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A Poisson Solver Based on Iterations on a Sylvester System

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Document pages: 15 pages

Abstract: We present an iterative scheme for solving Poisson’s equation in 2D. Using finitedifferences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations occuron this Sylvester system directly after introducing a deflation-type parameterthat enables optimized convergence. Analytical bounds are obtained on thespectral radii of the iteration matrices. Our method is comparable to SuccessiveOver-Relaxation (SOR) and amenable to compact programming via vector array operations. It can also be implemented within a multigrid frameworkwith considerable improvement in performance as shown herein.

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