Computer implementations of iterative and non-iterative crystal plasticity solvers on high performance graphics hardware

We present parallel implementations of Newton---Raphson iterative and spectral based non-iterative solvers for single-crystal visco-plasticity models on a specialized computer hardware integrating a graphics-processing unit (GPU). We explore two implementations for the iterative solver on GPU multiprocessors: one based on a thread per crystal parallelization on local memory and another based on multiple threads per crystal on shared memory. The non-iterative solver implementation on the GPU hardware is based on a divide-conquer approach for matrix operations. The reduction of computational time for the iterative scheme was found to approach one order of magnitude. From detailed performance comparisons of the developed GPU iterative and non-iterative implementations, we conclude that the spectral non-iterative solver programed on a GPU platform is superior over the iterative implementation in terms of runtime as well as ease of implementation. It provides remarkable speedup factors exceeding three orders of magnitude over the iterative scalar version of the solver.