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67 lines
2.0 KiB
67 lines
2.0 KiB
#include <medusa/Medusa_fwd.hpp>
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#include <medusa/bits/domains/BasicRelax.hpp>
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#include <medusa/bits/domains/GeneralFill.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 circle
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/// with mixed boundary conditions
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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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// construct BallShape and discretize the boundary
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BallShape<Vec2d> c(0.0, 1.0);
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double dx = 0.05;
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DomainDiscretization<Vec2d> domain = c.discretizeBoundaryWithStep(dx);
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// fill using GeneralFill, when filling the domain like this
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// it needs to be relaxed afterwards
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GeneralFill<Vec2d> fill;
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domain.fill(fill, dx);
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// relax the domain
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BasicRelax relax;
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relax.iterations(20).initialHeat(0.8).numNeighbours(3)
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.projectionType(BasicRelax::DO_NOT_PROJECT);
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relax(domain, dx);
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int N = domain.size();
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domain.findSupport(FindClosest(9));
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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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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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auto op = storage.implicitOperators(M, rhs);
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M.reserve(storage.supportSizes());
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for (int i : domain.interior()) {
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op.lap(i) = 1.0;
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}
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for (int i : domain.boundary()) {
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double x = domain.pos(i, 0);
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if (x > 0) {
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op.value(i) = 0.0; // dirichlet
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} else {
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op.neumann(i, domain.normal(i)) = 0.0; // neumann
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}
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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_circular_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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