static bool AddLinearSystem_Diffusion_P1b(
double rho, double alpha, double source,
double gamma, double dt,
CLinearSystem_Field& ls,
unsigned int id_field_val, const CFieldWorld& world,
unsigned int id_ea )
{
// std::cout << "Diffusion2D Tri P1b" << std::endl;
assert( world.IsIdEA(id_ea) );
const CElemAry& ea = world.GetEA(id_ea);
assert( ea.ElemType() == TRI );
if( !world.IsIdField(id_field_val) ) return false;
const CField& field_val = world.GetField(id_field_val);
const CElemAry::CElemSeg& es_c = field_val.GetElemSeg(id_ea,CORNER,true,world);
const CElemAry::CElemSeg& es_b = field_val.GetElemSeg(id_ea,BUBBLE,true,world);
const unsigned int nno_c = 3;
const unsigned int nno_b = 1;
const unsigned int ndim = 2;
unsigned int no_c[nno_c];
unsigned int no_b;
double val_c[nno_c], val_b;
double vval_c[nno_c], vval_b;
double coord_c[nno_c][ndim];
double dldx[nno_c][ndim];
double const_term[nno_c];
double eCmat_cc[nno_c][nno_c], eCmat_cb[nno_c], eCmat_bc[nno_c], eCmat_bb;
double eMmat_cc[nno_c][nno_c], eMmat_cb[nno_c], eMmat_bc[nno_c], eMmat_bb;
double eqf_out_c[nno_c], eqf_out_b;
double eqf_in_c[nno_c], eqf_in_b;
double emat_cc[nno_c][nno_c], emat_cb[nno_c], emat_bc[nno_c], emat_bb;
double eres_c[nno_c], eres_b; // 要素節点等価内力、外力、残差ベクトル
CMatDia_BlkCrs& mat_cc = ls.GetMatrix(id_field_val,CORNER, world);
CMatDia_BlkCrs& mat_bb = ls.GetMatrix(id_field_val,BUBBLE, world);
CMat_BlkCrs& mat_cb = ls.GetMatrix(id_field_val,CORNER, id_field_val, BUBBLE, world);
CMat_BlkCrs& mat_bc = ls.GetMatrix(id_field_val,BUBBLE, id_field_val, CORNER, world);
////////////////
CVector_Blk& res_c = ls.GetResidual(id_field_val,CORNER, world);
CVector_Blk& res_b = ls.GetResidual(id_field_val,BUBBLE, world);
const CNodeAry::CNodeSeg& ns_c_val = field_val.GetNodeSeg(CORNER,true,world,VALUE);//na_c_val.GetSeg(id_ns_c_val);
const CNodeAry::CNodeSeg& ns_c_vval = field_val.GetNodeSeg(CORNER,true,world,VELOCITY);//na_c_val.GetSeg(id_ns_c_vval);
const CNodeAry::CNodeSeg& ns_b_val = field_val.GetNodeSeg(BUBBLE,true,world,VALUE);//na_b_val.GetSeg(id_ns_b_val);
const CNodeAry::CNodeSeg& ns_b_vval = field_val.GetNodeSeg(BUBBLE,true,world,VELOCITY);//na_b_val.GetSeg(id_ns_b_vval);
const CNodeAry::CNodeSeg& ns_c_co = field_val.GetNodeSeg(CORNER,false,world,VALUE);//na_c_val.GetSeg(id_ns_c_co);
for(unsigned int ielem=0;ielem<ea.Size();ielem++){
// 要素配列から節点セグメントの節点番号を取り出す
es_c.GetNodes(ielem,no_c);
es_b.GetNodes(ielem,&no_b);
// 節点の値を取ってくる
for(unsigned int inoes=0;inoes<nno_c;inoes++){
ns_c_co.GetValue(no_c[inoes],coord_c[inoes]);
ns_c_val.GetValue(no_c[inoes],&val_c[inoes]);
ns_c_vval.GetValue(no_c[inoes],&vval_c[inoes]);
}
ns_b_val.GetValue(no_b,&val_b);
ns_b_vval.GetValue(no_b,&vval_b);
// 面積を求める
const double area = TriArea(coord_c[0],coord_c[1],coord_c[2]);
// 形状関数の微分を求める
