/// <summary>
/// ヘルムホルツの方程式 PML要素の全体行列の追加(要素アレイ単位)
/// </summary>
/// <param name="world">ワールド座標系</param>
/// <param name="fieldValId">値のフィールドID</param>
/// <param name="pmlStPosX">PML媒質開始位置X座標</param>
/// <param name="pmlLength">PML長さ</param>
/// <param name="dt">時刻刻み幅</param>
/// <param name="newmarkBeta">Newmark法β</param>
/// <param name="media">媒質</param>
/// <param name="eaId">要素アレイID</param>
/// <param name="node_cnt">解析領域全体の節点数</param>
/// <param name="free_node_cnt">解析領域全体の自由節点数（強制境界を除いた節点数)</param>
/// <param name="toSorted">節点番号→ソート済み（強制境界を除いた)節点リストのインデックスマップ</param>
/// <param name="AMat">全体行列</param>
/// <returns></returns>
private static bool addPmlMat_EachElementAry(
CFieldWorld world,
uint fieldValId,
bool isPmlYDirection,
double pmlStPosX,
double pmlLength,
double dt,
double newmarkBeta,
MediaInfo media,
uint eaId,
uint node_cnt,
uint free_node_cnt,
Dictionary<uint, uint> toSorted,
ref MyDoubleBandMatrix AMat)
{
System.Diagnostics.Debug.Assert(free_node_cnt == AMat.RowSize && free_node_cnt == AMat.ColumnSize);
System.Diagnostics.Debug.Assert(world.IsIdEA(eaId));
// 要素アレイを取得
CElemAry ea = world.GetEA(eaId);
System.Diagnostics.Debug.Assert(ea.ElemType() == ELEM_TYPE.TRI);
if (!world.IsIdField(fieldValId))
{
return false;
}
// 値のフィールドを取得
CField valField = world.GetField(fieldValId);
// 値の要素セグメント（コーナー)を取得
CElemAry.CElemSeg es_c_va = valField.GetElemSeg(eaId, ELSEG_TYPE.CORNER, true, world);
// 座標の要素セグメント(コーナー)を取得
CElemAry.CElemSeg es_c_co = valField.GetElemSeg(eaId, ELSEG_TYPE.CORNER, false, world);
uint nno = 3;
uint ndim = 2;
// 要素節点の全体節点番号
uint[] no_c = new uint[nno];
// 要素節点の値
Complex[] value_c = new Complex[nno];
// 要素節点の座標
double[,] coord_c = new double[nno, ndim];
// 要素行列
double[,] eMMat = new double[nno, nno];
double[,] eKXMat = new double[nno, nno];
double[,] eKYMat = new double[nno, nno];
CNodeAry.CNodeSeg ns_c_val = valField.GetNodeSeg(ELSEG_TYPE.CORNER, true, world);
CNodeAry.CNodeSeg ns_c_co = valField.GetNodeSeg(ELSEG_TYPE.CORNER, false, world);
for (uint ielem = 0; ielem < ea.Size(); ielem++)
{
// 要素配列から要素セグメントの節点番号を取り出す
es_c_co.GetNodes(ielem, no_c);
// 座標を取得
for (uint inoes = 0; inoes < nno; inoes++)
{
double[] tmpval = null;
ns_c_co.GetValue(no_c[inoes], out tmpval);
System.Diagnostics.Debug.Assert(tmpval.Length == ndim);
for (int i = 0; i < tmpval.Length; i++)
{
coord_c[inoes, i] = tmpval[i];
}
}
// 節点の値を取って来る
es_c_va.GetNodes(ielem, no_c);
for (uint inoes = 0; inoes < nno; inoes++)
{
Complex[] tmpval = null;
ns_c_val.GetValue(no_c[inoes], out tmpval);
System.Diagnostics.Debug.Assert(tmpval.Length == 1);
value_c[inoes] = tmpval[0];
}
// 節点座標
double[] p1 = new double[ndim];
double[] p2 = new double[ndim];
double[] p3 = new double[ndim];
for (int i = 0; i < ndim; i++)
{
p1[i] = coord_c[0, i];
p2[i] = coord_c[1, i];
p3[i] = coord_c[2, i];
}
// 面積を求める
double area = CKerEMatTri.TriArea(p1, p2, p3);
// 形状関数の微分を求める
double[,] dldx = null;
double[] const_term = null;
CKerEMatTri.TriDlDx(out dldx, out const_term, p1, p2, p3);
// ∫(dLi/dx)(dLj/dx) dxdy
double[,] integralDLDX = new double[3, 3];
// ∫(dLi/dy)(dLj/dy) dxdy
