Creating a sparse tridiagonal matrix (for 2D finite difference second order Laplacian)

Question

Raphaël 2018-8-16

0
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https://ww2.mathworks.cn/matlabcentral/answers/415176-creating-a-sparse-tridiagonal-matrix-for-2d-finite-difference-second-order-laplacian

回答： msaitta 2018-8-16

Hi,

I'm trying to solve a 2D finite difference problem. I simplified the problem to solving a Ax = B equation. My issue is building the A matrix in Matlab rapidly.

The matrix I need to create is a sparce matrix with 5 diagonal lines. Also, at some lines, the whole line will be filled with 0 except for a 1 at the diagonal for my Dirichlet condition.

How can I write it in Matlab so it can create this matrix rapidly? I'm simulating a 400x400 environment which means a 16000x16000 sparce matrix.

Let's say A is my sparce matrix, is there a way I can call my diagonal matrix with a vector? Like A(1:5) would select the 5 first diagonal values and the same for not centered diagonal.