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Preconditioning the $[1 quad-2 quad 1]$ Finite Difference matrix

Computational Science Asked on October 23, 2021

Let $A$ be the well known tridiagonal matrix coming from the 1D Finite difference discretization of the Laplacian, with stencil $frac{[1 quad-2 quad 1]}{h^2}$.

The system $Ax = b$ is very large, so an iterative method must be used. Also, it is symmetric and positive definite, so I could employ PCG to solve it. The big question is: what preconditioner should I set? I’ve searched on the web but, surprisingly, I couldn’t find anything.

Any reference, MatLab/C++ code or anything in between would be highly appreciated.

Best regards

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