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.

Highlights

  • Poisson’s equation ∇2u =f, an elliptic partial differential equation [1], was first published in 1813 in the Bulletin de la Société Philomatique by Siméon-Denis Poisson

  • We present an iterative scheme for solving Poisson’s equation in 2D

  • If we want to reduce our error to Ek ~ E0 and we wish to know how many iterations it will take to achieve this error reduction, using (32) we set ( ρ ( P) ρ (Q))k ~, and solving for k, we find it will take log ( )

Read more

Summary

A Poisson Solver Based on Iterations on a Sylvester System

How to cite this paper: Franklin, M.B. and Nadim, A. (2018) A Poisson Solver Based on Iterations on a Sylvester System.

Introduction
Sylvester Iterative Scheme
Finding Optimal Parameters α and β
Analysis
Results
Standard Sylvester Iterations
Multigrid Sylvester Iterations
Conclusion
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.