * si;
Ni_a[i, 1] = 0.25 * ri * ri;
Ni_a[i, 2] = 0.0;
Ni_a[i, 3] = 0.25 * ri * si;
Ni_a[i, 4] = 0.25 * ri * si * si;
Ni_a[i, 5] = 0.25 * si * si;
Ni_a[i, 6] = 0.0;
Ni_a[i, 7] = -0.25;
}
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
Ni_a[i, 0] = -0.5 * si;
Ni_a[i, 1] = -0.5;
Ni_a[i, 2] = 0.0;
Ni_a[i, 3] = 0.0;
Ni_a[i, 4] = 0.0;
Ni_a[i, 5] = 0.0;
Ni_a[i, 6] = 0.5 * si;
Ni_a[i, 7] = 0.5;
}
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
Ni_a[i, 0] = 0.0;
Ni_a[i, 1] = 0.0;
Ni_a[i, 2] = 0.5 * ri;
Ni_a[i, 3] = 0.0;
Ni_a[i, 4] = -0.5 * ri;
Ni_a[i, 5] = -0.5;
Ni_a[i, 6] = 0.0;
Ni_a[i, 7] = 0.5;
}
// dNidr = a0(r^2*s) + a1(r^2) + a2(r) + a3(rs) + a4(rs^2) + a5(s^2) + a6(s) + a7
double[,] dNidr_a = new double[nno, 8];
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNidr_a[i, 0] = 0.0;
dNidr_a[i, 1] = 0.0; // r^2
dNidr_a[i, 2] = 0.25 * 2.0 * ri * ri; // r
dNidr_a[i, 3] = 0.25 * 2.0 * ri * ri * si; // rs
dNidr_a[i, 4] = 0.0;
dNidr_a[i, 5] = 0.25 * ri * si * si; // s^2
dNidr_a[i, 6] = 0.25 * ri * si; // s
dNidr_a[i, 7] = 0.0; //1
}
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNidr_a[i, 0] = 0.0;
dNidr_a[i, 1] = 0.0; // r^2
dNidr_a[i, 2] = -1.0; // r
dNidr_a[i, 3] = -si; // rs
dNidr_a[i, 4] = 0.0;
dNidr_a[i, 5] = 0.0; // s^2
dNidr_a[i, 6] = 0.0; // s
dNidr_a[i, 7] = 0.0; // 1
}
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNidr_a[i, 0] = 0.0;
dNidr_a[i, 1] = 0.0; // r^2
dNidr_a[i, 2] = 0.0; // r
dNidr_a[i, 3] = 0.0; // rs
dNidr_a[i, 4] = 0.0;
dNidr_a[i, 5] = -0.5 * ri; // s^2
dNidr_a[i, 6] = 0.0; // s
dNidr_a[i, 7] = 0.5 * ri; // 1
}
// dNids = a0(r^2*s) + a1(r^2) + a2(r) + a3(rs) + a4(rs^2) + a5(s^2) + a6(s) + a7
double[,] dNids_a = new double[nno, 8];
for (int i = 0; i < 4; i++)
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNids_a[i, 0] = 0.0;
dNids_a[i, 1] = 0.25 * ri * ri * si; // r^2
dNids_a[i, 2] = 0.25 * ri * si; // r
dNids_a[i, 3] = 0.25 * 2.0 * ri * si * si; // rs
dNids_a[i, 4] = 0.0;
dNids_a[i, 5] = 0.0; // s^2
dNids_a[i, 6] = 0.25 * 2.0 * si * si; // s
dNids_a[i, 7] = 0.0; //1
}
foreach (int i in new int[] { 4, 6 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNids_a[i, 0] = 0.0;
dNids_a[i, 1] = -0.5 * si; // r^2
dNids_a[i, 2] = 0.0; // r
dNids_a[i, 3] = 0.0; // rs
dNids_a[i, 4] = 0.0;
dNids_a[i, 5] = 0.0; // s^2
dNids_a[i, 6] = 0.0; // s
dNids_a[i, 7] = 0.5 * si; //1
}
foreach (int i in new int[] { 5, 7 })
{
// 節点の局所座標
double ri = n_pts[i][0];
double si = n_pts[i][1];
dNids_a[i, 0] = 0.0;
dNids_a[i, 1] = 0.0; // r^2
dNids_a[i, 2] = 0.0; // r
dNids_a[i, 3] = -ri; // rs
dNids_a[i, 4] = 0.0;
