num::pde Namespace Reference

Classes
class	BackwardEulerOperator2D

Functions
SparseMatrix	backward_euler_matrix (int N, double coeff)
void	diffusion_step_2d (Vector &u, int N, double coeff, Backend b=best_backend)
void	diffusion_step_2d_dirichlet (Vector &u, int N, double coeff, Backend b=best_backend)
void	diffusion_step_2d_4th_dirichlet (Vector &u, int N, double coeff, Backend b=best_backend)
void	diffusion_step_2d_dirichlet (ScalarField2D &g, double coeff, Backend b=best_backend)
void	diffusion_step_2d_4th_dirichlet (ScalarField2D &g, double coeff, Backend b=best_backend)
SparseMatrix	laplacian_sparse_2d (int N)
SparseMatrix	backward_euler_matrix (const Grid2D &grid, double coeff)
BackwardEulerOperator2D	backward_euler_operator (int N, double coeff)
BackwardEulerOperator2D	backward_euler_operator (const Grid2D &grid, double coeff)
LinearSolver	make_cg_solver (const SparseMatrix &A, real tol=1e-6)
Matrix	poisson2d_fd (const Matrix &f, int N)
	Solve \(-\Delta u=f\) using finite-difference eigenvalues.
Matrix	poisson2d (const Matrix &f, int N)
	Solve \(-\Delta u=f\) using continuous eigenvalues \((k\pi)^2\).

Function Documentation

backward_euler_matrix() [1/2]

SparseMatrix num::pde::backward_euler_matrix ( const Grid2D &  grid, double  coeff  )

inline

Definition at line 150 of file diffusion.hpp.

References backward_euler_matrix(), and num::Grid2D::N.

backward_euler_matrix() [2/2]

SparseMatrix num::pde::backward_euler_matrix ( int  N, double  coeff  )

inline

Definition at line 112 of file diffusion.hpp.

References num::SparseMatrix::from_triplets().

Referenced by backward_euler_matrix().

backward_euler_operator() [1/2]

BackwardEulerOperator2D num::pde::backward_euler_operator ( const Grid2D &  grid, double  coeff  )

inline

Definition at line 158 of file diffusion.hpp.

References backward_euler_operator(), and num::Grid2D::N.

backward_euler_operator() [2/2]

BackwardEulerOperator2D num::pde::backward_euler_operator ( int  N, double  coeff  )

inline

Definition at line 154 of file diffusion.hpp.

Referenced by backward_euler_operator().

diffusion_step_2d()

void num::pde::diffusion_step_2d ( Vector &  u, int  N, double  coeff, Backend  b = best_backend  )

inline

Definition at line 38 of file diffusion.hpp.

References num::axpy(), num::laplacian_stencil_2d_periodic(), and num::BasicVector< T >::size().

diffusion_step_2d_4th_dirichlet() [1/2]

void num::pde::diffusion_step_2d_4th_dirichlet ( ScalarField2D &  g, double  coeff, Backend  b = best_backend  )

inline

Definition at line 68 of file diffusion.hpp.

References diffusion_step_2d_4th_dirichlet(), num::ScalarField2D::N(), and num::ScalarField2D::vec().

diffusion_step_2d_4th_dirichlet() [2/2]

void num::pde::diffusion_step_2d_4th_dirichlet ( Vector &  u, int  N, double  coeff, Backend  b = best_backend  )

inline

Definition at line 53 of file diffusion.hpp.

References num::axpy(), num::laplacian_stencil_2d_4th(), and num::BasicVector< T >::size().

Referenced by diffusion_step_2d_4th_dirichlet().

diffusion_step_2d_dirichlet() [1/2]

void num::pde::diffusion_step_2d_dirichlet ( ScalarField2D &  g, double  coeff, Backend  b = best_backend  )

inline

Definition at line 62 of file diffusion.hpp.

References diffusion_step_2d_dirichlet(), num::ScalarField2D::N(), and num::ScalarField2D::vec().

diffusion_step_2d_dirichlet() [2/2]

void num::pde::diffusion_step_2d_dirichlet ( Vector &  u, int  N, double  coeff, Backend  b = best_backend  )

inline

Definition at line 44 of file diffusion.hpp.

References num::axpy(), num::laplacian_stencil_2d(), and num::BasicVector< T >::size().

Referenced by diffusion_step_2d_dirichlet().

laplacian_sparse_2d()

SparseMatrix num::pde::laplacian_sparse_2d ( int  N )

inline

Definition at line 74 of file diffusion.hpp.

References num::SparseMatrix::from_triplets().

make_cg_solver()

LinearSolver num::pde::make_cg_solver ( const SparseMatrix &  A, real  tol = 1e-6  )

inline

Definition at line 162 of file diffusion.hpp.

References num::operators::assume_spd(), num::cg(), and make_cg_solver().

Referenced by make_cg_solver().

poisson2d()

Matrix num::pde::poisson2d	(	const Matrix &	f,
		int	N
	)

Solve \(-\Delta u=f\) using continuous eigenvalues \((k\pi)^2\).

Definition at line 141 of file poisson.cpp.

References num::pi.

poisson2d_fd()

Matrix num::pde::poisson2d_fd	(	const Matrix &	f,
		int	N
	)

Solve \(-\Delta u=f\) using finite-difference eigenvalues.

Definition at line 109 of file poisson.cpp.

References num::pi.