Efficient Numerical and Parallel Methods for Beam Dynamics Simulations

Efficient numerical and parallel methods have been used at Argonne National Laboratory (ANL) to develop petascalable software packages for beam dynamics simulations. This paper is an summary of the numerical methods and parallel algorithms used and developed in the past five years at ANL. It is an extension to the paper “Developing petascalable algorithms for beam dynamics simulations,” on proceeding of the first International Particle Accelerator Conference IPAC-2010 [33]. In this paper, numerical methods and parallel algorithms for our beam dynamics simulations are summarized. These include the standard particle-in-cell (PIC) method, direct Vlasov solvers and scalable Poisson solvers. Efficient parallel algorithms for these methods on supercomputers have been implemented and have successfully used tens of thousands processors on the IBM Blue Gene/P system at the Argonne Leadership Computing Facility (ALCF). Among them, scalable Poisson solvers in three dimensions, to account for space charge effects, are the most challenging. Several methods have been used to solve Poisson’s equation efficiently in different situations. The ALCF provides a suitable environment to perform large scale beam dynamics simulations. High-order numerical methods have been adopted to increase the accuracy. Domain decomposition methods have been used for parallelizing the solvers, and good scaling has been achieved. Preliminary results for the direct Vlasov solvers have been obtained in up to four dimensions. The parallel beam dynamics code PTRACK, which uses the PIC method to solve Poisson’s equation, has been used as a workhorse for end-to-end simulations and large-scale design optimizations for linear accelerators.