dNids_a[i, 5] = 0.0; // s^2
dNids_a[i, 6] = -1.0; // s
dNids_a[i, 7] = 0.0; //1
}
// ∫dN/dndN/dn dxdy
// integralDNDX[n, ino, jno] n = 0 --> ∫dN/dxdN/dx dxdy
// n = 1 --> ∫dN/dydN/dy dxdy
double[, ,] integralDNDX = new double[ndim, nno, nno];
// ∫N N dxdy
double[,] integralN = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralN[ino, jno] = lx * ly / 4.0 *
(
// r^4s^2
4.0 / 15.0 * Ni_a[ino, 0] * Ni_a[jno, 0]
// r^2s^2
+ 4.0 / 9.0 * (Ni_a[ino, 6] * Ni_a[jno, 0] + Ni_a[ino, 5] * Ni_a[jno, 1] + Ni_a[ino, 4] * Ni_a[jno, 2] + Ni_a[ino, 3] * Ni_a[jno, 3]
+ Ni_a[ino, 2] * Ni_a[jno, 4] + Ni_a[ino, 1] * Ni_a[jno, 5] + Ni_a[ino, 0] * Ni_a[jno, 6])
// r^4
+ 4.0 / 5.0 * Ni_a[ino, 1] * Ni_a[jno, 1]
// r^2
+ 4.0 / 3.0 * (Ni_a[ino, 7] * Ni_a[jno, 1] + Ni_a[ino, 2] * Ni_a[jno, 2] + Ni_a[ino, 1] * Ni_a[jno, 7])
// r^2s^4
+ 4.0 / 15.0 * Ni_a[ino, 4] * Ni_a[jno, 4]
// s^4
+ 4.0 / 5.0 * Ni_a[ino, 5] * Ni_a[jno, 5]
// s^2
+ 4.0 / 3.0 * (Ni_a[ino, 7] * Ni_a[jno, 5] + Ni_a[ino, 6] * Ni_a[jno, 6] + Ni_a[ino, 5] * Ni_a[jno, 7])
// 1
+ 4.0 * Ni_a[ino, 7] * Ni_a[jno, 7]
);
integralDNDX[0, ino, jno] = ly / lx *
(
// r^4s^2
4.0 / 15.0 * dNidr_a[ino, 0] * dNidr_a[jno, 0]
// r^2s^2
+ 4.0 / 9.0 * (dNidr_a[ino, 6] * dNidr_a[jno, 0] + dNidr_a[ino, 5] * dNidr_a[jno, 1] + dNidr_a[ino, 4] * dNidr_a[jno, 2]
+ dNidr_a[ino, 3] * dNidr_a[jno, 3]
+ dNidr_a[ino, 2] * dNidr_a[jno, 4] + dNidr_a[ino, 1] * dNidr_a[jno, 5] + dNidr_a[ino, 0] * dNidr_a[jno, 6])
// r^4
+ 4.0 / 5.0 * dNidr_a[ino, 1] * dNidr_a[jno, 1]
// r^2
+ 4.0 / 3.0 * (dNidr_a[ino, 7] * dNidr_a[jno, 1] + dNidr_a[ino, 2] * dNidr_a[jno, 2] + dNidr_a[ino, 1] * dNidr_a[jno, 7])
// r^2s^4
+ 4.0 / 15.0 * dNidr_a[ino, 4] * dNidr_a[jno, 4]
// s^4
+ 4.0 / 5.0 * dNidr_a[ino, 5] * dNidr_a[jno, 5]
// s^2
+ 4.0 / 3.0 * (dNidr_a[ino, 7] * dNidr_a[jno, 5] + dNidr_a[ino, 6] * dNidr_a[jno, 6] + dNidr_a[ino, 5] * dNidr_a[jno, 7])
// 1
+ 4.0 * dNidr_a[ino, 7] * dNidr_a[jno, 7]
);
integralDNDX[1, ino, jno] = lx / ly *
(
// r^4s^2
4.0 / 15.0 * dNids_a[ino, 0] * dNids_a[jno, 0]
// r^2s^2
+ 4.0 / 9.0 * (dNids_a[ino, 6] * dNids_a[jno, 0] + dNids_a[ino, 5] * dNids_a[jno, 1] + dNids_a[ino, 4] * dNids_a[jno, 2]
+ dNids_a[ino, 3] * dNids_a[jno, 3]
+ dNids_a[ino, 2] * dNids_a[jno, 4] + dNids_a[ino, 1] * dNids_a[jno, 5] + dNids_a[ino, 0] * dNids_a[jno, 6])
// r^4
+ 4.0 / 5.0 * dNids_a[ino, 1] * dNids_a[jno, 1]
// r^2
+ 4.0 / 3.0 * (dNids_a[ino, 7] * dNids_a[jno, 1] + dNids_a[ino, 2] * dNids_a[jno, 2] + dNids_a[ino, 1] * dNids_a[jno, 7])
// r^2s^4
+ 4.0 / 15.0 * dNids_a[ino, 4] * dNids_a[jno, 4]
// s^4
+ 4.0 / 5.0 * dNids_a[ino, 5] * dNids_a[jno, 5]
// s^2
