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A Poisson Solver Based on Iterations on a Sylvester System
Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, USA
Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, USA
- 1 Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, USA
- 2 Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, USA
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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.
KeywordsPoisson’s EquationSylvester SystemMultigrid
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