/// <summary> /// 要素境界を描画する /// </summary> /// <param name="g"></param> /// <param name="panel"></param> public void Draw(Graphics g, Size ofs, Size delta, Size regionSize, bool backFillFlg = false) { //const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ) Constants.FemElementShapeDV elemShapeDv; int order; int vertexCnt; FemMeshLogic.GetElementShapeDvAndOrderByElemNodeCnt(this.NodeNumbers.Length, out elemShapeDv, out order, out vertexCnt); // 三角形(or 四角形)の頂点を取得 Point[] points = new Point[vertexCnt]; for (int ino = 0; ino < vertexCnt; ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == 2); int x = (int)((double)node.Coord[0] * delta.Width); int y = (int)(regionSize.Height - (double)node.Coord[1] * delta.Height); points[ino] = new Point(x, y) + ofs; } // 三角形(or 四角形)を描画 if (backFillFlg) { // 要素の背景を塗りつぶす using (Brush brush = new SolidBrush(BackColor)) { g.FillPolygon(brush, points); } } using (Pen selectedPen = new Pen(LineColor, 1)) { // 境界線の描画 //selectedPen.DashStyle = System.Drawing.Drawing2D.DashStyle.Dot; g.DrawPolygon(selectedPen, points); } }
/// <summary> /// コピー /// </summary> /// <param name="src"></param> public void CP(FemNode src) { No = src.No; Coord = null; if (src.Coord != null) { Coord = new double[src.Coord.Length]; for (int i = 0; i < src.Coord.Length; i++) { Coord[i] = src.Coord[i]; } } }
/// <summary> /// コピー /// </summary> /// <param name="src"></param> public void CP(FemNode src) { No = src.No; Coord = null; if (src.Coord != null) { Coord = new double[src.Coord.Length]; for (int i = 0; i < src.Coord.Length; i++) { Coord[i] = src.Coord[i]; } } }
/// <summary> /// フィールドの回転を取得する /// </summary> /// <param name="rotXFValues"></param> /// <param name="rotYFValues"></param> protected override void calcRotField(out Complex[] rotXFValues, out Complex[] rotYFValues) { base.calcRotField(out rotXFValues, out rotYFValues); rotXFValues = new Complex[NodeNumbers.Length]; rotYFValues = new Complex[NodeNumbers.Length]; const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 //const int vertexCnt = Constants.QuadVertexCnt; //4; // 四角形形の頂点の数(2次要素でも同じ) //const int nodeCnt = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 四角形形2次要素 int nodeCnt = NodeNumbers.Length; if (nodeCnt != Constants.QuadNodeCnt_SecondOrder_Type2 && nodeCnt != Constants.QuadNodeCnt_FirstOrder) { return; } // 四角形の節点座標を取得 double[][] pp = new double[nodeCnt][]; for (int ino = 0; ino < pp.GetLength(0); ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); pp[ino] = new double[ndim]; pp[ino][0] = node.Coord[0]; pp[ino][1] = node.Coord[1]; } // 四角形内部を四角形で分割 // 要素節点座標( 局所r,s成分 ) // s // | // 3+ 6 +2 // | | | // ---7---+---5-->r // | | | // 0+ 4 +1 // | // double[][] n_pts = { // r, s new double[] { -1.0, -1.0 }, //0 new double[] { 1.0, -1.0 }, //1 new double[] { 1.0, 1.0 }, //2 new double[] { -1.0, 1.0 }, //3 new double[] { 0, -1.0 }, //4 new double[] { 1.0, 0 }, //5 new double[] { 0, 1.0 }, //6 new double[] { -1.0, 0 }, //7 }; // 節点上のrot(Ez)を求める int nno = nodeCnt; for (int ino = 0; ino < nno; ino++) { double r = n_pts[ino][0]; double s = n_pts[ino][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]; if (nodeCnt == Constants.QuadNodeCnt_SecondOrder_Type2) { // 節点0~3 : 四角形の頂点 for (int i = 0; i < 4; i++) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s) * (ri * r + si * s - 1.0); // 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); } } else if (nodeCnt == Constants.QuadNodeCnt_FirstOrder) { // 節点0~3 : 四角形の頂点 for (int i = 0; i < nno; i++) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s); // 形状関数のr方向微分 dNdr[i] = 0.25 * ri * (1.0 + si * s); // 形状関数のs方向微分 dNds[i] = 0.25 * si * (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 < 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; // 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]; } } rotXFValues[ino] = new Complex(); rotYFValues[ino] = new Complex(); for (int k = 0; k < nodeCnt; k++) { // (rot(Ez)x = dEz/dy rotXFValues[ino] += _FValues[k] * dNdX[1, k]; // (rot(Ez)y = - dEz/dx rotYFValues[ino] += -1.0 * _FValues[k] * dNdX[0, k]; } // rot(Ez)を磁界の値に変換する rotXFValues[ino] *= _FactorForRot / _media_Q[0, 0]; rotYFValues[ino] *= _FactorForRot / _media_Q[1, 1]; } }
/// <summary> /// フィールド値を描画する /// </summary> /// <param name="g"></param> /// <param name="ofs"></param> /// <param name="delta"></param> /// <param name="regionSize"></param> /// <param name="colorMap"></param> /// <param name="valueDv"></param> public override void DrawField(Graphics g, Size ofs, Size delta, Size regionSize, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv, ColorMap colorMap) { //base.DrawField(g, ofs, delta, regionSize, colorMap); if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null) { return; } Complex[] tagtValues = null; if (fieldDv == FemElement.FieldDV.Field) { tagtValues = _FValues; } else if (fieldDv == FemElement.FieldDV.RotX) { tagtValues = _RotXFValues; } else if (fieldDv == FemElement.FieldDV.RotY) { tagtValues = _RotYFValues; } else { return; } const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 const int vertexCnt = Constants.QuadVertexCnt; //3; // 四角形形の頂点の数(2次要素でも同じ) //const int nodeCnt = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 四角形2次要素 int nodeCnt = NodeNumbers.Length; if (nodeCnt != Constants.QuadNodeCnt_SecondOrder_Type2 && nodeCnt != Constants.QuadNodeCnt_FirstOrder) { return; } // 四角形節点座標を取得 double[][] pp = new double[nodeCnt][]; for (int ino = 0; ino < pp.GetLength(0); ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); pp[ino] = new double[ndim]; pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width; pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height; } // 四角形内部を四角形で分割 // 要素節点座標( 局所r,s成分 ) // s // | // 3+ 6 +2 // | | | // ---7---+---5-->r // | | | // 0+ 4 +1 // | // double[][] n_pts = { // r, s new double[] { -1.0, -1.0 }, //0 new double[] { 1.0, -1.0 }, //1 new double[] { 1.0, 1.0 }, //2 new double[] { -1.0, 1.0 }, //3 new double[] { 0, -1.0 }, //4 new double[] { 1.0, 0 }, //5 new double[] { 0, 1.0 }, //6 new double[] { -1.0, 0 }, //7 }; int ndiv = this.IsCoarseFieldMesh ? (Constants.TriDrawFieldMshDivCnt / 2) : Constants.TriDrawFieldMshDivCnt; double defdr = 2.0 / (double)ndiv; double defds = defdr; for (int i1 = 0; i1 < ndiv; i1++) { double r = -1.0 + i1 * defdr; double rNext = r + defdr; for (int i2 = 0; i2 < ndiv; i2++) { double s = -1.0 + i2 * defds; double sNext = s + defds; // 四角形の頂点 const int rectVCnt = 4; double[][] rect_local_p = new double[rectVCnt][] { new double[] { r, s }, new double[] { rNext, s }, new double[] { rNext, sNext }, new double[] { r, sNext } }; double[][] rectpp = new double[rectVCnt][]; for (int ino = 0; ino < rectVCnt; ino++) { double work_r = rect_local_p[ino][0]; double work_s = rect_local_p[ino][1]; double xx = 0.0; double yy = 0.0; for (int k = 0; k < vertexCnt; k++) { double ri = n_pts[k][0]; double si = n_pts[k][1]; xx += pp[k][0] * 0.25 * (1 + ri * work_r) * (1 + si * work_s); yy += pp[k][1] * 0.25 * (1 + ri * work_r) * (1 + si * work_s); } rectpp[ino] = new double[] { xx, yy }; } // 表示する位置 double[] disp_p = new double[] { (rect_local_p[0][0] + rect_local_p[1][0]) * 0.5, (rect_local_p[0][1] + rect_local_p[3][1]) * 0.5 }; // 表示する値 Complex cvalue = new Complex(0.0, 0.0); // 表示する位置の形状関数値 double[] workN = new double[nodeCnt]; if (nodeCnt == Constants.QuadNodeCnt_FirstOrder) { double work_r = disp_p[0]; double work_s = disp_p[1]; for (int i = 0; i < 4; i++) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; workN[i] = 0.25 * (1.0 + ri * work_r) * (1.0 + si * work_s); } } else { double work_r = disp_p[0]; double work_s = disp_p[1]; // 節点0~3 : 四角形の頂点 for (int i = 0; i < 4; i++) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N workN[i] = 0.25 * (1.0 + ri * work_r) * (1.0 + si * work_s) * (ri * work_r + si * work_s - 1.0); } // 節点4,6 : r方向辺上中点 foreach (int i in new int[] { 4, 6 }) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N workN[i] = 0.5 * (1.0 - work_r * work_r) * (1.0 + si * work_s); } // 節点5,7 : s方向辺上中点 foreach (int i in new int[] { 5, 7 }) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N workN[i] = 0.5 * (1.0 + ri * work_r) * (1.0 - work_s * work_s); } } for (int k = 0; k < nodeCnt; k++) { cvalue += tagtValues[k] * workN[k]; } // 四角形の頂点(描画用) Point[] rectp = new Point[rectVCnt]; for (int ino = 0; ino < rectVCnt; ino++) { rectp[ino] = new Point((int)rectpp[ino][0], (int)rectpp[ino][1]); } try { // 表示する値 double showValue = 0.0; if (valueDv == ValueDV.Real) { showValue = cvalue.Real; } else if (valueDv == ValueDV.Imaginary) { showValue = cvalue.Imaginary; } else { // 既定値は絶対値 showValue = Complex.Abs(cvalue); } // 塗りつぶし色の取得 Color fillColor = colorMap.GetColor(showValue); // 塗りつぶし using (Brush brush = new SolidBrush(fillColor)) { g.FillPolygon(brush, rectp); } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); } } } }
/// <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(clapack使用時)</param> /// <param name="mat_cc">マージされる全体行列(DelFEM使用時)</param> /// <param name="res_c">マージされる残差ベクトル(DelFEM使用時)</param> /// <param name="tmpBuffer">一時バッファ(DelFEM使用時)</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, ref DelFEM4NetMatVec.CZMatDia_BlkCrs_Ptr mat_cc, ref DelFEM4NetMatVec.CZVector_Blk_Ptr res_c, ref int[] tmpBuffer) { // 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 if (mat_cc != null) { // 全体節点番号→要素内節点インデックスマップ Dictionary <uint, int> inoGlobalDic = new Dictionary <uint, int>(); for (int ino = 0; ino < nno; ino++) { int iNodeNumber = no_c[ino]; if (ForceNodeNumberH.ContainsKey(iNodeNumber)) { continue; } uint inoGlobal = (uint)toSorted[iNodeNumber]; inoGlobalDic.Add(inoGlobal, ino); } // マージ用の節点番号リスト uint[] no_c_tmp = inoGlobalDic.Keys.ToArray <uint>(); // マージする節点数("col"と"row"のサイズ) uint ncolrow_tmp = (uint)no_c_tmp.Length; // Note: // 要素の節点がすべて強制境界の場合がある.