laplacian2.h File Reference

Helper routines for reordering/filling 2D structured grids. Used by many unit tests. More...

#include <myramath/MYRAMATH_EXPORT.h>
#include <myramath/utility/Number.h>
#include <utility>
#include <vector>

Include dependency graph for laplacian2.h:

Go to the source code of this file.

Classes
class	myra::SparseMatrix< Number >
	Stores an IxJ matrix A in compressed sparse column format. More...
class	myra::Natural2D
	A helper class that generates a natural ordering on a 2D structured grid of size IxJ. More...

Functions
Pattern	myra::stencil2 (int I, int J)
	Returns the Pattern of 5-point stencil on a 2D structured grid of size IxJ.
template<class Number >
SparseMatrix< Number >	myra::laplacian2 (int I, int J)
	Returns the graph laplacian of a 2D structured grid of size IxJ.
template<>
SparseMatrix< NumberS >	myra::laplacian2< NumberS > (int I, int J)
template<>
SparseMatrix< NumberD >	myra::laplacian2< NumberD > (int I, int J)
template<>
SparseMatrix< NumberC >	myra::laplacian2< NumberC > (int I, int J)
template<>
SparseMatrix< NumberZ >	myra::laplacian2< NumberZ > (int I, int J)
Permutation	myra::bisect2 (int I, int J)
	Reorders stencil2() / laplacian2() unknowns using nested bisection.
Pattern	myra::stencil2_unsymmetric (int I, int J, double density=0.5)
	Like stencil2(), but with entries randomly dropped to make it unsymmetric.

Detailed Description

Helper routines for reordering/filling 2D structured grids. Used by many unit tests.

For sake of example, the connectivity of laplacian2(5,5) is:

0—5–10–15–20 | | | | | 1—6–11–16–21 | | | | | 2—7–12–17–22 | | | | | 3—8–13–18–23 | | | | | 4—9–14–19–24

That is, a structured grid where orthogonal neighbors are connected with structural nonzeros.