+ 4.0 / 3.0 * (dNids_a[ino, 7] * dNids_a[jno, 5] + dNids_a[ino, 6] * dNids_a[jno, 6] + dNids_a[ino, 5] * dNids_a[jno, 7])
// 1
+ 4.0 * dNids_a[ino, 7] * dNids_a[jno, 7]
);
}
}
// 要素剛性行列を作る
double[,] emat = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
emat[ino, jno] = media_P[0, 0] * integralDNDX[1, ino, jno] + media_P[1, 1] * integralDNDX[0, ino, jno]
- k0 * k0 * media_Q[2, 2] * integralN[ino, jno];
}
}
// 要素剛性行列にマージする
for (int ino = 0; ino < nno; ino++)
{
int iNodeNumber = no_c[ino];
if (ForceNodeNumberH.ContainsKey(iNodeNumber))
{
continue;
}
int inoGlobal = toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
int jNodeNumber = no_c[jno];
if (ForceNodeNumberH.ContainsKey(jNodeNumber))
{
continue;
}
int jnoGlobal = toSorted[jNodeNumber];
//mat[inoGlobal, jnoGlobal] += emat[ino, jno];
//mat._body[inoGlobal + jnoGlobal * mat.RowSize] += emat[ino, jno];
// 実数部に加算する
//mat._body[inoGlobal + jnoGlobal * mat.RowSize].Real += emat[ino, jno];
// バンドマトリクス対応
mat._body[mat.GetBufferIndex(inoGlobal, jnoGlobal)].Real += emat[ino, jno];
}
}
}
/// <summary>
/// ヘルムホルツ方程式に対する有限要素マトリクス作成
/// </summary>
/// <param name="waveLength">波長</param>
/// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
/// <param name="element">有限要素</param>
/// <param name="Nodes">節点リスト</param>
/// <param name="Medias">媒質リスト</param>
/// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
/// <param name="WGStructureDv">導波路構造区分</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param>
/// <param name="mat">マージされる全体行列</param>
public static void AddElementMat(double waveLength,
Dictionary<int, int> toSorted,
FemElement element,
IList<FemNode> Nodes,
MediaInfo[] Medias,
Dictionary<int, bool> ForceNodeNumberH,
FemSolver.WGStructureDV WGStructureDv,
FemSolver.WaveModeDV WaveModeDv,
double waveguideWidthForEPlane,
ref MyComplexMatrix mat)
{
// 定数
const double pi = Constants.pi;
const double c0 = Constants.c0;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 要素頂点数
//const int vertexCnt = Constants.QuadVertexCnt; //4;
// 要素内節点数
const int nno = Constants.QuadNodeCnt_FirstOrder; //4; // 1次セレンディピティ
// 座標次元数
const int ndim = Constants.CoordDim2D; //2;
int[] nodeNumbers = element.NodeNumbers;
int[] no_c = new int[nno];
MediaInfo media = Medias[element.MediaIndex];
double[,] media_P = null;
double[,] media_Q = null;
// ヘルムホルツ方程式のパラメータP,Qを取得する
FemSolver.GetHelmholtzMediaPQ(
k0,
media,
WGStructureDv,
WaveModeDv,
waveguideWidthForEPlane,
out media_P,
out media_Q);
// 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
double[][] pp = new double[nno][];
for (int ino = 0; ino < nno; ino++)