その場合は、ncolrow_tmpが0 if (ncolrow_tmp > 0) { // マージする要素行列 DelFEM4NetCom.Complex[] ematBuffer = new DelFEM4NetCom.Complex[ncolrow_tmp * ncolrow_tmp]; for (int ino_tmp = 0; ino_tmp < ncolrow_tmp; ino_tmp++) { int ino = inoGlobalDic[no_c_tmp[ino_tmp]]; for (int jno_tmp = 0; jno_tmp < ncolrow_tmp; jno_tmp++) { int jno = inoGlobalDic[no_c_tmp[jno_tmp]]; double value = emat[ino, jno]; DelFEM4NetCom.Complex cvalueDelFEM = new DelFEM4NetCom.Complex(value, 0); // ematBuffer[ino_tmp, jno_tmp] 横ベクトルを先に埋める(clapack方式でないことに注意) ematBuffer[ino_tmp * ncolrow_tmp + jno_tmp] = cvalueDelFEM; } } // 全体行列に要素行列をマージする mat_cc.Mearge(ncolrow_tmp, no_c_tmp, ncolrow_tmp, no_c_tmp, 1, ematBuffer, ref tmpBuffer); } } else if (mat != null) { 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> /// 節点情報をセットする /// </summary> /// <param name="nodes">節点情報配列(強制境界を含む全節点を節点番号順に格納した配列)</param> public virtual void SetNodesFromAllNodes(FemNode[] nodes) { _Nodes = new FemNode[NodeNumbers.Length]; for (int i = 0; i < NodeNumbers.Length; i++) { int nodeNumber = NodeNumbers[i]; _Nodes[i] = nodes[nodeNumber - 1]; System.Diagnostics.Debug.Assert(nodeNumber == _Nodes[i].No); } }
/// <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(clapack使用時)</param> /// <param name="mat_cc">マージされる全体行列(DelFEM使用時)</param> /// <param name="res_c">マージされる残差ベクトル(DelFEM使用時)</param> /// <param name="tmpBuffer">一時バッファ(DelFEM使用時)</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, ref DelFEM4NetMatVec.CZMatDia_BlkCrs_Ptr mat_cc, ref DelFEM4NetMatVec.CZVector_Blk_Ptr res_c, ref int[] tmpBuffer) { // 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 if (mat_cc != null) { // 全体節点番号→要素内節点インデックスマップ Dictionary <uint, int> inoGlobalDic = new Dictionary <uint, int>(); for (int ino = 0; ino < nno; ino++) { int iNodeNumber = no_c[ino]; if (ForceNodeNumberH.ContainsKey(iNodeNumber)) { continue; } uint inoGlobal = (uint)toSorted[iNodeNumber]; inoGlobalDic.Add(inoGlobal, ino); } // マージ用の節点番号リスト uint[] no_c_tmp = inoGlobalDic.Keys.ToArray <uint>(); // マージする節点数("col"と"row"のサイズ) uint ncolrow_tmp = (uint)no_c_tmp.Length; // Note: // 要素の節点がすべて強制境界の場合がある.その場合は、ncolrow_tmpが0 if (ncolrow_tmp > 0) { // マージする要素行列 DelFEM4NetCom.Complex[] ematBuffer = new DelFEM4NetCom.Complex[ncolrow_tmp * ncolrow_tmp]; for (int ino_tmp = 0; ino_tmp < ncolrow_tmp; ino_tmp++) { int ino = inoGlobalDic[no_c_tmp[ino_tmp]]; for (int jno_tmp = 0; jno_tmp < ncolrow_tmp; jno_tmp++) { int jno = inoGlobalDic[no_c_tmp[jno_tmp]]; double value = emat[ino, jno]; DelFEM4NetCom.Complex cvalueDelFEM = new DelFEM4NetCom.Complex(value, 0); // ematBuffer[ino_tmp, jno_tmp] 横ベクトルを先に埋める(clapack方式でないことに注意) ematBuffer[ino_tmp * ncolrow_tmp + jno_tmp] = cvalueDelFEM; } } // 全体行列に要素行列をマージする mat_cc.Mearge(ncolrow_tmp, no_c_tmp, ncolrow_tmp, no_c_tmp, 1, ematBuffer, ref tmpBuffer); } } else if (mat != null) { 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); }
/// <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> /// <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.LinearSystemEqnSoverDV lsEqnSoverDv ) { 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; lsEqnSoverDv = Constants.DefLsEqnSolverDv; 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); } } } catch (Exception exception) { Console.WriteLine(exception.Message + " " + exception.StackTrace); MessageBox.Show(exception.Message, "", MessageBoxButtons.OK, MessageBoxIcon.Error); return false; } return true; }
/// <summary> /// フィールド値の回転を描画する /// </summary> /// <param name="g"></param> /// <param name="ofs"></param> /// <param name="delta"></param> /// <param name="regionSize"></param> /// <param name="drawColor"></param> /// <param name="fieldDv"></param> /// <param name="minRotFValue"></param> /// <param name="maxRotFValue"></param> public override void DrawRotField(Graphics g, Size ofs, Size delta, Size regionSize, Color drawColor, FemElement.FieldDV fieldDv, double minRotFValue, double maxRotFValue) { if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null) { return; } Complex[] tagtXValues = null; Complex[] tagtYValues = null; if (fieldDv == FemElement.FieldDV.PoyntingXY) { tagtXValues = _PoyntingXFValues; tagtYValues = _PoyntingYFValues; } else if (fieldDv == FemElement.FieldDV.RotXY) { tagtXValues = _RotXFValues; tagtYValues = _RotYFValues; } else { return; } const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ) //const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素 int nodeCnt = NodeNumbers.Length; if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder) { return; } // 三角形の節点座標を取得 double[][] pp = new double[nodeCnt][]; for (int ino = 0; ino < pp.GetLength(0); ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); pp[ino] = new double[ndim]; pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width; pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height; } // 表示する位置の面積座標 double[] Li = new double[vertexCnt] { 1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0 }; // 表示する位置の形状関数 double[] vNi = null; if (nodeCnt == Constants.TriNodeCnt_FirstOrder) { vNi = new double[] { Li[0], Li[1], Li[2] }; } else { vNi = new double[] { Li[0] * (2.0 * Li[0] - 1.0), Li[1] * (2.0 * Li[1] - 1.0), Li[2] * (2.0 * Li[2] - 1.0), 4.0 * Li[0] * Li[1], 4.0 * Li[1] * Li[2], 4.0 * Li[2] * Li[0], }; } // 表示する位置 double showPosX = 0; double showPosY = 0; for (int k = 0; k < nodeCnt; k++) { showPosX += pp[k][0] * vNi[k]; showPosY += pp[k][1] * vNi[k]; } Complex cvalueX = new Complex(0, 0); Complex cvalueY = new Complex(0, 0); for (int k = 0; k < nodeCnt; k++) { cvalueX += tagtXValues[k] * vNi[k]; cvalueY += tagtYValues[k] * vNi[k]; } try { double showScale = ((double)regionSize.Width / DefPanelWidth) * ArrowLength; // 実数部のベクトル表示 int lenX = 0; int lenY = 0; if (Math.Abs(maxRotFValue) >= Constants.PrecisionLowerLimit) { lenX = (int)((double)(cvalueX.Real / maxRotFValue) * showScale); lenY = (int)((double)(cvalueY.Real / maxRotFValue) * showScale); } if (lenX != 0 || lenY != 0) { // Y方向は表示上逆になる lenY = -lenY; using (Pen pen = new Pen(drawColor, 1)) { //pen.DashStyle = System.Drawing.Drawing2D.DashStyle.Dot; //pen.StartCap = System.Drawing.Drawing2D.LineCap.Round; pen.EndCap = System.Drawing.Drawing2D.LineCap.ArrowAnchor; //pen.CustomEndCap = new System.Drawing.Drawing2D.AdjustableArrowCap(3, 3, false); // 重い g.DrawLine(pen, (int)showPosX, (int)showPosY, (int)(showPosX + lenX), (int)(showPosY + lenY)); } } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); } }
/// <summary> /// フィールドの回転を取得する /// </summary> /// <param name="rotXFValues"></param> /// <param name="rotYFValues"></param> protected override void calcRotField(out Complex[] rotXFValues, out Complex[] rotYFValues) { base.calcRotField(out rotXFValues, out rotYFValues); rotXFValues = new Complex[NodeNumbers.Length]; rotYFValues = new Complex[NodeNumbers.Length]; const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ) //const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素 int nodeCnt = NodeNumbers.Length; if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder) { return; } // 三角形の頂点を取得 double[][] pp = new double[vertexCnt][]; for (int ino = 0; ino < pp.GetLength(0); ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); pp[ino] = new double[ndim]; pp[ino][0] = node.Coord[0]; pp[ino][1] = node.Coord[1]; } // 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 = null; if (nodeCnt == Constants.TriNodeCnt_FirstOrder) { dndxC = new double[Constants.TriNodeCnt_FirstOrder, ndim, vertexCnt + 1] { { { 0.0, 0.0, 0.0, dldx[0, 0] }, { 0.0, 0.0, 0.0, dldx[0, 1] }, }, { { 0.0, 0.0, 0.0, dldx[1, 0] }, { 0.0, 0.0, 0.0, dldx[1, 1] }, }, { { 0.0, 0.0, 0.0, dldx[2, 0] }, { 0.0, 0.0, 0.0, dldx[2, 1] }, }, }; } else { dndxC = new double[Constants.TriNodeCnt_SecondOrder, 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 }, }, }; } // 節点の面積座標 double[][] n_pts = null; if (nodeCnt == Constants.TriNodeCnt_FirstOrder) { n_pts = new double[Constants.TriNodeCnt_FirstOrder][] { new double[vertexCnt] { 1.0, 0.0, 0.0 }, new double[vertexCnt] { 0.0, 1.0, 0.0 }, new double[vertexCnt] { 0.0, 0.0, 1.0 }, }; } else { n_pts = new double[Constants.TriNodeCnt_SecondOrder][] { new double[vertexCnt] { 1.0, 0.0, 0.0 }, new double[vertexCnt] { 0.0, 1.0, 0.0 }, new double[vertexCnt] { 0.0, 0.0, 1.0 }, new double[vertexCnt] { 0.5, 0.5, 0.0 }, new double[vertexCnt] { 0.0, 0.5, 0.5 }, new double[vertexCnt] { 0.5, 0.0, 0.5 }, }; } for (int ino = 0; ino < nodeCnt; ino++) { double[] L = n_pts[ino]; double[] dNdx = new double[nodeCnt]; double[] dNdy = new double[nodeCnt]; for (int k = 0; k < nodeCnt; k++) { int direction; direction = 0; dNdx[k] = dndxC[k, direction, 0] * L[0] + dndxC[k, direction, 1] * L[1] + dndxC[k, direction, 2] * L[2] + dndxC[k, direction, 3]; direction = 1; dNdy[k] = dndxC[k, direction, 0] * L[0] + dndxC[k, direction, 1] * L[1] + dndxC[k, direction, 2] * L[2] + dndxC[k, direction, 3]; } rotXFValues[ino] = new Complex(); rotYFValues[ino] = new Complex(); for (int k = 0; k < nodeCnt; k++) { // (rot(Ez)x = dEz/dy rotXFValues[ino] += _FValues[k] * dNdy[k]; // (rot(Ez)y = - dEz/dx rotYFValues[ino] += -1.0 * _FValues[k] * dNdx[k]; } // rot(Ez)を磁界の値に変換する rotXFValues[ino] *= _FactorForRot / _media_Q[0, 0]; rotYFValues[ino] *= _FactorForRot / _media_Q[1, 1]; } }
