/// <summary>
/// 1Dヘルムホルツ方程式固有値問題の要素行列を加算する
/// </summary>
/// <param name="waveLength">波長(E面の場合のみ使用する)</param>
/// <param name="element">線要素</param>
/// <param name="coords">座標リスト</param>
/// <param name="toSorted">節点番号→ソート済み節点インデックスマップ</param>
/// <param name="Medias">媒質情報リスト</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="txx_1d">txx行列</param>
/// <param name="ryy_1d">ryy行列</param>
/// <param name="uzz_1d">uzz行列</param>
public static void AddElementMatOf1dEigenValueProblem(
double waveLength,
FemLineElement element,
IList<double> coords,
Dictionary<int, int> toSorted,
MediaInfo[] Medias,
FemSolver.WaveModeDV WaveModeDv,
ref MyDoubleMatrix txx_1d, ref MyDoubleMatrix ryy_1d, ref MyDoubleMatrix uzz_1d)
{
// 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;
// ２次線要素
const int nno = Constants.LineNodeCnt_SecondOrder; // 3;
int[] nodeNumbers = element.NodeNumbers;
System.Diagnostics.Debug.Assert(nno == nodeNumbers.Length);
// 座標の取得
double[] elementCoords = new double[nno];
for (int n = 0; n < nno; n++)
{
int nodeIndex = nodeNumbers[n] - 1;
elementCoords[n] = coords[nodeIndex];
}
// 線要素の長さ
double elen = Math.Abs(elementCoords[1] - elementCoords[0]);
// 媒質インデックス
int mediaIndex = element.MediaIndex;
// 媒質
MediaInfo media = Medias[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,
WaveModeDv,
out media_P,
out media_Q);
double[,] integralN = new double[nno, nno]
{
{ 4.0 / 30.0 * elen, -1.0 / 30.0 * elen, 2.0 / 30.0 * elen },
{ -1.0 / 30.0 * elen, 4.0 / 30.0 * elen, 2.0 / 30.0 * elen },
{ 2.0 / 30.0 * elen, 2.0 / 30.0 * elen, 16.0 / 30.0 * elen },
};
double[,] integralDNDY = new double[nno, nno]
{
{ 7.0 / (3.0 * elen), 1.0 / (3.0 * elen), -8.0 / (3.0 * elen) },
{ 1.0 / (3.0 * elen), 7.0 / (3.0 * elen), -8.0 / (3.0 * elen) },
{ -8.0 / (3.0 * elen), -8.0 / (3.0 * elen), 16.0 / (3.0 * elen) },
};
for (int ino = 0; ino < nno; ino++)
{
int inoBoundary = nodeNumbers[ino];
int inoSorted;
if (!toSorted.ContainsKey(inoBoundary)) continue;
inoSorted = toSorted[inoBoundary];
for (int jno = 0; jno < nno; jno++)
{
int jnoBoundary = nodeNumbers[jno];
int jnoSorted;
if (!toSorted.ContainsKey(jnoBoundary)) continue;
jnoSorted = toSorted[jnoBoundary];
// 対称バンド行列対応
if (ryy_1d is MyDoubleSymmetricBandMatrix && jnoSorted < inoSorted)
{
continue;
}
double e_txx_1d_inojno = media_P[0, 0] * integralDNDY[ino, jno];
double e_ryy_1d_inojno = media_P[1, 1] * integralN[ino, jno];
double e_uzz_1d_inojno = media_Q[2, 2] * integralN[ino, jno];
//txx_1d[inoSorted, jnoSorted] += e_txx_1d_inojno;
//ryy_1d[inoSorted, jnoSorted] += e_ryy_1d_inojno;
//uzz_1d[inoSorted, jnoSorted] += e_uzz_1d_inojno;
txx_1d._body[txx_1d.GetBufferIndex(inoSorted, jnoSorted)] += e_txx_1d_inojno;
