/* 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> /// Fem入力データをファイルへ書き込み /// </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="lsEqnSolverDv">線形方程式解法区分</param> /// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param> /// <returns></returns> public static void SaveToFile(string filename, IList<FemNode> nodes, IList<FemElement> elements, IList<IList<int>> ports, IList<int> forceBCNodes, int incidentPortNo, MediaInfo[] medias, double firstWaveLength, double lastWaveLength, int calcCnt, FemSolver.WGStructureDV wgStructureDv, FemSolver.WaveModeDV waveModeDv, FemSolver.LinearSystemEqnSoverDV lsEqnSolverDv, double waveguideWidthForEPlane ) { int nodeCnt = nodes.Count; IList<double[]> doubleCoords = new List<double[]>(); foreach (FemNode femNode in nodes) { doubleCoords.Add(femNode.Coord); } int elementCnt = elements.Count; IList<int[]> in_elements = new List<int[]>(); foreach (FemElement femElement in elements) { int cnt = 2 + femElement.NodeNumbers.Length; int[] in_element = new int[cnt]; in_element[0] = femElement.No; in_element[1] = femElement.MediaIndex; for (int ino = 0; ino < femElement.NodeNumbers.Length; ino++) { in_element[2 + ino] = femElement.NodeNumbers[ino]; } in_elements.Add(in_element); } int portCnt = ports.Count; int[] forceBCNodeNumbers = forceBCNodes.ToArray(); SaveToFileFromCad( filename, nodeCnt, doubleCoords, elementCnt, in_elements, portCnt, ports, forceBCNodeNumbers, incidentPortNo, medias, firstWaveLength, lastWaveLength, calcCnt, wgStructureDv, waveModeDv, lsEqnSolverDv, waveguideWidthForEPlane); }
/// <summary> /// Fem入力データファイルへ保存 /// I/FがCadの内部データ寄りになっているので、変更したいが後回し /// </summary> /// <param name="filename">ファイル名(*.fem)</param> /// <param name="nodeCnt">節点数</param> /// <param name="doubleCoords">節点座標リスト</param> /// <param name="elementCnt">要素数</param> /// <param name="elements">要素リスト</param> /// <param name="portCnt">ポート数</param> /// <param name="portList">ポートの節点番号リストのリスト</param> /// <param name="forceBCNodeNumbers">強制境界節点番号のリスト</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">計算周波数件数</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="lsEqnSolverDv">線形方程式解法区分</param> /// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param> public static void SaveToFileFromCad(string filename, int nodeCnt, IList<double[]> doubleCoords, int elementCnt, IList<int[]> elements, int portCnt, IList<IList<int>> portList, int[] forceBCNodeNumbers, int incidentPortNo, MediaInfo[] medias, double firstWaveLength, double lastWaveLength, int calcCnt, FemSolver.WGStructureDV wgStructureDv, FemSolver.WaveModeDV waveModeDv, FemSolver.LinearSystemEqnSoverDV lsEqnSolverDv, double waveguideWidthForEPlane) { ////////////////////////////////////////// // ファイル出力 ////////////////////////////////////////// try { using (StreamWriter sw = new StreamWriter(filename)) { string line; // 節点番号と座標の出力 line = string.Format("Nodes,{0}", nodeCnt); sw.WriteLine(line); for (int i = 0; i < doubleCoords.Count; i++) { double[] doubleCoord = doubleCoords[i]; int nodeNumber = i + 1; line = string.Format("{0},{1},{2}", nodeNumber, doubleCoord[0], doubleCoord[1]); sw.WriteLine(line); } // 要素番号と要素を構成する節点の全体節点番号の出力 line = string.Format("Elements,{0}", elementCnt); sw.WriteLine(line); foreach (int[] element in elements) { line = ""; foreach (int k in element) { line += string.Format("{0},", k); } line = line.Substring(0, line.Length - 1); // 最後の,を削除 sw.WriteLine(line); } // ポート境界条件節点 int portCounter = 0; line = string.Format("Ports,{0}", portList.Count); sw.WriteLine(line); foreach (IList<int> nodes in portList) { line = string.Format("{0},{1}", ++portCounter, nodes.Count); sw.WriteLine(line); int portNodeNumber = 0; foreach (int nodeNumber in nodes) { line = string.Format("{0},{1}", ++portNodeNumber, nodeNumber); sw.WriteLine(line); } } // 強制境界節点 line = string.Format("Force,{0}", forceBCNodeNumbers.Length); sw.WriteLine(line); foreach (int nodeNumber in forceBCNodeNumbers) { line = string.Format("{0}", nodeNumber); sw.WriteLine(line); } // 入射ポート番号 line = string.Format("IncidentPortNo,{0}", incidentPortNo); sw.WriteLine(line); ////////////////////////////////////////// //// Ver1.1.0.0からの追加情報 ////////////////////////////////////////// // 媒質情報の個数 sw.WriteLine("Medias,{0}", medias.Length); // 媒質情報の書き込み for (int i = 0; i < medias.Length; i++) { MediaInfo media = medias[i]; line = string.Format("{0},", i); double[,] p = media.P; for (int m = 0; m < p.GetLength(0); m++) { for (int n = 0; n < p.GetLength(1); n++) { line += string.Format("{0},", p[m, n]); } } double[,] q = media.Q; for (int m = 0; m < q.GetLength(0); m++) { for (int n = 0; n < q.GetLength(1); n++) { line += string.Format("{0},", q[m, n]); } } line = line.Remove(line.Length - 1); // 最後の,を削除 sw.WriteLine(line); } // 計算対象周波数 sw.WriteLine("WaveLengthRange,{0},{1},{2}", firstWaveLength, lastWaveLength, calcCnt); // 線形方程式解法区分 sw.WriteLine("LsEqnSolverDv,{0}", FemSolver.LinearSystemEqnSolverDVToStr(lsEqnSolverDv)); // 計算対象モード区分 sw.WriteLine("WaveModeDv,{0}", ((waveModeDv == FemSolver.WaveModeDV.TM) ? "TM" : "TE")); // 導波路構造区分 sw.WriteLine("WGStructureDv,{0}", FemSolver.WGStructureDVToStr(wgStructureDv)); // 導波路幅(E面解析用) sw.WriteLine("WaveguideWidthForEPlane,{0}", waveguideWidthForEPlane); } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); MessageBox.Show(exception.Message); } }
///////////////////////////////////////////////////////////////////////////// // 定数 ///////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////// // 型 ///////////////////////////////////////////////////////////////////////////// /// <summary> /// 図面情報を保存する /// </summary> /// <param name="filename"></param> /// <param name="areaSelection"></param> /// <param name="areaToMediaIndex"></param> /// <param name="edgeList"></param> /// <param name="incidentPortNo"></param> /// <param name="medias"></param> public static void SaveToFile( string filename, bool[,] AreaSelection, int[,] AreaToMediaIndex, IList <Edge> EdgeList, int IncidentPortNo, MediaInfo[] Medias ) { Size MaxDiv = Constants.MaxDiv; try { using (StreamWriter sw = new StreamWriter(filename)) { int counter; string line; // 領域: 書き込む個数の計算 counter = 0; for (int y = 0; y < MaxDiv.Height; y++) { for (int x = 0; x < MaxDiv.Width; x++) { if (AreaSelection[y, x]) { counter++; } } } // 領域: 書き込み sw.WriteLine("AreaSelection,{0}", counter); for (int y = 0; y < MaxDiv.Height; y++) { for (int x = 0; x < MaxDiv.Width; x++) { if (AreaSelection[y, x]) { // ver1.1.0.0から座標の後に媒質インデックスを追加 sw.WriteLine("{0},{1},{2}", x, y, AreaToMediaIndex[y, x]); } } } // ポート境界: 書き込み個数の計算 sw.WriteLine("EdgeList,{0}", EdgeList.Count); // ポート境界: 書き込み foreach (Edge edge in EdgeList) { sw.WriteLine("{0},{1},{2},{3},{4}", edge.No, edge.Points[0].X, edge.Points[0].Y, edge.Points[1].X, edge.Points[1].Y); } // 