/// <summary> /// 描画領域をセットアップ /// </summary> /// <param name="out_rectLiList"></param> private void setupDrawRect(out IList <double[][]> out_rectLiList, out int orginVertexNo) { orginVertexNo = 2; out_rectLiList = new List <double[][]>(); if (_Nodes == null) { return; } const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ) //const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素 int nodeCnt = NodeNumbers.Length; if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder) { return; } // 三角形の節点座標を取得 double[][] pp = new double[nodeCnt][]; for (int ino = 0; ino < pp.GetLength(0); ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); pp[ino] = new double[ndim]; // 取りあえず規格化した値で計算する pp[ino][0] = node.Coord[0]; pp[ino][1] = -node.Coord[1]; // Y方向は逆にする } // 下記分割ロジックの原点となる頂点 // 頂点0固定で計算していたが、原点の内角が直角のとき長方形メッシュになるので原点を2(頂点を0,1,2としたとき)にする //int orginVertexNo = 2; // 内角が最大の頂点を取得し、その頂点を原点とする(後のロジックは原点が頂点を0,1,2としたとき、2になっている { double minCosth = double.MaxValue; int minCosthVertexNo = 0; for (int ino = 0; ino < vertexCnt; ino++) { const int vecCnt = 2; double[][] vec = new double[vecCnt][] { new double[ndim] { 0, 0 }, new double[ndim] { 0, 0 } }; double[] len = new double[vecCnt]; double costh; { int n1 = ino; int n2 = (ino + 1) % 3; int n3 = (ino + 2) % 3; vec[0][0] = pp[n2][0] - pp[n1][0]; vec[0][1] = pp[n2][1] - pp[n1][1]; vec[1][0] = pp[n3][0] - pp[n1][0]; vec[1][1] = pp[n3][1] - pp[n1][1]; len[0] = FemMeshLogic.GetDistance(pp[n1], pp[n2]); len[1] = FemMeshLogic.GetDistance(pp[n1], pp[n3]); costh = (vec[0][0] * vec[1][0] + vec[0][1] * vec[1][1]) / (len[0] * len[1]); if (costh < minCosth) { minCosth = costh; minCosthVertexNo = ino; } } } orginVertexNo = (minCosthVertexNo + 2) % 3; } // 三角形内部を四角形で分割 // 面積座標L1方向分割数 //int ndiv = 4; int ndiv = this.IsCoarseFieldMesh ? (Constants.TriDrawFieldMshDivCnt / 2) : Constants.TriDrawFieldMshDivCnt; double defdL1 = 1.0 / (double)ndiv; double defdL2 = defdL1; for (int i1 = 0; i1 < ndiv; i1++) { double vL1 = i1 * defdL1; double vL1Next = (i1 + 1) * defdL1; if (i1 == ndiv - 1) { vL1Next = 1.0; } double vL2max = 1.0 - vL1; if (vL2max < 0.0) { // ERROR System.Diagnostics.Debug.WriteLine("logic error vL2max = {0}", vL2max); continue; } double fdiv2 = (double)ndiv * vL2max; int ndiv2 = (int)fdiv2; if (fdiv2 - (double)ndiv2 > Constants.PrecisionLowerLimit) { ndiv2++; } for (int i2 = 0; i2 < ndiv2; i2++) { double vL2 = i2 * defdL2; double vL2Next = (i2 + 1) * defdL2; if (i2 == ndiv2 - 1) { vL2Next = vL2max; } double vL3 = 1.0 - vL1 - vL2; if (vL3 < 0.0) { // ERROR System.Diagnostics.Debug.WriteLine("logic error vL3 = {0}", vL3); continue; } // 四角形の頂点 const int rectVCnt = 4; double[][] rectLi = new double[rectVCnt][] { new double[] { vL1, vL2, 0 }, new double[] { vL1Next, vL2, 0 }, new double[] { vL1Next, vL2Next, 0 }, new double[] { vL1, vL2Next, 0 } }; if ((i1 == ndiv - 1) || (i2 == ndiv2 - 1)) { for (int k = 0; k < 3; k++) { rectLi[2][k] = rectLi[3][k]; } } for (int ino = 0; ino < rectVCnt; ino++) { if (rectLi[ino][0] < 0.0) { rectLi[ino][0] = 0.0; System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][0] = {1}", ino, rectLi[ino][0]); } if (rectLi[ino][0] > 1.0) { rectLi[ino][0] = 1.0; System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][0] = {1}", ino, rectLi[ino][0]); } if (rectLi[ino][1] < 0.0) { rectLi[ino][1] = 0.0; System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][1] = {1}", ino, rectLi[ino][1]); } if (rectLi[ino][1] > (1.0 - rectLi[ino][0])) // L2最大値(1 - L1)チェック { rectLi[ino][1] = 1.0 - rectLi[ino][0]; } rectLi[ino][2] = 1.0 - rectLi[ino][0] - rectLi[ino][1]; if (rectLi[ino][2] < 0.0) { System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][2] = {1}", ino, rectLi[ino][2]); } } /* * double[][] shiftedRectLi = new double[rectVCnt][]; * for (int ino = 0; ino < rectVCnt; ino++) * { * shiftedRectLi[ino] = new double[vertexCnt]; * for (int k = 0; k < vertexCnt; k++) * { * shiftedRectLi[ino][k] = rectLi[ino][(k + orginVertexNo) % vertexCnt]; * } * } * out_rectLiList.Add(shiftedRectLi); */ out_rectLiList.Add(rectLi); } } }
/// <summary> /// フィールド値を描画する /// </summary> /// <param name="g"></param> /// <param name="ofs"></param> /// <param name="delta"></param> /// <param name="regionSize"></param> /// <param name="fieldDv"></param> /// <param name="valueDv"></param> /// <param name="colorMap"></param> /* * public override void DrawField(Graphics g, Size ofs, Size delta, Size regionSize, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv, ColorMap colorMap) * { * //base.DrawField(g, ofs, delta, regionSize, colorMap); * if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null) * { * return; * } * Complex[] tagtValues = null; * if (fieldDv == FemElement.FieldDV.Field) * { * tagtValues = _FValues; * } * else if (fieldDv == FemElement.FieldDV.RotX) * { * tagtValues = _RotXFValues; * } * else if (fieldDv == FemElement.FieldDV.RotY) * { * tagtValues = _RotYFValues; * } * else * { * return; * } * * const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 * const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ) * //const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素 * int nodeCnt = NodeNumbers.Length; * if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder) * { * return; * } * // 三角形の節点座標を取得 * double[][] pp = new double[nodeCnt][]; * for (int ino = 0; ino < pp.GetLength(0); ino++) * { * FemNode node = _Nodes[ino]; * System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); * pp[ino] = new double[ndim]; * pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width; * pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height; * } * * // 下記分割ロジックの原点となる頂点 * // 