A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations. (English) Zbl 1192.78010
Summary: 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.
MSC:
| 78A35 | Motion of charged particles |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 81V25 | Other elementary particle theory in quantum theory |
| 78A30 | Electro- and magnetostatics |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 65Y05 | Parallel numerical computation |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
Poisson equation; irregular domains; preconditioned conjugate gradient algorithm; algebraic multigrid; beam dynamics; space-chargeReferences:
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