diffusion.hpp File Reference

Diffusion operators and implicit system builders for 2D grids. More...

#include "pde/stencil.hpp"
#include "core/vector.hpp"
#include "core/policy.hpp"
#include "fields/grid2d.hpp"
#include "linalg/sparse/sparse.hpp"
#include "linalg/solvers/cg.hpp"
#include "linalg/solvers/linear_solver.hpp"

Go to the source code of this file.

Namespaces
namespace	num
namespace	num::pde

Functions
void	num::pde::diffusion_step_2d (Vector &u, int N, double coeff, Backend b=best_backend)
void	num::pde::diffusion_step_2d_dirichlet (Vector &u, int N, double coeff, Backend b=best_backend)
void	num::pde::diffusion_step_2d_4th_dirichlet (Vector &u, int N, double coeff, Backend b=best_backend)
void	num::pde::diffusion_step_2d_dirichlet (ScalarField2D &g, double coeff, Backend b=best_backend)
void	num::pde::diffusion_step_2d_4th_dirichlet (ScalarField2D &g, double coeff, Backend b=best_backend)
SparseMatrix	num::pde::laplacian_sparse_2d (int N)
SparseMatrix	num::pde::backward_euler_matrix (int N, double coeff)
SparseMatrix	num::pde::backward_euler_matrix (const Grid2D &grid, double coeff)
	Grid2D overload – N is read from the grid.
LinearSolver	num::pde::make_cg_solver (const SparseMatrix &A, real tol=1e-6)

Detailed Description

Diffusion operators and implicit system builders for 2D grids.

Explicit Euler stencil steps (periodic or Dirichlet BCs): diffusion_step_2d – periodic diffusion_step_2d_dirichlet – Dirichlet, 2nd-order diffusion_step_2d_4th_dirichlet – Dirichlet, 4th-order

Implicit system builders (backward Euler): laplacian_sparse_2d – bare N^2 x N^2 Laplacian matrix backward_euler_matrix – A = I - coeff*L (sparse, SPD)

Solver factory: make_cg_solver(A) – returns a LinearSolver using matrix-free CG

Time integration lives in ode/implicit.hpp: num::ode::advance(u, solver, p).

Definition in file diffusion.hpp.