A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations

Authors:
A. Adelmann;P. Arbenz;Y. Ineichen
Affiliations:
Paul Scherrer Institut, CH-5234 Villigen, Switzerland;ETH Zürich, Chair of Computational Science, Universitätsstrasse 6, CH-8092 Zürich, Switzerland;Paul Scherrer Institut, CH-5234 Villigen, Switzerland and ETH Zürich, Chair of Computational Science, Universitätsstrasse 6, CH-8092 Zürich, Switzerland
Venue:
Journal of Computational Physics
Year:
2010

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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 iterative solver with an FFT-based solver that is more commonly used for applications in beam dynamics.