double[,] integralDLDY = new double[3, 3];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralDLDX[ino, jno] = area * dldx[ino, 0] * dldx[jno, 0];
}
}
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralDLDY[ino, jno] = area * dldx[ino, 1] * dldx[jno, 1];
}
}
/*
// ∫(dLi/dx)Lj dxdy
double[,] integralDLDXL = new double[3, 3];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralDLDXL[ino, jno] = area * dldx[ino, 0] / 3.0;
}
}
// ∫(dLi/dy)Lj dxdy
double[,] integralDLDYL = new double[3, 3];
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
integralDLDYL[ino, jno] = area * dldx[ino, 1] / 3.0;
}
}
*/
// ∫LiLj dxdy
double[,] integralL = new double[3, 3]
{
{ area / 6.0 , area / 12.0, area / 12.0 },
{ area / 12.0, area / 6.0, area / 12.0 },
{ area / 12.0, area / 12.0, area / 6.0 },
};
// 要素剛性行列、要素質量行列を作る
for (int ino = 0; ino < nno; ino++)
{
for (int jno = 0; jno < nno; jno++)
{
// 要素剛性行列
eKXMat[ino, jno] = media.P[1, 1] * integralDLDX[ino, jno];
eKYMat[ino, jno] = media.P[0, 0] * integralDLDY[ino, jno];
// 要素質量行列
eMMat[ino, jno] = eps0 * myu0 * media.Q[2, 2] * integralL[ino, jno];
}
}
// PML媒質パラメータ
double posXG = (p1[0] + p2[0] + p3[0]) / 3.0;
if (isPmlYDirection)
{
posXG = (p1[1] + p2[1] + p3[1]) / 3.0;
}
double sigmaX_e = 0.0;
double c1_F_e = 0.0;
double c1_G_e = 0.0;
double c3_G_e = 0.0;
GetPmlParameter(
posXG,
pmlStPosX,
pmlLength,
dt,
out sigmaX_e,
out c1_F_e,
out c1_G_e,
out c3_G_e);
// 要素剛性行列にマージする
double[,] work_eKXMat = eKXMat;
double[,] work_eKYMat = eKYMat;
if (isPmlYDirection)
{
work_eKXMat = eKYMat;
work_eKYMat = eKXMat;
}
for (int ino = 0; ino < nno; ino++)
{
uint iNodeNumber = no_c[ino];
if (!toSorted.ContainsKey(iNodeNumber)) continue;
int inoGlobal = (int)toSorted[iNodeNumber];
for (int jno = 0; jno < nno; jno++)
{
uint jNodeNumber = no_c[jno];
if (!toSorted.ContainsKey(jNodeNumber)) continue;
int jnoGlobal = (int)toSorted[jNodeNumber];
// clapack形式の行列格納方法で格納(バンド行列)
AMat._body[AMat.GetBufferIndex(inoGlobal, jnoGlobal)] +=
(sigmaX_e / eps0) * (1.0 / (2.0 * dt)) * eMMat[ino, jno]
+ c1_F_e * newmarkBeta * work_eKYMat[ino, jno]
+ c1_G_e * newmarkBeta * work_eKXMat[ino, jno];
}
}
}
return true;
}
// {x} = [A]{v}
public static double[] product(MyDoubleBandMatrix matAB, double[] vec, int vec_row)
{
int a_row = matAB.RowSize;
int a_col = matAB.ColumnSize;
int subdiaSize = matAB.SubdiaSize;
int superdiaSize = matAB.SuperdiaSize;
System.Diagnostics.Debug.Assert(a_col == vec_row);
double[] retVec = new double[a_row];
/*
for (int i = 0; i < a_row; i++)
{
retVec[i] = 0.0;
for (int k = 0; k < a_col; k++)
{
if (Math.Max(0, k - superdiaSize) <= i && i <= Math.Min((a_row - 1), k + subdiaSize))
{
retVec[i] += matAB._body[matAB.GetBufferIndex(i, k)] * vec[k];
}
}
}
*/
for (int k = 0; k < a_col; k++)
{
// 対角成分
retVec[k] += matAB._body[matAB.GetBufferIndex(k, k)] * vec[k];
// subdiagonal成分
if (k < a_col - 1)
{
for (int i = k + 1; i <= k + subdiaSize && i < a_row; i++)
{
retVec[i] += matAB._body[matAB.GetBufferIndex(i, k)] * vec[k];
}
}
if (k > 0)
{
for (int i = k - 1; i >= k - superdiaSize && i >= 0; i--)
{
retVec[i] += matAB._body[matAB.GetBufferIndex(i, k)] * vec[k];
}
}
}
return retVec;
}