{
int nodeNumber = nodeNumbers[ino];
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
no_c[ino] = nodeNumber;
pp[ino] = new double[ndim];
for (int n = 0; n < ndim; n++)
{
pp[ino][n] = node.Coord[n];
}
}
// 四角形の辺の長さを求める
double[] le = new double[4];
le[0] = FemMeshLogic.GetDistance(pp[0], pp[1]);
le[1] = FemMeshLogic.GetDistance(pp[1], pp[2]);
le[2] = FemMeshLogic.GetDistance(pp[2], pp[3]);
le[3] = FemMeshLogic.GetDistance(pp[3], pp[0]);
System.Diagnostics.Debug.Assert(Math.Abs(le[0] - le[2]) < Constants.PrecisionLowerLimit);
System.Diagnostics.Debug.Assert(Math.Abs(le[1] - le[3]) < Constants.PrecisionLowerLimit);
double lx = le[0];
double ly = le[1];
// 要素節点座標( 局所r,s成分 )
// s
// |
// 3+ + +2
// | | |
// ---+---+---+-->r
// | | |
// 0+ + +1
// |
//
double[][] n_pts =
{
// r, s
new double[] {-1.0, -1.0}, //0
new double[] { 1.0, -1.0}, //1
new double[] { 1.0, 1.0}, //2
new double[] {-1.0, 1.0}, //3
};
// ∫dN/dndN/dn dxdy
// integralDNDX[n, ino, jno] n = 0 --> ∫dN/dxdN/dx dxdy
// n = 1 --> ∫dN/dydN/dy dxdy
double[, ,] integralDNDX = new double[ndim, nno, nno]
{
{
{ 2.0 * ly /(6.0 * lx), -2.0 * ly /(6.0 * lx), -1.0 * ly /(6.0 * lx), 1.0 * ly /(6.0 * lx) },
{ -2.0 * ly /(6.0 * lx), 2.0 * ly /(6.0 * lx), 1.0 * ly /(6.0 * lx), -1.0 * ly /(6.0 * lx) },
{ -1.0 * ly /(6.0 * lx), 1.0 * ly /(6.0 * lx), 2.0 * ly /(6.0 * lx), -2.0 * ly /(6.0 * lx) },
{ 1.0 * ly /(6.0 * lx), -1.0 * ly /(6.0 * lx), -2.0 * ly /(6.0 * lx), 2.0 * ly /(6.0 * lx) },
},
{
{ 2.0 * lx /(6.0 * ly), 1.0 * lx /(6.0 * ly), -1.0 * lx /(6.0 * ly), -2.0 * lx /(6.0 * ly) },
{ 1.0 * lx /(6.0 * ly), 2.0 * lx /(6.0 * ly), -2.0 * lx /(6.0 * ly), -1.0 * lx /(6.0 * ly) },
{ -1.0 * lx /(6.0 * ly), -2.0 * lx /(6.0 * ly), 2.0 * lx /(6.0 * ly), 1.0 * lx /(6.0 * ly) },
{ -2.0 * lx /(6.0 * ly), -1.0 * lx /(6.0 * ly), 1.0 * lx /(6.0 * ly), 2.0 * lx /(6.0 * ly) },
}
};
// ∫N N dxdy
double[,] integralN = new double[nno, nno]
{
{ 4.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 1.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0 },
{ 2.0 * lx * ly / 36.0, 4.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 1.0 * lx * ly / 36.0 },
{ 1.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 4.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0 },
{ 2.0 * lx * ly / 36.0, 1.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 4.0 * lx * ly / 36.0 },
};
// 要素剛性行列を作る
double[,] emat = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
emat[ino, jno] = media_P[0, 0] * integralDNDX[1, ino, jno] + media_P[1, 1] * integralDNDX[0, ino, jno]
- k0 * k0 * media_Q[2, 2] * integralN[ino, jno];