頂点0固定で計算していたが、原点の内角が直角のとき長方形メッシュになるので原点を2(頂点を0,1,2としたとき)にする * int orginVertexNo = 2; * // 内角が最大の頂点を取得し、その頂点を原点とする(後のロジックは原点が頂点を0,1,2としたとき、2になっている * { * double minCosth = double.MaxValue; * int minCosthVertexNo = 0; * for (int ino = 0; ino < vertexCnt; ino++) * { * const int vecCnt = 2; * double[][] vec = new double[vecCnt][] { new double[ndim]{0, 0}, new double[ndim]{0, 0} }; * double[] len = new double[vecCnt]; * double costh; * { * int n1 = ino; * int n2 = (ino + 1) % 3; * int n3 = (ino + 2) % 3; * vec[0][0] = pp[n2][0] - pp[n1][0]; * vec[0][1] = pp[n2][1] - pp[n1][1]; * vec[1][0] = pp[n3][0] - pp[n1][0]; * vec[1][1] = pp[n3][1] - pp[n1][1]; * len[0] = FemMeshLogic.GetDistance(pp[n1], pp[n2]); * len[1] = FemMeshLogic.GetDistance(pp[n1], pp[n3]); * costh = (vec[0][0] * vec[1][0] + vec[0][1] * vec[1][1]) / (len[0] * len[1]); * if (costh < minCosth) * { * minCosth = costh; * minCosthVertexNo = ino; * } * } * } * orginVertexNo = (minCosthVertexNo + 2) % 3; * } * // 三角形内部を四角形で分割 * // 面積座標L1方向分割数 * //int ndiv = 4; * int ndiv = Constants.TriDrawFieldMshDivCnt; * double defdL1 = 1.0 / (double)ndiv; * double defdL2 = defdL1; * for (int i1 = 0; i1 < ndiv; i1++) * { * double vL1 = i1 * defdL1; * double vL1Next = (i1 + 1) * defdL1; * if (i1 == ndiv - 1) * { * vL1Next = 1.0; * } * double vL2max = 1.0 - vL1; * if (vL2max < 0.0) * { * // ERROR * System.Diagnostics.Debug.WriteLine("logic error vL2max = {0}", vL2max); * continue; * } * double fdiv2 = (double)ndiv * vL2max; * int ndiv2 = (int)fdiv2; * if (fdiv2 - (double)ndiv2 > Constants.PrecisionLowerLimit) * { * ndiv2++; * } * for (int i2 = 0; i2 < ndiv2; i2++) * { * double vL2 = i2 * defdL2; * double vL2Next = (i2 + 1) * defdL2; * if (i2 == ndiv2 - 1) * { * vL2Next = vL2max; * } * double vL3 = 1.0 - vL1 - vL2; * if (vL3 < 0.0) * { * // ERROR * System.Diagnostics.Debug.WriteLine("logic error vL3 = {0}", vL3); * continue; * } * * // 四角形の頂点 * const int rectVCnt = 4; * double[][] rectLi = new double[rectVCnt][] * { * new double[]{vL1 , vL2 , 0}, * new double[]{vL1Next, vL2 , 0}, * new double[]{vL1Next, vL2Next, 0}, * new double[]{vL1 , vL2Next, 0} * }; * if ((i1 == ndiv - 1) || (i2 == ndiv2 - 1)) * { * for (int k = 0; k < 3; k++) * { * rectLi[2][k] = rectLi[3][k]; * } * } * double[][] rectpp = new double[rectVCnt][]; * for (int ino = 0; ino < rectVCnt; ino++) * { * if (rectLi[ino][0] < 0.0) * { * rectLi[ino][0] = 0.0; * System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][0] = {1}", ino, rectLi[ino][0]); * } * if (rectLi[ino][0] > 1.0) * { * rectLi[ino][0] = 1.0; * System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][0] = {1}", ino, rectLi[ino][0]); * } * if (rectLi[ino][1] < 0.0) * { * rectLi[ino][1] = 0.0; * System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][1] = {1}", ino, rectLi[ino][1]); * } * if (rectLi[ino][1] > (1.0 - rectLi[ino][0])) // L2最大値(1 - L1)チェック * { * rectLi[ino][1] = 1.0 - rectLi[ino][0]; * } * rectLi[ino][2] = 1.0 - rectLi[ino][0] - rectLi[ino][1]; * if (rectLi[ino][2] < 0.0) * { * System.Diagnostics.Debug.WriteLine("logical error rectLi[{0}][2] = {1}", ino, rectLi[ino][2]); * } * } * for (int ino = 0; ino < rectVCnt; ino++) * { * double[] vLpp = rectLi[ino]; * double xx = 0.0; * double yy = 0.0; * for (int k = 0; k < vertexCnt; k++) * { * xx += pp[k][0] * vLpp[(k + orginVertexNo) % vertexCnt]; * yy += pp[k][1] * vLpp[(k + orginVertexNo) % vertexCnt]; * } * rectpp[ino] = new double[] { xx, yy }; * } * // 表示する位置 * double[] vLi = new double[] { (rectLi[0][0] + rectLi[1][0]) * 0.5, (rectLi[0][1] + rectLi[3][1]) * 0.5, 0 }; * if (vLi[0] < 0.0) * { * vLi[0] = 0.0; * } * if (vLi[0] > 1.0) * { * vLi[0] = 1.0; * } * if (vLi[1] < 0.0) * { * vLi[1] = 0.0; * } * if (vLi[1] > (1.0 - vLi[0])) * { * vLi[1] = (1.0 - vLi[0]); * } * vLi[2] = 1.0 - vLi[0] - vLi[1]; * if (vLi[2] < 0.0) * { * System.Diagnostics.Debug.WriteLine("logic error vLi[2] = {0}", vLi[2]); * } * * // 表示する値 * Complex cvalue = new Complex(0.0, 0.0); * // 表示する位置の形状関数値 * double[] vNi = null; * double[] shiftedLi = new double[vertexCnt]; * for (int i = 0; i < vertexCnt; i++) * { * shiftedLi[i] = vLi[(i + orginVertexNo) % vertexCnt]; * } * if (nodeCnt == Constants.TriNodeCnt_FirstOrder) * { * vNi = new double[] * { * shiftedLi[0], * shiftedLi[1], * shiftedLi[2] * }; * } * else * { * vNi = new double[] * { * shiftedLi[0] * (2.0 * shiftedLi[0] - 1.0), * shiftedLi[1] * (2.0 * shiftedLi[1] - 1.0), * shiftedLi[2] * (2.0 * shiftedLi[2] - 1.0), * 4.0 * shiftedLi[0] * shiftedLi[1], * 4.0 * shiftedLi[1] * shiftedLi[2], * 4.0 * shiftedLi[2] * shiftedLi[0], * }; * } * * for (int k = 0; k < nodeCnt; k++) * { * cvalue += tagtValues[k] * vNi[k]; * } * // 四角形の頂点(描画用) * Point[] rectp = new Point[rectVCnt]; * for (int ino = 0; ino < rectVCnt; ino++) * { * rectp[ino] = new Point((int)rectpp[ino][0], (int)rectpp[ino][1]); * } * try * { * // 表示する値 * double showValue = 0.0; * if (valueDv == ValueDV.Real) * { * showValue = cvalue.Real; * } * else if (valueDv == ValueDV.Imaginary) * { * showValue = cvalue.Imaginary; * } * else * { * // 既定値は絶対値 * showValue = Complex.Abs(cvalue); * } * // 塗りつぶし色の取得 * Color fillColor = colorMap.GetColor(showValue); * // 塗りつぶし * using (Brush brush = new SolidBrush(fillColor)) * { * g.FillPolygon(brush, rectp); * } * } * catch (Exception exception) * { * System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); * } * } * } * } */ public override void DrawField(Graphics g, Size ofs, Size delta, Size regionSize, FemElement.FieldDV fieldDv, FemElement.ValueDV valueDv, ColorMap colorMap) { //base.DrawField(g, ofs, delta, regionSize, colorMap); if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null) { return; } Complex[] tagtValues = null; if (fieldDv == FemElement.FieldDV.Field) { tagtValues = _FValues; } else if (fieldDv == FemElement.FieldDV.RotX) { tagtValues = _RotXFValues; } else if (fieldDv == FemElement.FieldDV.RotY) { tagtValues = _RotYFValues; } else { return; } const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 const int vertexCnt = Constants.TriVertexCnt; //3; // 三角形の頂点の数(2次要素でも同じ) //const int nodeCnt = Constants.TriNodeCnt_SecondOrder; //6; // 三角形2次要素 int nodeCnt = NodeNumbers.Length; if (nodeCnt != Constants.TriNodeCnt_SecondOrder && nodeCnt != Constants.TriNodeCnt_FirstOrder) { return; } // 三角形の節点座標を取得 double[][] pp = new double[nodeCnt][]; for (int ino = 0; ino < pp.GetLength(0); ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); pp[ino] = new double[ndim]; pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width; pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height; } // 長方形描画領域のリスト IList <double[][]> rectLiList = _RectLiList; // 描画ロジック上の原点となる頂点 int orginVertexNo = _OrginVertexNo; // 四角形の頂点 const int rectVCnt = 4; foreach (double[][] rectLi in rectLiList) { double[][] rectpp = new double[rectVCnt][]; for (int ino = 0; ino < rectVCnt; ino++) { double[] vLpp = rectLi[ino]; double xx = 0.0; double yy = 0.0; for (int k = 0; k < vertexCnt; k++) { xx += pp[k][0] * vLpp[(k + orginVertexNo) % vertexCnt]; yy += pp[k][1] * vLpp[(k + orginVertexNo) % vertexCnt]; } rectpp[ino] = new double[] { xx, yy }; } // 表示する位置 double[] vLi = new double[] { (rectLi[0][0] + rectLi[1][0]) * 0.5, (rectLi[0][1] + rectLi[3][1]) * 0.5, 0 }; if (vLi[0] < 0.0) { vLi[0] = 0.0; } if (vLi[0] > 1.0) { vLi[0] = 1.0; } if (vLi[1] < 0.0) { vLi[1] = 0.0; } if (vLi[1] > (1.0 - vLi[0])) { vLi[1] = (1.0 - vLi[0]); } vLi[2] = 1.0 - vLi[0] - vLi[1]; if (vLi[2] < 0.0) { System.Diagnostics.Debug.WriteLine("logic error vLi[2] = {0}", vLi[2]); } // 表示する値 Complex cvalue = new Complex(0.0, 0.0); // 表示する位置の形状関数値 double[] vNi = null; double[] shiftedLi = new double[vertexCnt]; for (int i = 0; i < vertexCnt; i++) { shiftedLi[i] = vLi[(i + orginVertexNo) % vertexCnt]; } if (nodeCnt == Constants.TriNodeCnt_FirstOrder) { vNi = new double[] { shiftedLi[0], shiftedLi[1], shiftedLi[2] }; } else { vNi = new double[] { shiftedLi[0] * (2.0 * shiftedLi[0] - 1.0), shiftedLi[1] * (2.0 * shiftedLi[1] - 1.0), shiftedLi[2] * (2.0 * shiftedLi[2] - 1.0), 4.0 * shiftedLi[0] * shiftedLi[1], 4.0 * shiftedLi[1] * shiftedLi[2], 4.0 * shiftedLi[2] * shiftedLi[0], }; } for (int k = 0; k < nodeCnt; k++) { cvalue += tagtValues[k] * vNi[k]; } // 四角形の頂点(描画用) Point[] rectp = new Point[rectVCnt]; for (int ino = 0; ino < rectVCnt; ino++) { rectp[ino] = new Point((int)rectpp[ino][0], (int)rectpp[ino][1]); } try { // 表示する値 double showValue = 0.0; if (valueDv == ValueDV.Real) { showValue = cvalue.Real; } else if (valueDv == ValueDV.Imaginary) { showValue = cvalue.Imaginary; } else { // 既定値は絶対値 showValue = Complex.Abs(cvalue); } // 塗りつぶし色の取得 Color fillColor = colorMap.GetColor(showValue); // 塗りつぶし using (Brush brush = new SolidBrush(fillColor)) { g.FillPolygon(brush, rectp); } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); } } }
/// <summary> /// フィールド値の回転を描画する /// </summary> /// <param name="g"></param> /// <param name="ofs"></param> /// <param name="delta"></param> /// <param name="regionSize"></param> /// <param name="drawColor"></param> /// <param name="fieldDv"></param> /// <param name="minRotFValue"></param> /// <param name="maxRotFValue"></param> public override void DrawRotField(Graphics g, Size ofs, Size delta, Size regionSize, Color drawColor, FemElement.FieldDV fieldDv, double minRotFValue, double maxRotFValue) { if (_Nodes == null || _FValues == null || _RotXFValues == null || _RotYFValues == null || _PoyntingXFValues == null || _PoyntingYFValues == null) { return; } Complex[] tagtXValues = null; Complex[] tagtYValues = null; if (fieldDv == FemElement.FieldDV.PoyntingXY) { tagtXValues = _PoyntingXFValues; tagtYValues = _PoyntingYFValues; } else if (fieldDv == FemElement.FieldDV.RotXY) { tagtXValues = _RotXFValues; tagtYValues = _RotYFValues; } else { return; } const int ndim = Constants.CoordDim2D; //2; // 座標の次元数 //const int vertexCnt = Constants.QuadVertexCnt; //4; // 四角形形の頂点の数(2次要素でも同じ) //const