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66 lines
2.6 KiB
66 lines
2.6 KiB
#include <medusa/Medusa_fwd.hpp>
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#include <Eigen/SparseCore>
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#include <Eigen/IterativeLinearSolvers>
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/// Basic medusa example, we are solving 2D Poisson's equation on unit square with
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/// mixed boundary conditions in order to calculate
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/// quarter of the solution to the Dirichlet Boundary conditions (because of symmetry).
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/// Neumann boundary conditions on the upper and right side of the box
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/// and Dirichlet boundary conditions on the bottom and left side of the box
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/// http://e6.ijs.si/medusa/wiki/index.php/Poisson%27s_equation
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using namespace mm; // NOLINT
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int main() {
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// Create the domain and discretize it
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BoxShape<Vec2d> box(0.0, 0.5); // Square with a = 0.5
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double dx = 0.005;
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DomainDiscretization<Vec2d> domain = box.discretizeWithStep(dx);
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// Find support for the nodes
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int N = domain.size();
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domain.findSupport(FindClosest(9)); // the support for each node is the closest 9 nodes
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// Construct the approximation engine, in this case a weighted least squares using Gaussian RBF,
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// no weight, scale to farthest and LLT solver.
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WLS<Gaussians<Vec2d>, NoWeight<Vec2d>, ScaleToFarthest,
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Eigen::LLT<Eigen::MatrixXd>> wls({9, 30});
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// Laplacian for inside the domain and first derivative for the bc's
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auto storage = domain.computeShapes<sh::lap|sh::d1>(wls);
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Eigen::SparseMatrix<double, Eigen::RowMajor> M(N, N);
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Eigen::VectorXd rhs(N); rhs.setZero();
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M.reserve(storage.supportSizes());
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auto op = storage.implicitOperators(M, rhs); // construct implicit operators over our storage
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int BOTTOM = -3;
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int TOP = -4;
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int LEFT = -1;
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int RIGHT = -2;
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for (int i : domain.interior()) {
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double x = domain.pos(i, 0);
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double y = domain.pos(i, 1);
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op.lap(i) = -2*PI*PI*std::sin(PI*x)*std::sin(PI*y); // set the case for nodes in the domain
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}
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for (int i : (domain.types() == LEFT) + (domain.types() == BOTTOM)) {
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op.value(i) = 0.0; // Dirichlet boundary conditions on the left and bottom edge of the box
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}
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for (int i : (domain.types() == TOP) + (domain.types() == RIGHT)) {
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// Neumann boundary conditions on upper and right edge of the box
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op.neumann(i, domain.normal(i)) = 0.0;
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}
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Eigen::BiCGSTAB<decltype(M), Eigen::IncompleteLUT<double>> solver;
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solver.compute(M);
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ScalarFieldd u = solver.solve(rhs);
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std::ofstream out_file("poisson_mixed_2D_data.m");
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out_file << "positions = " << domain.positions() << ";" << std::endl;
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out_file << "solution = " << u << ";" << std::endl;
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out_file.close();
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return 0;
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}
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