`delsq`

Discrete Laplacian on a grid, as a sparse matrix.

Category: Other public functions: sparfun

Syntax

L = delsq(G)

Builds the five-point Laplacian for the grid numbered by G, with Dirichlet boundary.

Description

For each interior point, row k of L holds 4 on the diagonal and -1 in the column of every neighbor that is also interior. This is the matrix of the finite-difference approximation of the Laplace operator, scaled by the squared grid spacing. Combined with numgrid it gives test matrices for the Poisson equation on a square, L-shape or disk.

Input arguments

G: Grid numbering from numgrid: nonzero entries number the interior points, zeros are outside.

Output arguments

L: Sparse matrix with 4 on the diagonal and -1 for each neighbor.

Example

Square grid

G = numgrid('S', 4);
L = full(delsq(G))

Output

L = 4×4

     4    -1    -1     0
    -1     4     0    -1
    -1     0     4    -1
     0    -1    -1     4

See also

numgrid gallery spdiags sparse