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test_igfem_triangle_5.cc
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Sat, Nov 9, 21:54

test_igfem_triangle_5.cc
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/**
* @file test_igfem_triangle_5.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief patch tests with elements of type _igfem_triangle_5
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#include "solid_mechanics_model_igfem.hh"
#include "dumpable_inline_impl.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
class StraightInterfaceMatSelector : public MeshDataMaterialSelector<std::string> {
public:
StraightInterfaceMatSelector(const ID & id, SolidMechanicsModelIGFEM & model) :
MeshDataMaterialSelector<std::string>(id, model) {}
UInt operator()(const Element & elem) {
if(Mesh::getKind(elem.type) == _ek_igfem)
/// choose IGFEM material
return 2;
return MeshDataMaterialSelector<std::string>::operator()(elem);
}
};
Real computeL2Error(SolidMechanicsModelIGFEM & model);
int main(int argc, char *argv[]) {
initialize("material.dat", argc, argv);
/// create a mesh and read the regular elements from the mesh file
/// mesh creation
const UInt spatial_dimension = 2;
Mesh mesh(spatial_dimension);
mesh.read("plate.msh");
/// model creation
SolidMechanicsModelIGFEM model(mesh);
/// creation of material selector
MeshDataMaterialSelector<std::string> * mat_selector;
mat_selector = new StraightInterfaceMatSelector("physical_names", model);
model.setMaterialSelector(*mat_selector);
model.initFull();
/// add fields that should be dumped
model.setBaseName("regular_elements");
model.setBaseNameToDumper("igfem elements", "igfem elements");
model.addDumpField("material_index");
model.addDumpFieldVector("displacement");
model.addDumpField("blocked_dofs");
model.addDumpField("stress");
model.addDumpFieldToDumper("igfem elements", "lambda");
model.addDumpFieldVectorToDumper("igfem elements", "displacement");
model.addDumpFieldVectorToDumper("igfem elements", "real_displacement");
model.addDumpFieldToDumper("igfem elements","blocked_dofs");
model.addDumpFieldToDumper("igfem elements", "material_index");
model.addDumpFieldToDumper("igfem elements", "stress");
/// dump mesh before the IGFEM interface is created
model.dump();
model.dump("igfem elements");
/// create the interace: the bi-material interface is a straight line
/// since the SMMIGFEM has only a sphere intersector we generate a large
/// sphere so that the intersection points with the mesh lie almost along
/// the straight line x = 0.25. We then move the interface nodes to correct
/// their position and make them lie exactly along the line. This is a
/// workaround to generate a straight line with the sphere intersector.
/// Ideally, there should be a new type of IGFEM enrichment implemented to generate straight lines
std::list<SK::Sphere_3> sphere_list;
SK::Sphere_3 sphere_1(SK::Point_3(6.57, 0., 0.), 6.32 * 6.32);
sphere_list.push_back(sphere_1);
model.registerGeometryObject(sphere_list, "inside");
UInt nb_regular_nodes = mesh.getNbNodes();
model.update();
UInt nb_igfem_nodes = mesh.getNbNodes() - nb_regular_nodes;
/// adjust the positions of the node to have an exact straight line
Array<Real> & nodes = const_cast<Array<Real> &>(mesh.getNodes());
Array<Real>::vector_iterator nodes_it = nodes.begin(spatial_dimension);
nodes_it += nb_regular_nodes;
for (UInt i = 0; i < nb_igfem_nodes; ++i, ++nodes_it) {
Vector<Real> & node_coords = *nodes_it;
node_coords(0) = 0.25;
Int multiplier = std::round(node_coords(1) / 0.25);
node_coords(1) = 0.25 * multiplier;
}
/// reinitialize the shape functions because node coordinates have changed
model.getFEEngine("IGFEMFEEngine").initShapeFunctions(_not_ghost);
model.getFEEngine("IGFEMFEEngine").initShapeFunctions(_ghost);
/// dump mesh after the IGFEM interface is created
model.dump();
model.dump("igfem elements");
/// apply the boundary conditions: left and bottom side on rollers
/// imposed displacement along right side
mesh.computeBoundingBox();
const Vector<Real> & lower_bounds = mesh.getLowerBounds();
const Vector<Real> & upper_bounds = mesh.getUpperBounds();
Real bottom = lower_bounds(1);
Real left = lower_bounds(0);
Real right = upper_bounds(0);
Real eps = std::abs((right - left) * 1e-6);
const Array<Real> & pos = mesh.getNodes();
Array<Real> & disp = model.getDisplacement();
Array<bool> & boun = model.getBlockedDOFs();
for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
if(std::abs(pos(i,1) - bottom) < eps){
boun(i,1) = true;
disp(i,1) = 0.0;
}
if(std::abs(pos(i,0) - left) < eps){
boun(i,0) = true;
disp(i,0) = 0.0;
}
if(std::abs(pos(i,0) - right) < eps){
boun(i,0) = true;
disp(i,0) = 1.0;
}
}
/// compute the volume of the mesh
Real int_volume = 0.;
std::map<ElementKind, FEEngine *> fe_engines = model.getFEEnginesPerKind();