TriDlDx(dldx,const_term,coord_c[0],coord_c[1],coord_c[2]);
{ // 要素剛性行列を作る
double vc_b[4];
vc_b[0] = 1.0/3.0; vc_b[1] = 1.0/3.0; vc_b[2] = 1.0/3.0; vc_b[3] = 27.0;
const double tmp_val1 = vc_b[3]*vc_b[3]*alpha*area/180.0*(
dldx[0][0]*dldx[0][0]+dldx[0][1]*dldx[0][1]+
dldx[1][0]*dldx[1][0]+dldx[1][1]*dldx[1][1]+
dldx[2][0]*dldx[2][0]+dldx[2][1]*dldx[2][1] );
for(unsigned int ino_c=0;ino_c<nno_c;ino_c++){
for(unsigned int jno_c=0;jno_c<nno_c;jno_c++){
eCmat_cc[ino_c][jno_c]
= alpha*area*(dldx[ino_c][0]*dldx[jno_c][0]+dldx[ino_c][1]*dldx[jno_c][1])
+vc_b[ino_c]*vc_b[jno_c]*tmp_val1;
}
}
for(unsigned int ino_c=0;ino_c<nno_c;ino_c++){
const double tmp1 = -1.0*vc_b[ino_c]*tmp_val1;
eCmat_cb[ino_c] = tmp1;
eCmat_bc[ino_c] = tmp1;
}
eCmat_bb = tmp_val1;
Set_RhoTri_CB_Scalar(eMmat_cc,eMmat_cb,eMmat_bc,eMmat_bb, area, dldx,vc_b, rho);
}
// 要素外力ベクトルを求める
for(unsigned int ino_c=0;ino_c<nno_c;ino_c++){
eqf_out_c[ino_c] = source*area*11.0/60.0;
}
eqf_out_b = source*area*27.0/60.0;
////////////////////////////////////////////////////////////////
// 要素内力ベクトルを求める
for(unsigned int ino_c=0;ino_c<nno_c;ino_c++){
eqf_in_c[ino_c] = 0.0;
for(unsigned int jno_c=0;jno_c<nno_c;jno_c++){
eqf_in_c[ino_c] += eCmat_cc[ino_c][jno_c]*(val_c[jno_c]+dt*vval_c[jno_c])
+ eMmat_cc[ino_c][jno_c]*vval_c[jno_c];
}
eqf_in_c[ino_c] += eCmat_cb[ino_c]*(val_b+dt*vval_b) + eMmat_cb[ino_c]*vval_b;
}
eqf_in_b = 0.0;
for(unsigned int jno_c=0;jno_c<nno_c;jno_c++){
eqf_in_b += eCmat_bc[jno_c]*(val_c[jno_c]+dt*vval_c[jno_c]) + eMmat_bc[jno_c]*vval_c[jno_c];
}
eqf_in_b += eCmat_bb*(val_b+dt*vval_b) + eMmat_bb*vval_b;
{ // 要素係数行列を求める
double dtmp1 = gamma*dt;
for(unsigned int i=0;i<nno_c;i++){
for(unsigned int j=0;j<nno_c;j++){
emat_cc[i][j] = eMmat_cc[i][j]+dtmp1*eCmat_cc[i][j];
}
emat_cb[i] = eMmat_cb[i]+dtmp1*eCmat_cb[i];
emat_bc[i] = eMmat_bc[i]+dtmp1*eCmat_bc[i];
}
emat_bb = eMmat_bb+dtmp1*eCmat_bb;
}
////////////////////////////////////////////////////////////////
// 要素残差ベクトルを求める
for(unsigned int ino_c=0;ino_c<nno_c;ino_c++){
eres_c[ino_c] = eqf_out_c[ino_c] - eqf_in_c[ino_c];
}
eres_b = eqf_out_b - eqf_in_b;
// 要素剛性行列のマージ
mat_cc.Mearge(nno_c,no_c,nno_c,no_c, 1,&emat_cc[0][0]);
mat_cb.Mearge(nno_c,no_c,nno_b,&no_b, 1,&emat_cb[0] );
mat_bc.Mearge(nno_b,&no_b,nno_c,no_c, 1,&emat_bc[0] );
mat_bb.Mearge(nno_b,&no_b,nno_b,&no_b, 1,&emat_bb );
// 要素残差ベクトルのマージ
for(unsigned int inoes=0;inoes<nno_c;inoes++){
res_c.AddValue( no_c[inoes],0,eres_c[inoes]);
}
res_b.AddValue( no_b,0,eres_b );
}
return true;
}
static bool AddLinSys_AdvectionDiffusion_NonStatic_Newmark_P1P1(
double rho, double myu, double source,
double gamma, double dt,
CLinearSystem_Field& ls,
const unsigned int id_field_val, const unsigned int id_field_velo, const CFieldWorld& world,
unsigned int id_ea )
{
