AMG::Grid< EleType > Class Template Reference

Static functions for constructing A and b, the components of a linear system Au = b. More...

#include <grid.hpp>

Static Public Member Functions
static EleType	grid_spacing_h (size_t n)
	Compute the gridspacing h of a domain given n points in a direction.
static size_t	points_n_from_grid_spacing_h (EleType h=1./50)
	Compute the number of points in a direction given gridspacing h.
static Eigen::SparseMatrix< EleType >	second_order_central_difference (size_t n)
	Return second order central difference as linear operator on 1D function.
static Eigen::SparseMatrix< EleType >	laplacian (size_t n)
	Return coefficients matrix A for laplacian as linear operator on u(x,y) assuming homogenous dirichlet BCs.
static Eigen::Matrix< EleType, -1, 1 >	rhs (size_t n, std::function< EleType(EleType, EleType)> f=[](EleType x, EleType y) { return 5 *exp(-10 *(x *x+y *y));})
	Return right hand side vector b by evaluating f on a mesh grid in [-1, 1]^2.

Static Private Attributes
static const size_t	n_boundary_points = 2

Detailed Description

template<class EleType>
class AMG::Grid< EleType >

Static functions for constructing A and b, the components of a linear system Au = b.

Template Parameters

EleType

Member Function Documentation

grid_spacing_h()

template<class EleType >

static EleType AMG::Grid< EleType >::grid_spacing_h ( size_t n )

inlinestatic

Compute the gridspacing h of a domain given n points in a direction.

Parameters

n

Returns

EleType

laplacian()

template<class EleType >

static Eigen::SparseMatrix< EleType > AMG::Grid< EleType >::laplacian ( size_t n )

inlinestatic

Return coefficients matrix A for laplacian as linear operator on u(x,y) assuming homogenous dirichlet BCs.

References:

[1] : MIT Intro Linear PDEs

Parameters

n	Number of grid points in the x or y direction.

Returns

Eigen::SparseMatrix<EleType>

points_n_from_grid_spacing_h()

template<class EleType >

static size_t AMG::Grid< EleType >::points_n_from_grid_spacing_h ( EleType h = 1. / 50 )

inlinestatic

Compute the number of points in a direction given gridspacing h.

Parameters

h

Returns

size_t

rhs()

template<class EleType >

static Eigen::Matrix< EleType, -1, 1 > AMG::Grid< EleType >::rhs ( size_t n, std::function< EleType(EleType, EleType)> f = [](EleType x, EleType y) { return 5 * exp(-10 * (x * x + y * y)); } )

inlinestatic

Return right hand side vector b by evaluating f on a mesh grid in [-1, 1]^2.

Parameters

n	Number of interior grid points in the x or y direction.
f	Function to be evaluated at each mesh grid point.

Returns

Eigen::Matrix<EleType, -1, 1>

second_order_central_difference()

template<class EleType >

static Eigen::SparseMatrix< EleType > AMG::Grid< EleType >::second_order_central_difference ( size_t n )

inlinestatic

Return second order central difference as linear operator on 1D function.

Parameters

n	Number of grid points in the x or y direction.

Returns

Eigen::SparseMatrix<EleType>

Member Data Documentation

n_boundary_points

template<class EleType >

const size_t AMG::Grid< EleType >::n_boundary_points = 2

staticprivate

---

The documentation for this class was generated from the following file:

• include/amg/grid.hpp