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Saraniti, M., Rein, A., Zandler, G., Vogl, P. and Lugli, P. (1996) An Efficient Multigrid Poisson Solver for Device Simulations. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 15, 141-150.
https://doi.org/10.1109/43.486661

has been cited by the following article:

• TITLE: A Poisson Solver Based on Iterations on a Sylvester System

  AUTHORS: Michael B. Franklin, Ali Nadim

  KEYWORDS: Poisson’s Equation, Sylvester System, Multigrid

  JOURNAL NAME: Applied Mathematics, Vol.9 No.6, June 29, 2018

  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.