}
}
// 要素剛性行列にマージする
for (int ino = 0; ino < nno; ino++)
{
int iNodeNumber = no_c[ino];
if (ForceNodeNumberH.ContainsKey(iNodeNumber)) continue;
int inoGlobal = toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
int jNodeNumber = no_c[jno];
if (ForceNodeNumberH.ContainsKey(jNodeNumber)) continue;
int jnoGlobal = toSorted[jNodeNumber];
//mat[inoGlobal, jnoGlobal] += emat[ino, jno];
//mat._body[inoGlobal + jnoGlobal * mat.RowSize] += emat[ino, jno];
// 実数部に加算する
//mat._body[inoGlobal + jnoGlobal * mat.RowSize].Real += emat[ino, jno];
// バンドマトリクス対応
mat._body[mat.GetBufferIndex(inoGlobal, jnoGlobal)].Real += emat[ino, jno];
}
}
}
/// <summary>
/// 点が要素内に含まれる？
/// </summary>
/// <param name="element">要素</param>
/// <param name="test_pp">テストする点</param>
/// <param name="Nodes">節点リスト（要素は座標を持たないので節点リストが必要）</param>
/// <returns></returns>
public static bool IsPointInElement(FemElement element, double[] test_pp, IList<FemNode> nodes)
{
bool hit = false;
int eNodeCnt = element.NodeNumbers.Length;
Constants.FemElementShapeDV elemShapeDv;
int order;
int vertexCnt;
GetElementShapeDvAndOrderByElemNodeCnt(eNodeCnt, out elemShapeDv, out order, out vertexCnt);
if (vertexCnt == Constants.TriVertexCnt)
{
// ２次/１次三角形要素
hit = TriElement_IsPointInElement(element, test_pp, nodes);
}
else if (vertexCnt == Constants.QuadVertexCnt)
{
// ２次/１次四角形要素
hit = QuadElement_IsPointInElement(element, test_pp, nodes);
}
else
{
System.Diagnostics.Debug.Assert(false);
}
return hit;
}
/// <summary>
/// 凡例カラーマップ目盛の描画
/// </summary>
/// <param name="g"></param>
private void drawFValueLegendColorScale(Graphics g, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv)
{
const int cnt = LegendColorCnt;
const int ofsX = 22;
const int ofsY = 0;
const int height = 20; // 1目盛の高さ
//double divValue = 1.0 / (double)cnt;
double min = 0.0;
double max = 1.0;
if (fieldDv == FemElement.FieldDV.Field)
{
min = MinFValue;
max = MaxFValue;
}
else if (fieldDv == FemElement.FieldDV.RotX || fieldDv == FemElement.FieldDV.RotY)
{
min = MinRotFValue;
max = MaxRotFValue;
}
else
{
return;
}
if (valueDv == FemElement.ValueDV.Abs)
{
}
else
{
min = -max;
}
double divValue = (max - min) / (double)cnt;
using (Font font = new Font("MS UI Gothic", 9))
using (Brush brush = new SolidBrush(FValueLegendColorPanel.ForeColor))
{
for (int i = 0; i < cnt + 1; i++)
{
int y = i * height;
double value = min + (cnt - i) * divValue;
string text = string.Format("{0:E3}", value);
g.DrawString(text, font, brush, new Point(ofsX, y + ofsY));
}
}
}
/// <summary>
/// 四角形要素：点が要素内に含まれる？
/// </summary>
/// <param name="element">要素</param>
