void assemble_LHS ( RBFFD& der, Grid& grid, STL_Sparse_Mat& A){
unsigned int N = grid.getNodeListSize();
unsigned int n = grid.getMaxStencilSize();
//A_ptr = new MatType( N );
// MatType& A = *A_ptr;
for (unsigned int i = 0; i < N; i++) {
StencilType& sten = grid.getStencil(i);
double* lapl = der.getStencilWeights(RBFFD::LSFC, i);
// Off diagonals
for (unsigned int j = 0; j < n; j++) {
A[i][sten[j]] = -lapl[j];
}
}
}
void assemble_System_Stokes( RBFFD& der, Grid& grid, UBLAS_MAT_t& A, UBLAS_VEC_t& F, UBLAS_VEC_t& U_exact, UBLAS_VEC_t& U_exact_compressed){
double eta = 1.;
//double Ra = 1.e6;
// We have different nb_stencils and nb_nodes when we parallelize. The subblocks might not be full
unsigned int nb_stencils = grid.getStencilsSize();
// unsigned int nb_nodes = grid.getNodeListSize();
// unsigned int max_stencil_size = grid.getMaxStencilSize();
unsigned int N = nb_stencils;
unsigned int nb_bnd = grid.getBoundaryIndicesSize();
// ---------------------------------------------------
//------------- Fill the RHS of the System -------------
// This is our manufactured solution:
SphericalHarmonic::Sph32 UU;
SphericalHarmonic::Sph32105 VV;
SphericalHarmonic::Sph32 WW;
SphericalHarmonic::Sph32 PP;
std::vector<NodeType>& nodes = grid.getNodeList();
//------------- Fill F -------------
// U
for (unsigned int j = 0; j < nb_bnd; j++) {
unsigned int row_ind = j + 0*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(row_ind) = UU.eval(Xx, Yy, Zz);
}
for (unsigned int j = nb_bnd; j < N; j++) {
unsigned int row_ind = j + 0*(N-nb_bnd);
unsigned int uncompressed_row_ind = j + 0*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(uncompressed_row_ind) = UU.eval(Xx,Yy,Zz);
U_exact_compressed(row_ind-nb_bnd) = UU.eval(Xx,Yy,Zz);
F(row_ind-nb_bnd) = -eta * UU.lapl(Xx,Yy,Zz) + PP.d_dx(Xx,Yy,Zz);
}
// V
for (unsigned int j = 0; j < nb_bnd; j++) {
unsigned int row_ind = j + 1*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(row_ind) = VV.eval(Xx,Yy,Zz);
}
for (unsigned int j = nb_bnd; j < N; j++) {
unsigned int row_ind = j + 1*(N-nb_bnd);
unsigned int uncompressed_row_ind = j + 1*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(uncompressed_row_ind) = VV.eval(Xx,Yy,Zz);
U_exact_compressed(row_ind-nb_bnd) = VV.eval(Xx,Yy,Zz);
F(row_ind-nb_bnd) = -eta * VV.lapl(Xx,Yy,Zz) + PP.d_dy(Xx,Yy,Zz);
}
// W
for (unsigned int j = 0; j < nb_bnd; j++) {
unsigned int row_ind = j + 2*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(row_ind) = WW.eval(Xx,Yy,Zz);
}
for (unsigned int j = nb_bnd; j < N; j++) {
unsigned int row_ind = j + 2*(N-nb_bnd);
unsigned int uncompressed_row_ind = j + 2*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(uncompressed_row_ind) = WW.eval(Xx,Yy,Zz);
U_exact_compressed(row_ind-nb_bnd) = WW.eval(Xx,Yy,Zz);
F(row_ind-nb_bnd) = -eta * WW.lapl(Xx,Yy,Zz) + PP.d_dz(Xx,Yy,Zz);
}
// P
for (unsigned int j = 0; j < nb_bnd; j++) {
unsigned int row_ind = j + 3*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(row_ind) = PP.eval(Xx,Yy,Zz);
}
for (unsigned int j = nb_bnd; j < N; j++) {
unsigned int row_ind = j + 3*(N-nb_bnd);
unsigned int uncompressed_row_ind = j + 3*(N);
NodeType& node = nodes[j];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
U_exact(uncompressed_row_ind) = PP.eval(Xx,Yy,Zz);
U_exact_compressed(row_ind-nb_bnd) = PP.eval(Xx,Yy,Zz);
F(row_ind-nb_bnd) = UU.d_dx(Xx,Yy,Zz) + VV.d_dy(Xx,Yy,Zz) + WW.d_dz(Xx,Yy,Zz);
}
// ----------------- Fill LHS --------------------
//
// U (block) row
for (unsigned int i = nb_bnd; i < N; i++) {
StencilType& st = grid.getStencil(i);
// System has form:
// -lapl(U) + grad(P) = f
// div(U) = 0
// TODO: change these to *SFC weights (when computed)
double* ddx = der.getStencilWeights(RBFFD::XSFC, i);
double* lapl = der.getStencilWeights(RBFFD::LSFC, i);
unsigned int diag_row_ind = i + 0*(N-nb_bnd);
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 0*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
// Need the exact solution at stencil node j
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= -eta * UU.lapl(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = -eta * lapl[j];
}
}
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 3*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
// Need the exact solution at stencil node j
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= PP.d_dx(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = ddx[j];
}
}
}
// V (block) row
for (unsigned int i = nb_bnd; i < N; i++) {
StencilType& st = grid.getStencil(i);
double* ddy = der.getStencilWeights(RBFFD::YSFC, i);
double* lapl = der.getStencilWeights(RBFFD::LSFC, i);
unsigned int diag_row_ind = i + 1*(N-nb_bnd);
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 1*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
// Need the exact solution at stencil node j
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= -eta * VV.lapl(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = -eta * lapl[j];
}
}
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 3*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
// Need the exact solution at stencil node j
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= PP.d_dy(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = ddy[j];
}
}
}
// W (block) row
for (unsigned int i = nb_bnd; i < N; i++) {
StencilType& st = grid.getStencil(i);
double* ddz = der.getStencilWeights(RBFFD::ZSFC, i);
double* lapl = der.getStencilWeights(RBFFD::LSFC, i);
unsigned int diag_row_ind = i + 2*(N-nb_bnd);
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 2*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= -eta * WW.lapl(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = -eta * lapl[j];
}
}
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 3*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= PP.d_dz(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = ddz[j];
}
}
}
// P (block) row
for (unsigned int i = nb_bnd; i < N; i++) {
StencilType& st = grid.getStencil(i);
double* ddx = der.getStencilWeights(RBFFD::XSFC, i);
double* ddy = der.getStencilWeights(RBFFD::YSFC, i);
double* ddz = der.getStencilWeights(RBFFD::ZSFC, i);
unsigned int diag_row_ind = i + 3*(N-nb_bnd);
// ddx(U)-component
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 0*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= UU.d_dx(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = ddx[j];
}
}
// ddy(V)-component
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 1*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= VV.d_dx(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = ddy[j];
}
}
// ddz(W)-component
for (unsigned int j = 0; j < st.size(); j++) {
unsigned int diag_col_ind = st[j] + 2*(N-nb_bnd);
if (st[j] < (int)nb_bnd) {
NodeType& node = nodes[st[j]];
double Xx = node.x();
double Yy = node.y();
double Zz = node.z();
F[diag_row_ind-nb_bnd] -= WW.d_dx(Xx, Yy, Zz);
} else {
A(diag_row_ind-nb_bnd, diag_col_ind-nb_bnd) = ddz[j];
}
}
}
}