// std::cout << "Advection Diffusion NonStatic 2D Triangle 3-point 1st order" << std::endl;
assert( world.IsIdEA(id_ea) );
const CElemAry& ea = world.GetEA(id_ea);
assert( ea.ElemType() == TRI );
if( !world.IsIdField(id_field_val) ) return false;
const CField& val_field = world.GetField(id_field_val);
if( !world.IsIdField(id_field_velo) ) return false;
const CField& field_velo = world.GetField(id_field_velo);
const unsigned int nno = 3;
const unsigned int ndim = 2;
const CElemAry::CElemSeg& es_c_val = val_field.GetElemSeg(id_ea,CORNER,true,world);
double val_c[nno]; // 要素節点の値
double vval_c[nno]; // 要素節点の値
double coord_c[nno][ndim]; // 要素節点の座標
double velo_c[nno][ndim];
double eCmat[nno][nno];
double eMmat[nno][nno];
double emat[nno][nno]; // 要素剛性行列
double eres_c[nno]; // 要素節点等価内力、外力、残差ベクトル
CMatDia_BlkCrs& mat_cc = ls.GetMatrix( id_field_val,CORNER,world);
CVector_Blk& res_c = ls.GetResidual(id_field_val,CORNER,world);
const CNodeAry::CNodeSeg& ns_c_val = val_field.GetNodeSeg(CORNER,true,world,VALUE);
const CNodeAry::CNodeSeg& ns_c_vval = val_field.GetNodeSeg(CORNER,true,world,VELOCITY);
const CNodeAry::CNodeSeg& ns_c_velo = field_velo.GetNodeSeg(CORNER,true,world,VELOCITY);
const CNodeAry::CNodeSeg& ns_c_co = field_velo.GetNodeSeg(CORNER,false,world,VALUE);
for(unsigned int ielem=0;ielem<ea.Size();ielem++)
{
// 要素配列から要素セグメントの節点番号を取り出す
unsigned int no_c[nno]; // 要素節点の全体節点番号
es_c_val.GetNodes(ielem,no_c);
// 節点の値を取って来る
for(unsigned int inoes=0;inoes<nno;inoes++){
ns_c_co.GetValue(no_c[inoes],coord_c[inoes]);
ns_c_val.GetValue(no_c[inoes],&val_c[inoes]);
ns_c_vval.GetValue(no_c[inoes],&vval_c[inoes]);
ns_c_velo.GetValue(no_c[inoes],velo_c[inoes]);
}
////////////////////////////////////////////////////////////////
// 面積を求める
const double area = TriArea(coord_c[0],coord_c[1],coord_c[2]);
// 形状関数の微分を求める
double dldx[nno][ndim]; // 形状関数のxy微分
double const_term[nno]; // 形状関数の定数項
TriDlDx(dldx,const_term,coord_c[0],coord_c[1],coord_c[2]);
// 要素剛性行列を作る
for(unsigned int ino=0;ino<nno;ino++){
for(unsigned int jno=0;jno<nno;jno++){
eCmat[ino][jno] = myu*area*(dldx[ino][0]*dldx[jno][0]+dldx[ino][1]*dldx[jno][1]);
}
}
{
const double dtmp1 = rho*area*0.0833333333333333333333;
for(unsigned int ino=0;ino<nno;ino++){
const double dtmp_0 = dtmp1*(velo_c[0][0]+velo_c[1][0]+velo_c[2][0]+velo_c[ino][0]);
const double dtmp_1 = dtmp1*(velo_c[0][1]+velo_c[1][1]+velo_c[2][1]+velo_c[ino][1]);
for(unsigned int jno=0;jno<nno;jno++){
eCmat[ino][jno] += dldx[jno][0]*dtmp_0+dldx[jno][1]*dtmp_1;
}
}
}
// Calc Stabilization Parameter
double tau;
{
const double velo_ave[2] = {
(velo_c[0][0]+velo_c[1][0]+velo_c[2][0])*0.3333333333333333,
(velo_c[0][1]+velo_c[1][1]+velo_c[2][1])*0.3333333333333333 };
const double norm_v = sqrt(velo_ave[0]*velo_ave[0]+velo_ave[1]*velo_ave[1]);
