Development of a GPU-accelerated implicit material point method for geotechnical engineering

A graphic processing unit (GPU)-accelerated implicit material point method (IMPM) is proposed in this paper, aiming at solving large-scale geotechnical engineering problems efficiently. The Cholesky decomposition direct solution method and the preconditioned conjugate gradient (PCG) iteration method are implemented to solve the governing equation implicitly. In order to build an efficient parallel computation framework, the sequential processes in these solution methods are optimized by adopting advancing parallel computational algorithms. The risk of data race during parallel computation is avoided using atomic operation. The GPU-accelerated IMPM is firstly tested by a 1-D compress column and cantilever beam simulation to validate the accuracy of the proposed IMPM. Then, the computational efficiency is tested using the sand column collapse simulation. The solution of the governing equation is the most time-consuming process, occupying more than 95% of the computational time. The PCG iteration method shows higher efficiency compared to Cholesky decomposition direct solution method. By analysing the memory usage, it is found that memory occupation is the primary limitation on the simulation scale of IMPM, especially using the Cholesky decomposition direct solution method. Finally, the GPU-accelerated IMPM is implemented in the simulation of the Xinmo landslide, showing high accuracy and computational efficiency.