入射ポート番号 sw.WriteLine("IncidentPortNo,{0}", IncidentPortNo); ////////////////////////////////////////// //// Ver1.1.0.0からの追加情報 ////////////////////////////////////////// // 媒質情報の個数 sw.WriteLine("Medias,{0}", Medias.Length); // 媒質情報の書き込み for (int i = 0; i < Medias.Length; i++) { MediaInfo media = Medias[i]; line = string.Format("{0},", i); double[,] p = media.P; for (int m = 0; m < p.GetLength(0); m++) { for (int n = 0; n < p.GetLength(1); n++) { line += string.Format("{0},", p[m, n]); } } double[,] q = media.Q; for (int m = 0; m < q.GetLength(0); m++) { for (int n = 0; n < q.GetLength(1); n++) { line += string.Format("{0},", q[m, n]); } } line = line.Remove(line.Length - 1); // 最後の,を削除 sw.WriteLine(line); } } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); MessageBox.Show(exception.Message); } }
/// <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> /// 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.WGStructureDV WGStructureDv, FemSolver.WaveModeDV WaveModeDv, double waveguideWidthForEPlane, 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; // 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; // 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); 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; } } }
/// <summary> /// 初期化処理 /// </summary> protected void init() { _CadMode = CadModeType.None; for (int y = 0; y < MaxDiv.Height; y++) { for (int x = 0; x < MaxDiv.Width; x++) { AreaSelection[y, x] = false; AreaToMediaIndex[y, x] = 0; } } for (int x = 0; x < MaxDiv.Width + 1; x++) { for (int y = 0; y < MaxDiv.Height; y++) { YBoundarySelection[y, x] = false; } } for (int y = 0; y < MaxDiv.Height + 1; y++) { for (int x = 0; x < MaxDiv.Width; x++) { XBoundarySelection[y, x] = false; } } EdgeList.Clear(); IncidentPortNo = 1; for (int i = 0; i < Medias.Length; i++) { MediaInfo media = new MediaInfo(); media.BackColor = MediaBackColors[i]; Medias[i] = media; } }
/* 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> /// 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); }
///////////////////////////////////////////////////////////////////////////// // 定数 ///////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////// // 型 ///////////////////////////////////////////////////////////////////////////// /// <summary> /// 図面情報を保存する /// </summary> /// <param name="filename"></param> /// <param name="areaSelection"></param> /// <param name="areaToMediaIndex"></param> /// <param name="edgeList"></param> /// <param name="incidentPortNo"></param> /// <param name="medias"></param> public static void SaveToFile( string filename, bool[,] AreaSelection, int[,] AreaToMediaIndex, IList<Edge> EdgeList, int IncidentPortNo, MediaInfo[] Medias ) { Size MaxDiv = Constants.MaxDiv; try { using (StreamWriter sw = new StreamWriter(filename)) { int counter; string line; // 領域: 書き込む個数の計算 counter = 0; for (int y = 0; y < MaxDiv.Height; y++) { for (int x = 0; x < MaxDiv.Width; x++) { if (AreaSelection[y, x]) { counter++; } } } // 領域: 書き込み sw.WriteLine("AreaSelection,{0}", counter); for (int y = 0; y < MaxDiv.Height; y++) { for (int x = 0; x < MaxDiv.Width; x++) { if (AreaSelection[y, x]) { // ver1.1.0.0から座標の後に媒質インデックスを追加 sw.WriteLine("{0},{1},{2}", x, y, AreaToMediaIndex[y, x]); } } } // ポート境界: 書き込み個数の計算 sw.WriteLine("EdgeList,{0}", EdgeList.Count); // ポート境界: 