std::map<ElementKind, FEEngine *>::const_iterator fe_it = fe_engines.begin();
for (; fe_it != fe_engines.end(); ++fe_it) {
ElementKind kind = fe_it->first;
FEEngine & fe_engine = *(fe_it->second);
Mesh::type_iterator it = mesh.firstType(spatial_dimension, _not_ghost, kind);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension, _not_ghost, kind);
for(; it != last_type ; ++it) {
ElementType type = *it;
Array<Real> Volume(mesh.getNbElement(type) * fe_engine.getNbIntegrationPoints(type), 1, 1.);
int_volume += fe_engine.integrate(Volume, type);
}
}
if (!Math::are_float_equal(int_volume, 4)) {
std::cout << "Error in area computation of the 2D mesh" << std::endl;
return EXIT_FAILURE;
}
std::cout << "the area of the mesh is: " << int_volume << std::endl;
/// solve the system
model.assembleStiffnessMatrix();
Real error = 0;
bool converged = false;
bool factorize = false;
converged = model.solveStep<_scm_newton_raphson_tangent, _scc_increment>(1e-12, error, 2, factorize);
if (!converged) {
std::cout << "The solver did not converge!!! The error is: " << error << std::endl;
finalize();
return EXIT_FAILURE;
}
/// dump the deformed mesh
model.dump();
model.dump("igfem elements");
Real L2_error = computeL2Error(model);
std::cout << "Error: " << L2_error << std::endl;
if (L2_error > 1e-12) {
finalize();
std::cout << "The patch test did not pass!!!!" << std::cout;
return EXIT_FAILURE;
}
finalize();
return EXIT_SUCCESS;
}
/* -------------------------------------------------------------------------- */
Real computeL2Error(SolidMechanicsModelIGFEM & model) {
/// store the error on each element for visualization
ElementTypeMapReal error_per_element("error_per_element");
Real error = 0;
Real normalization = 0;
/// Young's moduli for the two materials
Real E_1 = 10.;
Real E_2 = 1.;
Mesh & mesh = model.getMesh();
UInt spatial_dimension = mesh.getSpatialDimension();
mesh.addDumpFieldExternal("error_per_element", error_per_element, spatial_dimension, _not_ghost, _ek_regular);
mesh.addDumpFieldExternalToDumper("igfem elements","error_per_element", error_per_element, spatial_dimension, _not_ghost, _ek_igfem);
ElementTypeMapReal quad_coords("quad_coords");
GhostType ghost_type = _not_ghost;
const std::map<ElementKind, FEEngine *> & fe_engines = model.getFEEnginesPerKind();
std::map<ElementKind, FEEngine *>::const_iterator fe_it = fe_engines.begin();
for (; fe_it != fe_engines.end(); ++fe_it) {
ElementKind kind = fe_it->first;
FEEngine & fe_engine = *(fe_it->second);
mesh.initElementTypeMapArray(quad_coords, spatial_dimension, spatial_dimension, false, kind, true);
mesh.initElementTypeMapArray(error_per_element, 1, spatial_dimension, false, kind, true);
fe_engine.computeIntegrationPointsCoordinates(quad_coords);
Mesh::type_iterator it = mesh.firstType(spatial_dimension, ghost_type, kind);
Mesh::type_iterator last_type = mesh.lastType(spatial_dimension, ghost_type, kind);
for(; it != last_type ; ++it) {
ElementType type = *it;
UInt nb_elements = mesh.getNbElement(type, ghost_type);
UInt nb_quads = fe_engine.getNbIntegrationPoints(type);
/// interpolate the displacement at the quadrature points
Array<Real> displ_on_quads(nb_quads * nb_elements, spatial_dimension, "displ_on_quads");
Array<Real> quad_coords(nb_quads * nb_elements, spatial_dimension, "quad_coords");
fe_engine.interpolateOnIntegrationPoints(model.getDisplacement(), displ_on_quads, spatial_dimension, type);
fe_engine.computeIntegrationPointsCoordinates(quad_coords, type, ghost_type);
Array<Real> & el_error = error_per_element(type, ghost_type);
Array<Real>::const_vector_iterator displ_it = displ_on_quads.begin(spatial_dimension);
Array<Real>::const_vector_iterator coord_it = quad_coords.begin(spatial_dimension);
Vector<Real> error_vec(spatial_dimension);
for (UInt e = 0; e < nb_elements; ++e) {
Vector<Real> error_per_quad(nb_quads);
Vector<Real> normalization_per_quad(nb_quads);
for (UInt q = 0; q < nb_quads; ++q, ++displ_it, ++coord_it) {
Real exact = 0.;
Real x = (*coord_it)(0);
if (x < 0.25)
exact = (4. * x * E_2) /(3. * E_1 + 5. * E_2)+(4. * E_2)/(3. * E_1 + 5. * E_2);
else
exact = 4. * x *E_1 /(3. * E_1 + 5. *E_2)-(E_1-5.*E_2)/(3.*E_1+5.*E_2);
error_vec = *displ_it;
error_vec(0) -= exact;
error_per_quad(q) = error_vec.dot(error_vec);
normalization_per_quad(q) = std::abs(exact) * std::abs(exact);
std::cout << error_vec << std::endl;
}
/// integrate the error in the element and the corresponding
/// normalization
Real int_error = fe_engine.integrate(error_per_quad, type, e, ghost_type);
error += int_error;
el_error(e) = std::sqrt(int_error);
normalization += fe_engine.integrate(normalization_per_quad, type, e, ghost_type);
}
}
}
model.dump();
model.dump("igfem elements");
return (std::sqrt(error) / std::sqrt(normalization));
}

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