ryy_1d._body[ryy_1d.GetBufferIndex(inoSorted, jnoSorted)] += e_ryy_1d_inojno;
uzz_1d._body[uzz_1d.GetBufferIndex(inoSorted, jnoSorted)] += e_uzz_1d_inojno;
}
}
}
/// <summary>
/// 1Dヘルムホルツ方程式固有値問題の要素行列を加算する
/// </summary>
/// <param name="element">線要素</param>
/// <param name="coords">座標リスト</param>
/// <param name="toSorted">節点番号→ソート済み節点インデックスマップ</param>
/// <param name="Medias">媒質情報リスト</param>
/// <param name="WaveModeDv">計算する波のモード区分</param>
/// <param name="txx_1d">txx行列</param>
/// <param name="ryy_1d">ryy行列</param>
/// <param name="uzz_1d">uzz行列</param>
public static void AddElementMatOf1dEigenValueProblem(
FemLineElement element,
IList<double> coords,
Dictionary<int, int> toSorted,
MediaInfo[] Medias,
FemSolver.WaveModeDV WaveModeDv,
ref MyDoubleMatrix txx_1d, ref MyDoubleMatrix ryy_1d, ref MyDoubleMatrix uzz_1d)
{
// １次線要素
const int nno = Constants.LineNodeCnt_FirstOrder; // 2;
int[] nodeNumbers = element.NodeNumbers;
System.Diagnostics.Debug.Assert(nno == nodeNumbers.Length);
// 座標の取得
double[] elementCoords = new double[nno];
for (int n = 0; n < nno; n++)
{
int nodeIndex = nodeNumbers[n] - 1;
elementCoords[n] = coords[nodeIndex];
}
// 線要素の長さ
double elen = Math.Abs(elementCoords[1] - elementCoords[0]);
// 媒質インデックス
int mediaIndex = element.MediaIndex;
// 媒質
MediaInfo media = Medias[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);
}
media_P = MyMatrixUtil.matrix_Inverse(media_P);
double[,] integralN = new double[nno, nno]
{
{ elen / 3.0, elen / 6.0 },
{ elen / 6.0, elen / 3.0 },
};
double[,] integralDNDY = new double[nno, nno]
{
{ 1.0 / elen, -1.0 / elen },
{ -1.0 / elen, 1.0 / elen },
};
for (int ino = 0; ino < nno; ino++)
{
int inoBoundary = nodeNumbers[ino];
int inoSorted;
if (!toSorted.ContainsKey(inoBoundary)) continue;
inoSorted = toSorted[inoBoundary];
for (int jno = 0; jno < nno; jno++)
{
int jnoBoundary = nodeNumbers[jno];
int jnoSorted;
if (!toSorted.ContainsKey(jnoBoundary)) continue;
jnoSorted = toSorted[jnoBoundary];
// 対称バンド行列対応
if (ryy_1d is MyDoubleSymmetricBandMatrix && jnoSorted < inoSorted)
{
continue;
}
double e_txx_1d_inojno = media_P[0, 0] * integralDNDY[ino, jno];
double e_ryy_1d_inojno = media_P[1, 1] * integralN[ino, jno];
double e_uzz_1d_inojno = media_Q[2, 2] * integralN[ino, jno];
//txx_1d[inoSorted, jnoSorted] += e_txx_1d_inojno;
//ryy_1d[inoSorted, jnoSorted] += e_ryy_1d_inojno;
//uzz_1d[inoSorted, jnoSorted] += e_uzz_1d_inojno;
txx_1d._body[txx_1d.GetBufferIndex(inoSorted, jnoSorted)] += e_txx_1d_inojno;
ryy_1d._body[ryy_1d.GetBufferIndex(inoSorted, jnoSorted)] += e_ryy_1d_inojno;
uzz_1d._body[uzz_1d.GetBufferIndex(inoSorted, jnoSorted)] += e_uzz_1d_inojno;
}
}
}