書き込み foreach (Edge edge in EdgeList) { sw.WriteLine("{0},{1},{2},{3},{4}", edge.No, edge.Points[0].X, edge.Points[0].Y, edge.Points[1].X, edge.Points[1].Y); } // 入射ポート番号 sw.WriteLine("IncidentPortNo,{0}", IncidentPortNo); ////////////////////////////////////////// //// Ver1.1.0.0からの追加情報 ////////////////////////////////////////// // 媒質情報の個数 sw.WriteLine("Medias,{0}", Medias.Length); // 媒質情報の書き込み for(int i = 0; i < Medias.Length; i++) { MediaInfo media = Medias[i]; line = string.Format("{0},", i); double[,] p = media.P; for (int m = 0; m < p.GetLength(0); m++) { for (int n = 0; n < p.GetLength(1); n++) { line += string.Format("{0},", p[m, n]); } } double[,] q = media.Q; for (int m = 0; m < q.GetLength(0); m++) { for (int n = 0; n < q.GetLength(1); n++) { line += string.Format("{0},", q[m, n]); } } line = line.Remove(line.Length - 1); // 最後の,を削除 sw.WriteLine(line); } } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); MessageBox.Show(exception.Message); } }
/// <summary> /// 図面情報を読み込む /// </summary> /// <param name="filename"></param> /// <param name="areaSelection"></param> /// <param name="areaToMediaIndex"></param> /// <param name="edgeList"></param> /// <param name="yBoundarySelection">2次的な情報(edgeListから生成される)</param> /// <param name="xBoundarySelection">2次的な情報(edgeListから生成される)</param> /// <param name="incidentPortNo"></param> /// <param name="medias"></param> /// <returns></returns> public static bool LoadFromFile( string filename, ref bool[,] AreaSelection, ref int[,] AreaToMediaIndex, ref IList<Edge> EdgeList, ref bool[,] YBoundarySelection, ref bool[,] XBoundarySelection, ref int IncidentPortNo, ref MediaInfo[] Medias ) { bool success = false; Size MaxDiv = Constants.MaxDiv; int DefMediaIndex = 0;// CadLogic.DefMediaIndex; int MaxMediaCount = Medias.Length; try { using (StreamReader sr = new StreamReader(filename)) { string line; string[] tokens; const char delimiter = ','; int cnt = 0; // 領域選択 line = sr.ReadLine(); tokens = line.Split(delimiter); if (tokens[0] != "AreaSelection") { MessageBox.Show("領域選択情報がありません", "", MessageBoxButtons.OK, MessageBoxIcon.Error); return success; } cnt = int.Parse(tokens[1]); for (int i = 0; i < cnt; i++) { line = sr.ReadLine(); tokens = line.Split(delimiter); if (tokens.Length != 2 && tokens.Length != 3) // ver1.1.0.0で媒質インデックス追加 { MessageBox.Show("領域選択情報が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error); return success; } int x = int.Parse(tokens[0]); int y = int.Parse(tokens[1]); int mediaIndex = DefMediaIndex; if (tokens.Length == 3) { mediaIndex = int.Parse(tokens[2]); } if ((x >= 0 && x < MaxDiv.Width) && (y >= 0 && y < MaxDiv.Height)) { AreaSelection[y, x] = true; } else { MessageBox.Show("領域選択座標値が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error); return success; } // ver1.1.0.0で追加 AreaToMediaIndex[y, x] = mediaIndex; } // ポート境界 line = sr.ReadLine(); tokens = line.Split(delimiter); if (tokens[0] != "EdgeList") { MessageBox.Show("境界選択情報がありません", "", MessageBoxButtons.OK, MessageBoxIcon.Error); return success; } cnt = int.Parse(tokens[1]); for (int i = 0; i < cnt; i++) { line = sr.ReadLine(); tokens = line.Split(delimiter); if (tokens.Length != 5) { MessageBox.Show("境界選択情報が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error); return success; } int edgeNo = int.Parse(tokens[0]); Point[] p = new Point[2]; for (int