void create_stage_wf(double current_time, double time_step, ButcherTable* bt,
DiscreteProblem* dp, WeakForm* stage_wf_left,
WeakForm* stage_wf_right)
{
// First let's do the mass matrix (only one block ndof times ndof).
WeakForm::MatrixFormVol mfv_00;
mfv_00.i = 0;
mfv_00.j = 0;
mfv_00.sym = HERMES_SYM;
mfv_00.area = HERMES_ANY;
mfv_00.fn = l2_form<double, scalar>;
mfv_00.ord = l2_form<Ord, Ord>;
mfv_00.ext = Hermes::vector<MeshFunction*> ();
mfv_00.scaling_factor = 1.0;
mfv_00.u_ext_offset = 0;
stage_wf_left->add_matrix_form(&mfv_00);
// In the rest we will take the stationary jacobian and residual forms
// (right-hand side) and use them to create a block Jacobian matrix of
// size (num_stages*ndof times num_stages*ndof) and a block residual
// vector of length num_stages*ndof.
// Number of stages.
int num_stages = bt->get_size();
// Original weak formulation.
WeakForm* wf = dp->get_weak_formulation();
// Extract mesh from (the first space of) the original discrete problem.
Mesh* mesh = dp->get_space(0)->get_mesh();
// Create constant Solutions to represent the stage times,
// stage_time = current_time + c_i*time_step.
// (Temporary workaround. these should be passed as numbers.)
Solution** stage_time_sol = new Solution*[num_stages];
for (int i = 0; i < num_stages; i++) {
stage_time_sol[i] = new Solution(mesh);
stage_time_sol[i]->set_const(mesh, current_time + bt->get_C(i)*time_step);
}
// Extracting volume and surface matrix and vector forms from the
// original weak formulation.
if (wf->get_neq() != 1) error("wf->neq != 1 not implemented yet.");
Hermes::vector<WeakForm::MatrixFormVol> mfvol_base = wf->get_mfvol();
Hermes::vector<WeakForm::MatrixFormSurf> mfsurf_base = wf->get_mfsurf();
Hermes::vector<WeakForm::VectorFormVol> vfvol_base = wf->get_vfvol();
Hermes::vector<WeakForm::VectorFormSurf> vfsurf_base = wf->get_vfsurf();
// Duplicate matrix volume forms, scale them according
// to the Butcher's table, enhance them with additional
// external solutions, and anter them as blocks to the
// new stage Jacobian.
for (unsigned int m = 0; m < mfvol_base.size(); m++) {
WeakForm::MatrixFormVol mfv_base = mfvol_base[m];
for (int i = 0; i < num_stages; i++) {
for (int j = 0; j < num_stages; j++) {
WeakForm::MatrixFormVol mfv_ij;
mfv_ij.i = i;
mfv_ij.j = j;
mfv_ij.sym = mfv_base.sym;
mfv_ij.area = mfv_base.area;
mfv_ij.fn = mfv_base.fn;
mfv_ij.ord = mfv_base.ord;
std::copy(mfv_base.ext.begin(), mfv_base.ext.end(), mfv_ij.ext.begin());
mfv_ij.scaling_factor = -time_step * bt->get_A(i, j);
// Set offset for u_ext[] external solutions.
mfv_ij.u_ext_offset = i;
// Add stage_time_sol[i] as an external function to the form.
mfv_ij.ext.push_back(stage_time_sol[i]);
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_matrix_form(&mfv_ij);
}
}
}
// Duplicate matrix surface forms, enhance them with
// additional external solutions, and anter them as
// blocks of the stage Jacobian.
for (unsigned int m = 0; m < mfsurf_base.size(); m++) {
WeakForm::MatrixFormSurf mfs_base = mfsurf_base[m];
for (int i = 0; i < num_stages; i++) {
for (int j = 0; j < num_stages; j++) {
WeakForm::MatrixFormSurf mfs_ij;
mfs_ij.i = i;
mfs_ij.j = j;
mfs_ij.area = mfs_base.area;
mfs_ij.fn = mfs_base.fn;
mfs_ij.ord = mfs_base.ord;
std::copy(mfs_base.ext.begin(), mfs_base.ext.end(), mfs_ij.ext.begin());
mfs_ij.scaling_factor = -time_step * bt->get_A(i, j);
// Set offset for u_ext[] external solutions.
mfs_ij.u_ext_offset = i;
// Add stage_time_sol[i] as an external function to the form.
mfs_ij.ext.push_back(stage_time_sol[i]);
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_matrix_form_surf(&mfs_ij);
}
}
}
// Duplicate vector volume forms, enhance them with
// additional external solutions, and anter them as
// blocks of the stage residual.
for (unsigned int m = 0; m < vfvol_base.size(); m++) {
WeakForm::VectorFormVol vfv_base = vfvol_base[m];
for (int i = 0; i < num_stages; i++) {
WeakForm::VectorFormVol vfv_i;
vfv_i.i = i;
vfv_i.area = vfv_base.area;
vfv_i.fn = vfv_base.fn;
vfv_i.ord = vfv_base.ord;
std::copy(vfv_base.ext.begin(), vfv_base.ext.end(), vfv_i.ext.begin());
vfv_i.scaling_factor = -1.0;
// Set offset for u_ext[] external solutions.
