A high-performance backend-agnostic Material Point Method solver in Julia

Abstract

We develop a user-friendly, high-performance Material Point Method (MPM) solver, MaterialPointSolver.jl, using the Julia language. The dual storage and interaction between material particles and the background grid limits the use of high-resolution models, and few solutions offer both performance and ease of use. Our backend-agnostic solver leverages GPU computing, enabling high-performance implementations across various platforms with a single codebase. We propose an effective memory throughput approach to evaluate GPU efficiency. The accuracy and efficiency of the solver are validated by four numerical examples, showing a 3.5$\times$ speedup on a single-threaded CPU and a 19.4$\times$ speedup on a 20-threaded CPU compared to optimized vectorized MATLAB code. Among four tested GPUs, it achieves a maximum average memory bandwidth utilization of 67%, reaching up to 78% (1453 GiB/s) in 2D tests. On the GH200 platform, the GPU shows a 21.3$\times$ speedup over its multi-threaded CPU. Our solver can handle approximately 19.7 million double-precision material particles on a consumer-grade GPU with 10 GB memory, while on the GH200, it can manage around 190 million material particles. This study introduces advanced software capabilities along with backend-agnostic framework expertise to the field of geotechnical engineering. By utilizing parallel algorithms specifically designed for MPM and integrating a newly developed performance evaluation approach, it ensures rapid prototyping and seamless transition to production. This implementation empowers researchers and practitioners to promote the widespread adoption of high-resolution MPM models in geotechnical engineering.