/// <param name="test_pp">テストする点</param>
/// <param name="Nodes">節点リスト（要素は座標を持たないので節点リストが必要）</param>
/// <returns></returns>
public static bool QuadElement_IsPointInElement(FemElement element, double[] test_pp, IList<FemNode> nodes)
{
bool hit = false;
// 四角形の頂点数
const int vertexCnt = Constants.QuadVertexCnt;
double[][] pps = new double[vertexCnt][];
int[] nodeNumbers = new int[vertexCnt];
// 2次四角形要素の最初の４点＝頂点の座標を取得
for (int ino = 0; ino < vertexCnt; ino++)
{
int nodeNumber = element.NodeNumbers[ino];
FemNode node = nodes[nodeNumber - 1];
System.Diagnostics.Debug.Assert(node.No == nodeNumber);
pps[ino] = node.Coord;
nodeNumbers[ino] = nodeNumber;
}
// バウンディングボックス取得
double minX = double.MaxValue;
double maxX = double.MinValue;
double minY = double.MaxValue;
double maxY = double.MinValue;
foreach (double[] pp in pps)
{
double xx = pp[0];
double yy = pp[1];
if (minX > xx)
{
minX = xx;
}
if (maxX < xx)
{
maxX = xx;
}
if (minY > yy)
{
minY = yy;
}
if (maxY < yy)
{
maxY = yy;
}
}
// バウンディングボックスでチェック
if (test_pp[0] < minX || test_pp[0] > maxX)
{
return hit;
}
if (test_pp[1] < minY || test_pp[1] > maxY)
{
return hit;
}
// ２つの三角形に分ける
// s
// |
// 3+ + +2
// | | |
// ---|---+---|-->r
// | | |
// 0+ + +1
// |
FemElement[] tris = new FemElement[2];
tris[0] = new FemElement();
tris[0].NodeNumbers = new int[] { nodeNumbers[0], nodeNumbers[1], nodeNumbers[3], 0, 0, 0 };
tris[1] = new FemElement();
tris[1].NodeNumbers = new int[] { nodeNumbers[2], nodeNumbers[3], nodeNumbers[1], 0, 0, 0 };
foreach (FemElement tri in tris)
{
bool hitInsideTri = TriElement_IsPointInElement(tri, test_pp, nodes);
if (hitInsideTri)
{
hit = true;
break;
}
}
return hit;
}
/// <summary>
/// フィールドの回転ベクトル描画
/// </summary>
/// <param name="g"></param>
/// <param name="panel"></param>
public void DrawRotFieldEx(Graphics g, Panel panel, Rectangle clientRectangle, FemElement.FieldDV fieldDv)
{
if (!isInputDataReady())
{
return;
}
if (!isOutputDataReady())
{
return;
}
Size delta;
Size ofs;
Size regionSize;
//getFitDrawRegion(panel, out delta, out ofs, out regionSize);
getFitDrawRegion(clientRectangle.Width, clientRectangle.Height, out delta, out ofs, out regionSize);
ofs.Width += clientRectangle.Left;
ofs.Height += clientRectangle.Top;
Color drawColor = Color.Gray;
double min = 0.0;
double max = 1.0;
if (fieldDv == FemElement.FieldDV.PoyntingXY)
{
drawColor = Color.Green;//Color.YellowGreen;
min = -MaxPoyntingFValue;
max = MaxPoyntingFValue;
}
else if (fieldDv == FemElement.FieldDV.RotXY)
{
drawColor = Color.Red;
if (WGStructureDv == FemSolver.WGStructureDV.EPlane2D)
{