vfv_i.u_ext_offset = i;
// Add stage_time_sol[i] as an external function to the form.
vfv_i.ext.push_back(stage_time_sol[i]);
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_vector_form(&vfv_i);
}
}
// Duplicate vector surface forms, enhance them with
// additional external solutions, and anter them as
// blocks of the stage residual.
for (unsigned int m = 0; m < vfsurf_base.size(); m++) {
WeakForm::VectorFormSurf vfs_base = vfsurf_base[m];
for (int i = 0; i < num_stages; i++) {
WeakForm::VectorFormSurf vfs_i;
vfs_i.i = i;
vfs_i.area = vfs_base.area;
vfs_i.fn = vfs_base.fn;
vfs_i.ord = vfs_base.ord;
std::copy(vfs_base.ext.begin(), vfs_base.ext.end(), vfs_i.ext.begin());
vfs_i.scaling_factor = -1.0;
// Set offset for u_ext[] external solutions.
vfs_i.u_ext_offset = i;
// Add stage_time_sol[i] as an external function to the form.
vfs_i.ext.push_back(stage_time_sol[i]);
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_vector_form_surf(&vfs_i);
}
}
}
void create_stage_wf(double current_time, double time_step, ButcherTable* bt,
DiscreteProblem* dp, WeakForm* stage_wf_left,
WeakForm* stage_wf_right, Solution** stage_time_sol)
{
// First let's do the mass matrix (only one block ndof times ndof).
WeakForm::MatrixFormVol mfv_00;
mfv_00.i = 0;
mfv_00.j = 0;
mfv_00.sym = HERMES_SYM;
mfv_00.area = HERMES_ANY;
mfv_00.fn = l2_form<double, scalar>;
mfv_00.ord = l2_form<Ord, Ord>;
mfv_00.ext = Hermes::vector<MeshFunction*> ();
mfv_00.scaling_factor = 1.0;
mfv_00.u_ext_offset = 0;
mfv_00.adapt_eval = false;
mfv_00.adapt_order_increase = -1;
mfv_00.adapt_rel_error_tol = -1;
stage_wf_left->add_matrix_form_internal(&mfv_00);
// In the rest we will take the stationary jacobian and residual forms
// (right-hand side) and use them to create a block Jacobian matrix of
// size (num_stages*ndof times num_stages*ndof) and a block residual
// vector of length num_stages*ndof.
// Number of stages.
int num_stages = bt->get_size();
// Original weak formulation.
WeakForm* wf = dp->get_weak_formulation();
// Extract mesh from (the first space of) the original discrete problem.
Mesh* mesh = dp->get_space(0)->get_mesh();
// Create constant Solutions to represent the stage times,
// stage_time = current_time + c_i*time_step.
// WARNING - THIS IS A TEMPORARY HACK. THE STAGE TIME SHOULD BE ENTERED
// AS A NUMBER, NOT IN THIS WAY. IT WILL BE ADDED AFTER EXISTING EXTERNAL
// SOLUTIONS IN ExtData.
for (int i = 0; i < num_stages; i++) {
stage_time_sol[i] = new Solution(mesh);
stage_time_sol[i]->set_const(mesh, current_time + bt->get_C(i)*time_step);
}
// Extracting volume and surface matrix and vector forms from the
// original weak formulation.
if (wf->get_neq() != 1) error("wf->neq != 1 not implemented yet.");
Hermes::vector<WeakForm::MatrixFormVol> mfvol_base = wf->get_mfvol();
Hermes::vector<WeakForm::MatrixFormSurf> mfsurf_base = wf->get_mfsurf();
Hermes::vector<WeakForm::VectorFormVol> vfvol_base = wf->get_vfvol();
Hermes::vector<WeakForm::VectorFormSurf> vfsurf_base = wf->get_vfsurf();
// Duplicate matrix volume forms, scale them according
// to the Butcher's table, enhance them with additional
// external solutions, and anter them as blocks to the
// new stage Jacobian.
for (unsigned int m = 0; m < mfvol_base.size(); m++) {
WeakForm::MatrixFormVol mfv_base = mfvol_base[m];
for (int i = 0; i < num_stages; i++) {
for (int j = 0; j < num_stages; j++) {
WeakForm::MatrixFormVol mfv_ij;
mfv_ij.i = i;
mfv_ij.j = j;
mfv_ij.sym = mfv_base.sym;
mfv_ij.area = mfv_base.area;
mfv_ij.fn = mfv_base.fn;
mfv_ij.ord = mfv_base.ord;
mfv_ij.scaling_factor = -time_step * bt->get_A(i, j);
// Duplicate external solutions.
