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60 lines
2.1 KiB
60 lines
2.1 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 1D Poisson's equation on unit line with Dirichlet
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/// 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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// Create the domain and discretize it
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BoxShape <Vec1d> box(0.0, 1.0);
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double dx = 0.01;
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DomainDiscretization <Vec1d> 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(4)); // the support for each node is the closest 4 nodes
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// Construct the approximation engine, in this case a weighted least squares using monomials
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// as basis functions, Gaussian weight, and scale to farthest
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int m = 2; // basis order
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Monomials <Vec1d> basis(m); // construct monomial basis
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WLS <Monomials<Vec1d>, GaussianWeight<Vec1d>,
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ScaleToFarthest> wls(basis); // basis of monomials up to order 2
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// compute the shapes (only Laplacian in this case) using our WLS
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auto storage = domain.computeShapes<sh::lap>(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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// construct implicit operators over our storage
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auto op = storage.implicitOperators(M, rhs);
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for (int i : domain.interior()) {
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double x = domain.pos(i, 0);
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// set the case for nodes in the domain
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op.lap(i) = -PI * PI * std::sin(PI * x);
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}
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for (int i : domain.boundary()) {
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// enforce the boundary conditions
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op.value(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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// solve the system
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ScalarFieldd u = solver.solve(rhs);
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// Write the solution into file
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std::ofstream out_file("poisson_dirichlet_1D_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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