実装

要素整合熱容量行列を数値積分により求める 関数は、以下のようになる。

/* 要素整合熱容量行列：三次元 */
void WH_ThermalFem3D__Linear__C_arrayInJn
(WH_Fem__Shape3DType shapeType,
 WH_Fem__Element3DType elementType,
 int nNodes,
 double whV_x_arrayIn[/* nNodes */][3],
 double rho,
 double c,
 double OUT__C_arrayInJn[/* nNodes * nNodes */])
/*
  入力引数:
    shapeType は要素形状のタイプ
    elementType は要素のタイプ
    nNodes は整数で、要素節点数
    whV_x_arrayIn はベクトルの節点配列で、位置（節点座標）
    rho はスカラーで、質量密度
    c はスカラーで、比熱
  出力引数:
    OUT__C_arrayInJn はスカラーの配列(節点、節点)で、
      要素整合熱容量行列
*/
{
  int order;
  int nPoints;
  int Ip;
  int In, Jn;
 
  switch (elementType) {
  case WH_FEM__ELEMENT3D__TETRA4N:    
    order = 2; 
    break;
  case WH_FEM__ELEMENT3D__TETRA10N:
  case WH_FEM__ELEMENT3D__HEXA8N:
    order = 3;
    break;
  case WH_FEM__ELEMENT3D__HEXA20N:
  case WH_FEM__ELEMENT3D__HEXA27N:
    order = 4;
    break;
  default:
    assert(0);
    break;
  }

  for (In = 0; In < nNodes; In++) {
    for (Jn = 0; Jn < nNodes; Jn++) {
      OUT__C_arrayInJn[In * nNodes + Jn] = 0.0;
    }
  }

  WH_Fem__NumInt__Gauss3D__nPoints 
    (shapeType, order,
     &nPoints);
  for (Ip = 0; Ip < nPoints; Ip++) {
    double whV_xi_Ip[3];
    double w_Ip;
    double whP_N_whV_xi_arrayIn[WH_FEM__MAX_ELEMENT_NODES][3];
    double N_arrayIn[WH_FEM__MAX_ELEMENT_NODES];
    double whPt_whV_x_whV_xi[3][3];
    double J_V;
    
    WH_Fem__NumInt__Gauss3D__whV_xi_Ip
      (shapeType, order, Ip,
       whV_xi_Ip);
    WH_Fem__NumInt__Gauss3D__w_Ip
      (shapeType, order, Ip,
       &w_Ip);
    WH_Fem__Shape3D__whP_N_whV_xi_arrayIn
      (elementType, nNodes, whV_xi_Ip,
       whP_N_whV_xi_arrayIn);
    WH_Fem__Shape3D__N_arrayIn
      (elementType, nNodes, whV_xi_Ip,
       N_arrayIn);

    WH_Fem__Isoparam3D__Volume__whPt_whV_x_whV_xi
      (nNodes, whP_N_whV_xi_arrayIn, whV_x_arrayIn,
       whPt_whV_x_whV_xi);
    WH_Fem__Isoparam3D__Volume__J_V
      (shapeType, whPt_whV_x_whV_xi,
       &J_V);

    for (In = 0; In < nNodes; In++) {
      for (Jn = 0; Jn < nNodes; Jn++) {
        double C;
      
        C = rho * c * N_arrayIn[In] * N_arrayIn[Jn];
        OUT__C_arrayInJn[In * nNodes + Jn] 
          += C * J_V * w_Ip;
      }
    }
  }
}