// THIS WAS WRONG, ONE CANNOT COPY INTO AN EMPTY STD::VECTOR:
// std::copy(mfv_base.ext.begin(), mfv_base.ext.end(), mfv_ij.ext.begin());
for (unsigned int f_idx = 0; f_idx < mfv_base.ext.size(); f_idx++)
mfv_ij.ext.push_back(mfv_base.ext[f_idx]);
// Add stage_time_sol[i] as an external function to the form.
mfv_ij.ext.push_back(stage_time_sol[i]);
// Set offset for u_ext[] external solutions.
mfv_ij.u_ext_offset = i;
// This form will not be integrated adaptively.
mfv_ij.adapt_eval = false;
mfv_ij.adapt_order_increase = -1;
mfv_ij.adapt_rel_error_tol = -1;
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_matrix_form_internal(&mfv_ij);
}
}
}
// Duplicate matrix surface forms, enhance them with
// additional external solutions, and anter them as
// blocks of the stage Jacobian.
for (unsigned int m = 0; m < mfsurf_base.size(); m++) {
WeakForm::MatrixFormSurf mfs_base = mfsurf_base[m];
for (int i = 0; i < num_stages; i++) {
for (int j = 0; j < num_stages; j++) {
WeakForm::MatrixFormSurf mfs_ij;
mfs_ij.i = i;
mfs_ij.j = j;
mfs_ij.area = mfs_base.area;
mfs_ij.fn = mfs_base.fn;
mfs_ij.ord = mfs_base.ord;
mfs_ij.scaling_factor = -time_step * bt->get_A(i, j);
// Duplicate external solutions.
// THIS WAS WRONG, ONE CANNOT COPY INTO AN EMPTY STD::VECTOR:
// std::copy(mfs_base.ext.begin(), mfs_base.ext.end(), mfs_ij.ext.begin());
for (unsigned int f_idx = 0; f_idx < mfs_base.ext.size(); f_idx++)
mfs_ij.ext.push_back(mfs_base.ext[f_idx]);
// Add stage_time_sol[i] as an external function to the form.
mfs_ij.ext.push_back(stage_time_sol[i]);
// Set offset for u_ext[] external solutions.
mfs_ij.u_ext_offset = i;
// This form will not be integrated adaptively.
mfs_ij.adapt_eval = false;
mfs_ij.adapt_order_increase = -1;
mfs_ij.adapt_rel_error_tol = -1;
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_matrix_form_surf_internal(&mfs_ij);
}
}
}
// Duplicate vector volume forms, enhance them with
// additional external solutions, and anter them as
// blocks of the stage residual.
for (unsigned int m = 0; m < vfvol_base.size(); m++) {
WeakForm::VectorFormVol vfv_base = vfvol_base[m];
for (int i = 0; i < num_stages; i++) {
WeakForm::VectorFormVol vfv_i;
vfv_i.i = i;
vfv_i.area = vfv_base.area;
vfv_i.fn = vfv_base.fn;
vfv_i.ord = vfv_base.ord;
vfv_i.scaling_factor = -1.0;
// Duplicate external solutions.
// THIS WAS WRONG, ONE CANNOT COPY INTO AN EMPTY STD::VECTOR:
// std::copy(vfv_base.ext.begin(), vfv_base.ext.end(), vfv_ij.ext.begin());
for (unsigned int f_idx = 0; f_idx < vfv_base.ext.size(); f_idx++)
vfv_i.ext.push_back(vfv_base.ext[f_idx]);
// Add stage_time_sol[i] as an external function to the form.
vfv_i.ext.push_back(stage_time_sol[i]);
// Set offset for u_ext[] external solutions.
vfv_i.u_ext_offset = i;
// This form will not be integrated adaptively.
vfv_i.adapt_eval = false;
vfv_i.adapt_order_increase = -1;
vfv_i.adapt_rel_error_tol = -1;
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_vector_form_internal(&vfv_i);
}
}
// Duplicate vector surface forms, enhance them with
// additional external solutions, and anter them as
// blocks of the stage residual.
for (unsigned int m = 0; m < vfsurf_base.size(); m++) {
WeakForm::VectorFormSurf vfs_base = vfsurf_base[m];
for (int i = 0; i < num_stages; i++) {
WeakForm::VectorFormSurf vfs_i;
vfs_i.i = i;
vfs_i.area = vfs_base.area;
vfs_i.fn = vfs_base.fn;
vfs_i.ord = vfs_base.ord;
vfs_i.scaling_factor = -1.0;
// Duplicate external solutions.
// THIS WAS WRONG, ONE CANNOT COPY INTO AN EMPTY STD::VECTOR:
// std::copy(vfv_base.ext.begin(), vfv_base.ext.end(), vfv_ij.ext.begin());
for (unsigned int f_idx = 0; f_idx < vfs_base.ext.size(); f_idx++)
vfs_i.ext.push_back(vfs_base.ext[f_idx]);
// Add stage_time_sol[i] as an external function to the form.
vfs_i.ext.push_back(stage_time_sol[i]);
// Set offset for u_ext[] external solutions.
vfs_i.u_ext_offset = i;
// This form will not be integrated adaptively.
vfs_i.adapt_eval = false;
vfs_i.adapt_order_increase = -1;
vfs_i.adapt_rel_error_tol = -1;
// Add the matrix form to the corresponding block of the
// stage Jacobian matrix.
stage_wf_right->add_vector_form_surf_internal(&vfs_i);
}
}
}