drawColor = (WaveModeDv == FemSolver.WaveModeDV.TM) ? Color.Red : Color.Blue;
}
else
{
drawColor = (WaveModeDv == FemSolver.WaveModeDV.TM) ? Color.Blue : Color.Red;
}
min = -MaxRotFValue;
max = MaxRotFValue;
}
else
{
return;
}
foreach (FemElement element in Elements)
{
// 回転ベクトル描画
element.DrawRotField(g, ofs, delta, regionSize, drawColor, fieldDv, min, max);
}
}
/// <summary>
/// ヘルムホルツ方程式に対する有限要素マトリクス作成
/// </summary>
/// <param name="waveLength">波長</param>
/// <param name="toSorted">ソートされた節点インデックス（ 2D節点番号→ソート済みリストインデックスのマップ）</param>
/// <param name="element">有限要素</param>
/// <param name="Nodes">節点リスト</param>
/// <param name="Medias">媒質リスト</param>
/// <param name="ForceNodeNumberH">強制境界節点ハッシュ</param>
/// <param name="WGStructureDv">導波路構造区分</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param>
/// <param name="mat">マージされる全体行列</param>
public static void AddElementMat(double waveLength,
Dictionary <int, int> toSorted,
FemElement element,
IList <FemNode> Nodes,
MediaInfo[] Medias,
Dictionary <int, bool> ForceNodeNumberH,
FemSolver.WGStructureDV WGStructureDv,
FemSolver.WaveModeDV WaveModeDv,
double waveguideWidthForEPlane,
ref MyComplexMatrix mat)
{
// 定数
const double pi = Constants.pi;
const double c0 = Constants.c0;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 要素頂点数
//const int vertexCnt = Constants.QuadVertexCnt; //4;
// 要素内節点数
const int nno = Constants.QuadNodeCnt_FirstOrder; //4; // 1次セレンディピティ
// 座標次元数
const int ndim = Constants.CoordDim2D; //2;
int[] nodeNumbers = element.NodeNumbers;
int[] no_c = new int[nno];
MediaInfo media = Medias[element.MediaIndex];
double[,] media_P = null;
double[,] media_Q = null;
// ヘルムホルツ方程式のパラメータP,Qを取得する
FemSolver.GetHelmholtzMediaPQ(
k0,
media,
WGStructureDv,
WaveModeDv,
waveguideWidthForEPlane,
out media_P,
out media_Q);
// 節点座標(IFの都合上配列の配列形式の2次元配列を作成)
double[][] pp = new double[nno][];
for (int ino = 0; ino < nno; ino++)
{
int nodeNumber = nodeNumbers[ino];
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
no_c[ino] = nodeNumber;
pp[ino] = new double[ndim];
for (int n = 0; n < ndim; n++)
{
pp[ino][n] = node.Coord[n];
}
}
// 四角形の辺の長さを求める
double[] le = new double[4];
le[0] = FemMeshLogic.GetDistance(pp[0], pp[1]);
le[1] = FemMeshLogic.GetDistance(pp[1], pp[2]);
le[2] = FemMeshLogic.GetDistance(pp[2], pp[3]);
le[3] = FemMeshLogic.GetDistance(pp[3], pp[0]);
System.Diagnostics.Debug.Assert(Math.Abs(le[0] - le[2]) < Constants.PrecisionLowerLimit);
System.Diagnostics.Debug.Assert(Math.Abs(le[1] - le[3]) < Constants.PrecisionLowerLimit);
double lx = le[0];
double ly = le[1];
// 要素節点座標( 局所r,s成分 )
// s
