Boundary Integral Solver Approaches for Particle Accelerator Simulation Problems and Deployment on NERSC Hardware

Abstract

Reservoir Labs, through a project titled MACHB (Multipole Accelerator Codes for Hadron Beams) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> , is developing a Fast Multipole Method [1]–[7] (FMM)-based tool for higher fidelity modeling of particle accelerators for high-energy physics with an initial focus on the next generation of Fermilab’s Synergia simulation package [8]. MACH-B incorporates (1) highly-scalable, high-performance and generally-applicable FMM-based algorithms [5]–[7], [9] to accurately model space-charge effects in high-intensity hadron beams and (2) boundary integral approaches [10]–[12] to handle singular effects near the beam pipe using advanced quadratures. MACH-B will allow for more complex beam dynamics simulations that more accurately capture bunch effects and predict beam loss. By introducing an abstraction layer to hide FMM implementation and parallelization complexities, this project will also remove one of the key impediments to the adoption of FMMs by the accelerator physics community.In this work, we focus on the following results for the boundary integral solver components of the MACH-B project:•Study of the relative accuracies of the hedgehog [12] boundary integral solver when evaluating potential and gradient solutions to Laplace’s equation with Dirichlet boundary conditions•Study of a single-bunch, Gaussian-distributed set of charges within a conducting pipe, using an embedded boundary solverResults show the ability to simulate charge densities inside of a pipe-shaped object for accelerator simulations, running experiments on a collection of NERSC’s Cori Cray XC40 Intel Xeon "Haswell" processor nodes <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and Reservoir’s internal computational resources.