int nodeCnt = Constants.QuadNodeCnt_SecondOrder_Type2; //8; // 四角形形2次要素 int nodeCnt = NodeNumbers.Length; if (nodeCnt != Constants.QuadNodeCnt_SecondOrder_Type2 && nodeCnt != Constants.QuadNodeCnt_FirstOrder) { return; } // 四角形の節点座標を取得 double[][] pp = new double[nodeCnt][]; for (int ino = 0; ino < pp.GetLength(0); ino++) { FemNode node = _Nodes[ino]; System.Diagnostics.Debug.Assert(node.Coord.Length == ndim); pp[ino] = new double[ndim]; pp[ino][0] = node.Coord[0] * delta.Width + ofs.Width; pp[ino][1] = regionSize.Height - node.Coord[1] * delta.Height + ofs.Height; } // 四角形内部を四角形で分割 // 要素節点座標( 局所r,s成分 ) // s // | // 3+ 6 +2 // | | | // ---7---+---5-->r // | | | // 0+ 4 +1 // | // double[][] n_pts = { // r, s new double[] { -1.0, -1.0 }, //0 new double[] { 1.0, -1.0 }, //1 new double[] { 1.0, 1.0 }, //2 new double[] { -1.0, 1.0 }, //3 new double[] { 0, -1.0 }, //4 new double[] { 1.0, 0 }, //5 new double[] { 0, 1.0 }, //6 new double[] { -1.0, 0 }, //7 }; // 節点上のrot(Ez)を求める int nno = nodeCnt; { double r = 0; double s = 0; // 形状関数 double[] N = new double[nno]; if (nodeCnt == Constants.QuadNodeCnt_SecondOrder_Type2) { // 節点0~3 : 四角形の頂点 for (int i = 0; i < 4; i++) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s) * (ri * r + si * s - 1.0); } // 節点4,6 : r方向辺上中点 foreach (int i in new int[] { 4, 6 }) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N N[i] = 0.5 * (1.0 - r * r) * (1.0 + si * s); } // 節点5,7 : s方向辺上中点 foreach (int i in new int[] { 5, 7 }) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N N[i] = 0.5 * (1.0 + ri * r) * (1.0 - s * s); } } else if (nodeCnt == Constants.QuadNodeCnt_FirstOrder) { // 節点0~3 : 四角形の頂点 for (int i = 0; i < nno; i++) { // 節点の局所座標 double ri = n_pts[i][0]; double si = n_pts[i][1]; // 形状関数N N[i] = 0.25 * (1.0 + ri * r) * (1.0 + si * s); } } // 表示する位置 double showPosX = 0; double showPosY = 0; for (int k = 0; k < nodeCnt; k++) { showPosX += pp[k][0] * N[k]; showPosY += pp[k][1] * N[k]; } Complex cvalueX = new Complex(0, 0); Complex cvalueY = new Complex(0, 0); for (int k = 0; k < nodeCnt; k++) { cvalueX += tagtXValues[k] * N[k]; cvalueY += tagtYValues[k] * N[k]; } try { double showScale = ((double)regionSize.Width / DefPanelWidth) * ArrowLength; // 実数部のベクトル表示 int lenX = (int)((double)(cvalueX.Real / maxRotFValue) * showScale); int lenY = (int)((double)(cvalueY.Real / maxRotFValue) * showScale); if (lenX != 0 || lenY != 0) { // Y方向は表示上逆になる lenY = -lenY; using (Pen pen = new Pen(drawColor, 1)) { //pen.DashStyle = System.Drawing.Drawing2D.DashStyle.Dot; //pen.StartCap = System.Drawing.Drawing2D.LineCap.Round; pen.EndCap = System.Drawing.Drawing2D.LineCap.ArrowAnchor; //pen.CustomEndCap = new System.Drawing.Drawing2D.AdjustableArrowCap(3, 3, false); // 重い g.DrawLine(pen, (int)showPosX, (int)showPosY, (int)(showPosX + lenX), (int)(showPosY + lenY)); } } } catch (Exception exception) { System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace); } } }
/// <summary> /// 節点情報を設定する /// </summary> /// <param name="nodes"></param> public override void SetNodesFromAllNodes(FemNode[] nodes) { // ベースクラスの処理を実行 base.SetNodesFromAllNodes(nodes); // 描画領域を準備する setupDrawRect(out _RectLiList, out _OrginVertexNo); }
/* 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(clapack使用時)</param> /// <param name="mat_cc">マージされる全体行列(DelFEM使用時)</param> /// <param name="res_c">マージされる残差ベクトル(DelFEM使用時)</param> /// <param name="tmpBuffer">一時バッファ(DelFEM使用時)</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, ref DelFEM4NetMatVec.CZMatDia_BlkCrs_Ptr mat_cc, ref DelFEM4NetMatVec.CZVector_Blk_Ptr res_c, ref int[] tmpBuffer) { // 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 if (mat_cc != null) { // 全体節点番号→要素内節点インデックスマップ Dictionary <uint, int> inoGlobalDic = new Dictionary <uint, int>(); for (int ino = 0; ino < nno; ino++) { int iNodeNumber = no_c[ino]; if (ForceNodeNumberH.ContainsKey(iNodeNumber)) { continue; } uint inoGlobal = (uint)toSorted[iNodeNumber]; inoGlobalDic.Add(inoGlobal, ino); } // マージ用の節点番号リスト uint[] no_c_tmp = inoGlobalDic.Keys.ToArray <uint>(); // マージする節点数("col"と"row"のサイズ) uint ncolrow_tmp = (uint)no_c_tmp.Length; // Note: // 要素の節点がすべて強制境界の場合がある.その場合は、ncolrow_tmpが0 if (ncolrow_tmp > 0) { // マージする要素行列 DelFEM4NetCom.Complex[] ematBuffer = new DelFEM4NetCom.Complex[ncolrow_tmp * ncolrow_tmp]; for (int ino_tmp = 0; ino_tmp < ncolrow_tmp; ino_tmp++) { int ino = inoGlobalDic[no_c_tmp[ino_tmp]]; for (int jno_tmp = 0; jno_tmp < ncolrow_tmp; jno_tmp++) { int jno = inoGlobalDic[no_c_tmp[jno_tmp]]; double value = emat[ino, jno]; DelFEM4NetCom.Complex cvalueDelFEM = new DelFEM4NetCom.Complex(value, 0); // ematBuffer[ino_tmp, jno_tmp] 横ベクトルを先に埋める(clapack方式でないことに注意) ematBuffer[ino_tmp * ncolrow_tmp + jno_tmp] = cvalueDelFEM; } } // 全体行列に要素行列をマージする mat_cc.Mearge(ncolrow_tmp, no_c_tmp, ncolrow_tmp, no_c_tmp, 1, ematBuffer, ref tmpBuffer); } } else if (mat != null) { 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]; } } } }