// |
// 3+ + +2
// | | |
// ---+---+---+-->r
// | | |
// 0+ + +1
// |
//
double[][] n_pts =
{
// r, s
new double[] { -1.0, -1.0 }, //0
new double[] { 1.0, -1.0 }, //1
new double[] { 1.0, 1.0 }, //2
new double[] { -1.0, 1.0 }, //3
};
// ∫dN/dndN/dn dxdy
// integralDNDX[n, ino, jno] n = 0 --> ∫dN/dxdN/dx dxdy
// n = 1 --> ∫dN/dydN/dy dxdy
double[, ,] integralDNDX = new double[ndim, nno, nno]
{
{
{ 2.0 * ly / (6.0 * lx), -2.0 * ly / (6.0 * lx), -1.0 * ly / (6.0 * lx), 1.0 * ly / (6.0 * lx) },
{ -2.0 * ly / (6.0 * lx), 2.0 * ly / (6.0 * lx), 1.0 * ly / (6.0 * lx), -1.0 * ly / (6.0 * lx) },
{ -1.0 * ly / (6.0 * lx), 1.0 * ly / (6.0 * lx), 2.0 * ly / (6.0 * lx), -2.0 * ly / (6.0 * lx) },
{ 1.0 * ly / (6.0 * lx), -1.0 * ly / (6.0 * lx), -2.0 * ly / (6.0 * lx), 2.0 * ly / (6.0 * lx) },
},
{
{ 2.0 * lx / (6.0 * ly), 1.0 * lx / (6.0 * ly), -1.0 * lx / (6.0 * ly), -2.0 * lx / (6.0 * ly) },
{ 1.0 * lx / (6.0 * ly), 2.0 * lx / (6.0 * ly), -2.0 * lx / (6.0 * ly), -1.0 * lx / (6.0 * ly) },
{ -1.0 * lx / (6.0 * ly), -2.0 * lx / (6.0 * ly), 2.0 * lx / (6.0 * ly), 1.0 * lx / (6.0 * ly) },
{ -2.0 * lx / (6.0 * ly), -1.0 * lx / (6.0 * ly), 1.0 * lx / (6.0 * ly), 2.0 * lx / (6.0 * ly) },
}
};
// ∫N N dxdy
double[,] integralN = new double[nno, nno]
{
{ 4.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 1.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0 },
{ 2.0 * lx * ly / 36.0, 4.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 1.0 * lx * ly / 36.0 },
{ 1.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 4.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0 },
{ 2.0 * lx * ly / 36.0, 1.0 * lx * ly / 36.0, 2.0 * lx * ly / 36.0, 4.0 * lx * ly / 36.0 },
};
// 要素剛性行列を作る
double[,] emat = new double[nno, nno];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
emat[ino, jno] = media_P[0, 0] * integralDNDX[1, ino, jno] + media_P[1, 1] * integralDNDX[0, ino, jno]
- k0 * k0 * media_Q[2, 2] * integralN[ino, jno];
}
}
// 要素剛性行列にマージする
for (int ino = 0; ino < nno; ino++)
{
int iNodeNumber = no_c[ino];
if (ForceNodeNumberH.ContainsKey(iNodeNumber))
{
continue;
}
int inoGlobal = toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
int jNodeNumber = no_c[jno];
if (ForceNodeNumberH.ContainsKey(jNodeNumber))
{
continue;
}
int jnoGlobal = toSorted[jNodeNumber];
//mat[inoGlobal, jnoGlobal] += emat[ino, jno];
//mat._body[inoGlobal + jnoGlobal * mat.RowSize] += emat[ino, jno];
// 実数部に加算する
//mat._body[inoGlobal + jnoGlobal * mat.RowSize].Real += emat[ino, jno];
// バンドマトリクス対応
mat._body[mat.GetBufferIndex(inoGlobal, jnoGlobal)].Real += emat[ino, jno];
}
}
}