if( norm_v < 1.0e-10 ){ tau = 0.0; }
else{
const double velo_dir[2] = { velo_ave[0]/norm_v, velo_ave[1]/norm_v };
// calc element length along the direction of velocity
double h;
{
double dtmp1 = 0;
for(int inode=0;inode<3;inode++){
dtmp1 += fabs(velo_dir[0]*dldx[inode][0]+velo_dir[1]*dldx[inode][1]);
}
h = 2.0/dtmp1;
}
// calc stabilization parameter
if( norm_v*h*rho < 6.0*myu ){
const double re_c = 0.5*norm_v*h*rho/myu; // 0.5*norm_v*h*rho/myu;
tau = h * 0.5 / norm_v * re_c / 3.0;
}
else{ tau = h * 0.5 / norm_v; }
tau *= 0.5;
}
}
{
double tmp_mat[ndim][ndim];
for(unsigned int idim=0;idim<ndim;idim++){
for(unsigned int jdim=0;jdim<ndim;jdim++){
double dtmp1 = 0.0;
for(unsigned int ino=0;ino<nno;ino++){
for(unsigned int jno=0;jno<nno;jno++){
dtmp1 += velo_c[ino][idim]*velo_c[jno][jdim];
}
dtmp1 += velo_c[ino][idim]*velo_c[ino][jdim];
}
tmp_mat[idim][jdim] = area*tau*dtmp1*0.0833333333333333;
}
}
for(unsigned int ino=0;ino<nno;ino++){
for(unsigned int jno=0;jno<nno;jno++){
double dtmp1 = 0.0;
for(unsigned int idim=0;idim<ndim;idim++){
for(unsigned int jdim=0;jdim<ndim;jdim++){
dtmp1 += dldx[ino][idim]*dldx[jno][jdim]*tmp_mat[idim][jdim];
}
}
eCmat[ino][jno] += dtmp1*rho;
}
}
}
{
const double dtmp1 = rho*area*0.083333333333333333;
for(unsigned int ino=0;ino<nno;ino++){
for(unsigned int jno=0;jno<nno;jno++){
eMmat[ino][jno] = dtmp1;
}
eMmat[ino][ino] += dtmp1;
}
}
// 要素節点等価外力ベクトルを求める
for(unsigned int ino=0;ino<nno;ino++){
eres_c[ino] = source*area*0.333333333333333;
}
////////////////////////////////////////////////////////////////
// 要素節点等価内力ベクトルを求める
for(unsigned int ino=0;ino<nno;ino++){
for(unsigned int jno=0;jno<nno;jno++){
eres_c[ino] -= eCmat[ino][jno]*(val_c[jno]+dt*vval_c[jno])
+ eMmat[ino][jno]*vval_c[jno];
}
}
{ // 要素係数行列を求める
double dtmp1 = gamma*dt;
for(unsigned int i=0;i<nno*nno;i++){
(&emat[0][0])[i] = (&eMmat[0][0])[i]+dtmp1*(&eCmat[0][0])[i];
}
}
// 要素剛性行列にマージする
mat_cc.Mearge(nno,no_c,nno,no_c,1,&emat[0][0]);
// 残差ベクトルにマージする
for(unsigned int inoes=0;inoes<nno;inoes++){
res_c.AddValue( no_c[inoes],0,eres_c[inoes]);
}
}
return true;
}
static bool AddLinearSystem_Diffusion2D_AxSym_P1(
double rho, double alpha, double source,
double gamma, double dt,
CLinearSystem_Field& ls,
unsigned int id_field_val, const CFieldWorld& world,
const unsigned int id_ea)
{
// std::cout << "Diffusion2D Axial Symmetry Tri P1" << std::endl;
assert( world.IsIdEA(id_ea) );
const CElemAry& ea = world.GetEA(id_ea);
assert( ea.ElemType() == TRI );
if( !world.IsIdField(id_field_val) ) return false;
const CField& field_val = world.GetField(id_field_val);
const CElemAry::CElemSeg& es_c_va = field_val.GetElemSeg(id_ea,CORNER,true, world);
const CElemAry::CElemSeg& es_c_co = field_val.GetElemSeg(id_ea,CORNER,false,world);
const unsigned int nno = 3;
const unsigned int ndim = 2;
