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Five-point Dirichlet Laplacian as a Kronecker sum

If

T

is the one-dimensional Dirichlet second-difference matrix on

m

interior points, the two directional parts of the two-dimensional five-point Laplacian are

A_{x} = T \otimes I_{m}, A_{y} = I_{m} \otimes T .

They commute, and

A_{x} + A_{y}

is the Kronecker-sum discretization of the Laplacian.

Table of contents 125 3
- One-implicit-direction diffusion splitting Five-point Dirichlet Laplacian as a Kronecker sum 87 2
  - Stability limit of one-implicit-direction diffusion splitting One-implicit-direction diffusion splitting 37
  - Unconditionally stable corrected directional diffusion splitting One-implicit-direction diffusion splitting 26

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