k = 0; k < p.Length; k++) { p[k] = new Point(); p[k].X = int.Parse(tokens[1 + k * 2]); p[k].Y = int.Parse(tokens[1 + k * 2 + 1]); } Size delta = new Size(0, 0); if (p[0].X == p[1].X) { // Y方向境界 delta = new Size(0, 1); } else if (p[0].Y == p[1].Y) { // X方向境界 delta = new Size(1, 0); } else { MessageBox.Show("境界選択情報が不正です", "", MessageBoxButtons.OK, MessageBoxIcon.Error); return success; } Edge edge = new Edge(delta); edge.No = edgeNo; edge.Set(p[0], p[1]); EdgeList.Add(edge); } foreach (Edge edge in EdgeList) { if (edge.Delta.Width == 0) { // Y方向境界 int x = edge.Points[0].X; int sty = edge.Points[0].Y; int edy = edge.Points[1].Y; for (int y = sty; y < edy; y++) { YBoundarySelection[y, x] = true; } } else if(edge.Delta.Height == 0) { // X方向境界 int y = edge.Points[0].Y; int stx = edge.Points[0].X; int edx = edge.Points[1].X; for (int x = stx; x < edx; x++) { XBoundarySelection[y, x] = true; } } else { MessageBox.Show("Not implemented"); } } line = sr.ReadLine(); if (line.Length == 0) { MessageBox.Show("入射ポート番号がありません"); return success; } tokens = line.Split(delimiter); if (tokens[0] != "IncidentPortNo") { MessageBox.Show("入射ポート番号がありません"); return success; } 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 success; } cnt = int.Parse(tokens[1]); if (cnt > MaxMediaCount) { MessageBox.Show("媒質情報の個数が不正です"); return success; } 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 success; } tokens = line.Split(delimiter); if (tokens.Length != 1 + 9 + 9) { MessageBox.Show("媒質情報が不正です"); return success; } 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); } } } success = true; } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); MessageBox.Show(exception.Message); } return success; }
/// <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_FirstOrder; //3; // 1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]); // ∫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 ino = 0; ino < nno; ino++) { for (int jno = 0; jno < nno; jno++) { integralDNDX[0, ino, jno] = area * dldx[ino, 0] * dldx[jno, 0]; integralDNDX[1, ino, jno] = area * dldx[ino, 1] * dldx[jno, 1]; } } // ∫N N dxdy double[,] integralN = new double[nno, nno] { { 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> /// 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="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="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.WGStructureDV WGStructureDv, FemSolver.WaveModeDV WaveModeDv, double waveguideWidthForEPlane, 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, WGStructureDv, WaveModeDv, waveguideWidthForEPlane, 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; } } }
public object Clone() { MediaInfo media = new MediaInfo(this.p, this.q); media.BackColor = this.BackColor; return (object)media; }
/// <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> /// Fem入力データファイルへ保存 /// I/FがCadの内部データ寄りになっているので、変更したいが後回し /// </summary> /// <param name="filename">ファイル名(*.fem)</param> /// <param name="nodeCnt">節点数</param> /// <param name="doubleCoords">節点座標リスト</param> /// <param name="elementCnt">要素数</param> /// <param name="elements">要素リスト</param> /// <param name="portCnt">ポート数</param> /// <param name="portList">ポートの節点番号リストのリスト</param> /// <param name="forceBCNodeNumbers">強制境界節点番号のリスト</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">計算周波数件数</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="lsEqnSolverDv">線形方程式解法区分</param> /// <param