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#include <medusa/Medusa_fwd.hpp>
#include <medusa/bits/domains/GeneralFill.hpp>
#include <Eigen/SparseCore>
#include <Eigen/SparseLU>
using namespace mm; // NOLINT
using namespace std; // NOLINT
using namespace Eigen; // NOLINT
/// Solving 3D Poisson's equation on unit ball
/// with mixed boundary conditions and ghost nodes for Neumann boundary.
/// http://e6.ijs.si/medusa/wiki/index.php/Ghost_nodes
using namespace mm; // NOLINT
typedef Vec3d vec; // Change to 2D or 1D
int main() {
BallShape<vec> b1(0.0, 1.0);
BallShape<vec> b2(1.0, 1.5);
auto b = b1 - b2;
double dx = 0.05;
DomainDiscretization<vec> domain = b.discretizeBoundaryWithStep(dx);
auto fn = [=](const vec&) { return dx; };
GeneralFill<vec> fill; fill.seed(1337);
fill(domain, fn);
// Node indexes for interior, Dirichlet and Neumann BC.
Range<int> interior = domain.interior();
Range<int> neu, dir;
for (int i : domain.boundary()) {
double x = domain.pos(i, 0);
if (x < 0) dir.push_back(i);
else neu.push_back(i);
}
auto gh = domain.addGhostNodes(dx, 0, neu);
// Find stencil.
int N = domain.size();
prn(N);
int n = 25;
domain.findSupport(FindClosest(n));
// Declare approximation.
std::cout << "Computing shapes..." << std::endl;
Polyharmonic<double, 3> phs;
RBFFD<decltype(phs), vec, ScaleToClosest> approx(phs, Monomials<vec>(2));
auto storage = domain.computeShapes<sh::lap|sh::d1>(approx);
Eigen::SparseMatrix<double, Eigen::RowMajor> M(N, N);
M.reserve(Range<int>(N, n));
Eigen::VectorXd rhs(N); rhs.setZero();
auto op = storage.implicitOperators(M, rhs);
std::cout << "Assembling..." << std::endl;
for (int i : interior) {
op.lap(i) = 1.0; // Equation
}
for (int i : dir) {
op.value(i) = 0.0; // Dirichlet
}
for (int i : neu) {
op.neumann(i, domain.normal(i)) = 0.0; // Neumann
// Equation holds also on the boundary, write it in the row corresponding to the ghost node.
op.lap(i, gh[i]) = 1.0;
}
std::cout << "Solving..." << std::endl;
// Solve the problem
SparseLU<decltype(M)> solver;
solver.compute(M);
ScalarFieldd u = solver.solve(rhs);
std::ofstream out_file("poisson_mixed_3D_ghost_data.m");
out_file << "positions = " << domain.positions() << ";" << std::endl;
out_file << "types = " << domain.types() << ";" << std::endl;
out_file << "solution = " << u << ";" << std::endl;
out_file.close();
return 0;
}