int main()
{
// Try to read mesh contents from a .msh file (for information about the
// structure of these files, see FreeFem++ documentation).
TriangleMesh mesh;
try {
mesh.read_file_msh("squared-mesh-2x2.msh"); }
catch (...) {
std::cerr << "Error reading mesh file" << std::endl;
exit(1); }
// Define quadrature rule with nodes located at vertices of the reference triangle
VerticesQuadRule quad_rule;
// Define a finite element space on current mesh
P1_FE_Space fe_space(mesh, quad_rule);
// Start chronometer
auto start = std::chrono::high_resolution_clock::now();
// Repeat several times (to increase computation time)
for (int num=0; num<20; ++num) {
// For each cell, r:
for (Index r=0; r<mesh.get_ncel(); ++r)
{
std::cout << "###### Cell: r=" << r << std::endl << std::endl;
// In C++11, one can use "auto" instead of "FiniteElement"
auto fe = fe_space.get_element(r); // Build a finite element on cell r
// Get x-derivatives of all the shape functions on curent element.
//
// The get_dx_phi() member function returns (a const reference
// to) a vector containng FE_Functions (one for each dof). A
// FE_Function objetct contains the values resulting from the
// evaluation of the corresponding shape function on the
// quadrature points.
//
// You can use "auto" instead of "std::vector<FE_Function>",
// but performance seems better using references ("auto&")
auto& dx_phi = fe.get_dx_phi();
// Get also y-derivatives of shape functions
auto& dy_phi = fe.get_dy_phi();
Index ndofs = fe.get_ndofs();
// For each degree of freedom, i:
for (Index i = 0; i < ndofs; ++i)
{
// For each degree of freedom, j:
for (Index j = 0; j < ndofs; ++j)
{
// Compute integral of product of x-derivatives
Real Kx_ij = fe.integrate(dx_phi[i], dx_phi[j]);
std::cout << "Kx[" << i << "][" << j << "]=" << Kx_ij << std::endl;
// Compute integral of product of y-derivatives
Real Ky_ij = fe.integrate(dy_phi[i], dy_phi[j]);
std::cout << "Ky[" << i << "][" << j << "]=" << Ky_ij << std::endl;
// Compute integral on element r of gradient(phi_i)*gradient(phi_j),
// i.e. dx(phi_i)*dx(phi_j) + dy(phi_i)*dy(phi_j)
Real K_ij = Kx_ij + Ky_ij;
std::cout << "K[" << i << "][" << j << "]=" << K_ij << std::endl;
std::cout << std::endl;
}
}
}
}
// Store final time and print elapsed time
auto end = std::chrono::high_resolution_clock::now();
std::cout << "Elapsed time: " <<
std::chrono::duration_cast<std::chrono::milliseconds>(end-start).count() <<
" miliseconds" << std::endl;
}