name="waveguideWidthForEPlane">導波路幅(E面解析用)</param> public static void SaveToFileFromCad (string filename, int nodeCnt, IList <double[]> doubleCoords, int elementCnt, IList <int[]> elements, int portCnt, IList <IList <int> > portList, int[] forceBCNodeNumbers, int incidentPortNo, MediaInfo[] medias, double firstWaveLength, double lastWaveLength, int calcCnt, FemSolver.WGStructureDV wgStructureDv, FemSolver.WaveModeDV waveModeDv, FemSolver.LinearSystemEqnSoverDV lsEqnSolverDv, double waveguideWidthForEPlane) { ////////////////////////////////////////// // ファイル出力 ////////////////////////////////////////// try { using (StreamWriter sw = new StreamWriter(filename)) { string line; // 節点番号と座標の出力 line = string.Format("Nodes,{0}", nodeCnt); sw.WriteLine(line); for (int i = 0; i < doubleCoords.Count; i++) { double[] doubleCoord = doubleCoords[i]; int nodeNumber = i + 1; line = string.Format("{0},{1},{2}", nodeNumber, doubleCoord[0], doubleCoord[1]); sw.WriteLine(line); } // 要素番号と要素を構成する節点の全体節点番号の出力 line = string.Format("Elements,{0}", elementCnt); sw.WriteLine(line); foreach (int[] element in elements) { line = ""; foreach (int k in element) { line += string.Format("{0},", k); } line = line.Substring(0, line.Length - 1); // 最後の,を削除 sw.WriteLine(line); } // ポート境界条件節点 int portCounter = 0; line = string.Format("Ports,{0}", portList.Count); sw.WriteLine(line); foreach (IList <int> nodes in portList) { line = string.Format("{0},{1}", ++portCounter, nodes.Count); sw.WriteLine(line); int portNodeNumber = 0; foreach (int nodeNumber in nodes) { line = string.Format("{0},{1}", ++portNodeNumber, nodeNumber); sw.WriteLine(line); } } // 強制境界節点 line = string.Format("Force,{0}", forceBCNodeNumbers.Length); sw.WriteLine(line); foreach (int nodeNumber in forceBCNodeNumbers) { line = string.Format("{0}", nodeNumber); sw.WriteLine(line); } // 入射ポート番号 line = string.Format("IncidentPortNo,{0}", incidentPortNo); sw.WriteLine(line); ////////////////////////////////////////// //// Ver1.1.0.0からの追加情報 ////////////////////////////////////////// // 媒質情報の個数 sw.WriteLine("Medias,{0}", medias.Length); // 媒質情報の書き込み for (int i = 0; i < medias.Length; i++) { MediaInfo media = medias[i]; line = string.Format("{0},", i); double[,] p = media.P; for (int m = 0; m < p.GetLength(0); m++) { for (int n = 0; n < p.GetLength(1); n++) { line += string.Format("{0},", p[m, n]); } } double[,] q = media.Q; for (int m = 0; m < q.GetLength(0); m++) { for (int n = 0; n < q.GetLength(1); n++) { line += string.Format("{0},", q[m, n]); } } line = line.Remove(line.Length - 1); // 最後の,を削除 sw.WriteLine(line); } // 計算対象周波数 sw.WriteLine("WaveLengthRange,{0},{1},{2}", firstWaveLength, lastWaveLength, calcCnt); // 線形方程式解法区分 sw.WriteLine("LsEqnSolverDv,{0}", FemSolver.LinearSystemEqnSolverDVToStr(lsEqnSolverDv)); // 計算対象モード区分 sw.WriteLine("WaveModeDv,{0}", ((waveModeDv == FemSolver.WaveModeDV.TM) ? "TM" : "TE")); // 導波路構造区分 sw.WriteLine("WGStructureDv,{0}", FemSolver.WGStructureDVToStr(wgStructureDv)); // 導波路幅(E面解析用) sw.WriteLine("WaveguideWidthForEPlane,{0}", waveguideWidthForEPlane); } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); MessageBox.Show(exception.Message); } }
/// <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> /// 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]; } } }