A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations

TL;DR

This paper presents a scalable parallel Poisson solver using algebraic multigrid preconditioning for irregular domains, demonstrating improved performance and scalability in beam dynamic simulations.

Contribution

Introduces a fast, scalable parallel Poisson solver with optimized algebraic multigrid preconditioning for irregular domains in beam simulations.

Findings

Good scalability on up to 2048 processors

Significant improvements with variants of SA-AMG implementation

Outperforms FFT-based solver in certain scenarios

Abstract

We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences. Depending on the treatment of the Dirichlet boundary the resulting system of equations is symmetric or `mildly' nonsymmetric positive definite. In all cases, the system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. We demonstrate good scalability of the solver on distributed memory parallel processor with up to 2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver that is more commonly used for applications in beam dynamics.