double solve_vs_exact(Options options, Mesh* mesh, std::vector<Element2D*> &elements) {
PetscFunctionBegin;
// Setup values.
int it = 0;
double time = 0.0;
double timeStep = options.TimeStep();
double duration = options.Duration();
if(options.SaveMovie()) mesh->setUpMovie(options.OutputMovieFile());
// Over-allocate matrices to avoid re-allocations.
int max_dims = 3;
int int_pnts = elements[0]->NumberIntegrationPoints();
Eigen::MatrixXd f(int_pnts, max_dims);
Eigen::MatrixXd u(int_pnts, max_dims);
Eigen::MatrixXd ku(int_pnts, max_dims);
Eigen::MatrixXd fMinusKu(int_pnts, max_dims);
Eigen::MatrixXd fMinusKu_boundary(int_pnts, max_dims);
double max_error = 0.0;
while (time < duration) {
// Collect all global fields to the local partitions.
for (auto &field : elements[0]->PullElementalFields()) {
mesh->checkOutField(field);
}
// Zero all fields to which we will sum.
for (auto &field : elements[0]->PushElementalFields()) {
mesh->zeroFields(field);
}
for (auto &element : elements) {
// Get fields on element, store in successive rows. (e.g.,
// "u" for acoustic, "ux, uz" for elastic)
int fitr = 0;
for (auto &field : element->PullElementalFields()) {
u.col(fitr) = mesh->getFieldOnElement(field, element->Number(),
element->ElementClosure());
fitr++;
}
double element_error = element->checkTest(mesh, options, u.block(0,0,int_pnts,fitr), time);
if(element_error > max_error) { max_error = element_error; }
// Compute stiffness, only passing those rows which are occupied.
ku.block(0,0,int_pnts,fitr) = element->computeStiffnessTerm(
u.block(0,0,int_pnts,fitr));
// Compute acceleration.
fMinusKu.block(0,0,int_pnts,fitr) = -1 * ku.block(0,0,int_pnts,fitr).array();
// Sum fields into local partition.
fitr = 0;
for (auto &field : element->PushElementalFields()) {
mesh->addFieldFromElement(field, element->Number(),
element->ElementClosure(),
fMinusKu.col(fitr));
fitr++;
}
}
// boundary condition happens after full Ku
for( auto &element : elements) {
// we can now apply boundary conditions (after fields are set)
if(element->OnBoundary()) {
// apply boundary condition
element->applyBoundaryConditions(mesh,
options,
"a");
}
}
// Sum fields into global partitions.
for (auto &field : elements[0]->PushElementalFields()) {
mesh->checkInFieldBegin(field);
mesh->checkInFieldEnd(field);
}
// Take a time step.
mesh->applyInverseMassMatrix();
mesh->advanceField(timeStep);
if(options.SaveMovie() && (it%options.SaveFrameEvery()==0 || it == 0) ) {
// GlobalFields[0] == "u" for acoustic and == "ux" for elastic
mesh->saveFrame(mesh->GlobalFields()[0], it);
// mesh->setLocalFieldToGlobal("u_exact");
// mesh->saveFrame("u_exact", it);
if(max_error > 5) {
std::cerr << "ERROR: Solution blowing up!\n";
exit(1);
}
PRINT_ROOT() << "TIME: " << time;
}
it++;
time += timeStep;
}
PRINT_ROOT() << "Max Error @ T=end: " << max_error << std::endl;
if(options.SaveMovie()) mesh->finalizeMovie();
return max_error;
}