CMatDia_BlkCrs& mat_cc = ls.GetMatrix( id_field_val,CORNER,world);
CVector_Blk& res_c = ls.GetResidual(id_field_val,CORNER,world);
const CNodeAry::CNodeSeg& ns_c_val = field_val.GetNodeSeg(CORNER,true,world,VALUE);
const CNodeAry::CNodeSeg& ns_c_vval = field_val.GetNodeSeg(CORNER,true,world,VELOCITY);
const CNodeAry::CNodeSeg& ns_c_co = field_val.GetNodeSeg(CORNER,false,world,VALUE);
for(unsigned int ielem=0;ielem<ea.Size();ielem++)
{
// 要素配列から要素セグメントの節点番号を取り出す
unsigned int no[nno]; // 要素節点の全体節点番号
es_c_co.GetNodes(ielem,no);
// 座標を取り出す
double coord[nno][ndim]; // 要素節点の座標
for(unsigned int ino=0;ino<nno;ino++){
ns_c_co.GetValue(no[ino],coord[ino]);
}
es_c_va.GetNodes(ielem,no);
// 節点の値を取って来る
double val_c[nno]; // 要素節点の値
double vval_c[nno]; // 要素節点の値
for(unsigned int inoes=0;inoes<nno;inoes++){
ns_c_val.GetValue(no[inoes],&val_c[inoes]);
ns_c_vval.GetValue(no[inoes],&vval_c[inoes]);
}
const double rad[3] = {
fabs( coord[0][0] ),
fabs( coord[1][0] ),
fabs( coord[2][0] )
};
const double ave_rad = (rad[0]+rad[1]+rad[2])*0.33333333333333333333;
////////////////////////////////////////////////////////////////
// 面積を求める
const double area = TriArea(coord[0],coord[1],coord[2]);
// 形状関数の微分を求める
double dldx[nno][ndim]; // 形状関数のxy微分
double const_term[nno]; // 形状関数の定数項
TriDlDx(dldx,const_term,coord[0],coord[1],coord[2]);
// 要素剛性行列を作る
double eCmat[nno][nno]; // 要素剛性行列
for(unsigned int ino=0;ino<nno;ino++){
for(unsigned int jno=0;jno<nno;jno++){
eCmat[ino][jno] = alpha*area*ave_rad*(dldx[ino][0]*dldx[jno][0]+dldx[ino][1]*dldx[jno][1]);
}
}
double eMmat[nno][nno]; // 要素剛性行列
{
const double dtmp1 = rho*area/60.0;
eMmat[0][0] = dtmp1*(6*rad[0] + 2*rad[1] + 2*rad[2]);
eMmat[1][1] = dtmp1*(2*rad[0] + 6*rad[1] + 2*rad[2]);
eMmat[2][2] = dtmp1*(2*rad[0] + 2*rad[1] + 6*rad[2]);
eMmat[0][1] = dtmp1*(2*rad[0] + 2*rad[1] + 1*rad[2]);
eMmat[1][0] = eMmat[0][1];
eMmat[0][2] = dtmp1*(2*rad[0] + 1*rad[1] + 2*rad[2]);
eMmat[2][0] = eMmat[0][2];
eMmat[1][2] = dtmp1*(1*rad[0] + 2*rad[1] + 2*rad[2]);
eMmat[2][1] = eMmat[1][2];
}
double eres_c[nno]; // 残差ベクトル
// 要素節点等価外力ベクトルを求める
for(unsigned int ino=0;ino<nno;ino++){
eres_c[ino] = source*area*0.333333333333333333;
}
////////////////////////////////////////////////////////////////
double emat[nno][nno];
{ // 要素係数行列を求める
double dtmp1 = gamma*dt;
for(unsigned int i=0;i<nno*nno;i++){
(&emat[0][0])[i] = (&eMmat[0][0])[i]+dtmp1*(&eCmat[0][0])[i];
}
}
// 要素節点等価内力ベクトルを求める
for(unsigned int ino=0;ino<nno;ino++){
for(unsigned int jno=0;jno<nno;jno++){
eres_c[ino] -= eCmat[ino][jno]*(val_c[jno]+dt*vval_c[jno])
+ eMmat[ino][jno]*vval_c[jno];
}
}
// 要素剛性行列にマージする
mat_cc.Mearge(nno,no,nno,no,1,&emat[0][0]);
// 残差ベクトルにマージする
for(unsigned int ino=0;ino<nno;ino++){
res_c.AddValue( no[ino],0,eres_c[ino]);
}
}
return true;
}
