A pseudoinverse preconditioner built from the Kronecker structure of the finite-difference Laplacian makes PCG solve cuboid Poisson problems in two or three iterations.
Fiedler: Special matrices and their applications in numerical mathematics (2nd ed.), Dover Publications, Dover, 2008
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Tensor-structured PCG for finite difference solver of domain patterns in ferroelectric material
A pseudoinverse preconditioner built from the Kronecker structure of the finite-difference Laplacian makes PCG solve cuboid Poisson problems in two or three iterations.