A Poisson Solver Based on Iterations on a Sylvester System ()
ABSTRACT
We present an iterative scheme for solving Poisson’s equation in 2D. Using finite
differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations occur
on this Sylvester system directly after introducing a deflation-type parameter
that enables optimized convergence. Analytical bounds are obtained on the
spectral radii of the iteration matrices. Our method is comparable to Successive
Over-Relaxation (SOR) and amenable to compact programming via vector/array operations. It can also be implemented within a multigrid framework
with considerable improvement in performance as shown herein.
Share and Cite:
Franklin, M. and Nadim, A. (2018) A Poisson Solver Based on Iterations on a Sylvester System.
Applied Mathematics,
9, 749-763. doi:
10.4236/am.2018.96052.
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