Optimizing the GPU based method calculating energy deposition of beams coupling with discrete materials in dynamical and thermal simulations for higher computing efficiency

Abstract

In order to obtain more accurate energy deposition simulation results of beams coupling with discrete materials especially the granular materials in dynamical and thermal simulations, a discrete energy deposition calculation method was proposed previously to replace the equivalent homogenization method and accelerated with GPUs (Tian et al., 2021 [10]). However, it was found that the computing efficiency drops so severely with the increasing of the energy space size and the time required for simulations increases greatly unacceptably. In this work, for higher computing performance, based on the bottleneck analyses of CUDA (Compute Unified Device Architecture) kernels of the previous method, two improvements were made to the space cell marking phase and the energy deposition phase. In the space cell marking phase, a new proposed Lagrange-Euler Mapping Method searching the fixed space cells through flowing grains replaced the previous Euler Searching Method searching the flowing grains from fixed space cells. In the energy deposition phase, a warp aggregation method was used, assigning fewer threads to perform atomic operations. In the simulation of a granular-flow target bombarded by a 1 GeV proton beam setting a large energy computing space with a number of cells up to ∼108, the improved algorithm can effectively reduce the number of memory access instructions of CUDA warps. As a result, the computing performance was improved by 85% on A100 GPUs and 206% on K80 GPUs, making the dynamical and thermal simulations of granular-flow targets more efficient. Our method also could be beneficial for simulating the interactions between arbitrary source (or field) with a fixed spatial distribution and discrete materials.