MATRIX-FREE FINITE-ELEMENT COMPUTATIONS ON GRAPHICS PROCESSORS WITH ADAPTIVELY REFINED UNSTRUCTURED MESHES

摘要

This paper concerns efficient matrix-free finite-element algorithms on modern manycore processors such as graphics cards (GPUs) as an alternative to sparse matrix-vector products. In matrix-free finite element algorithms, the assembly and solution phases are merged, yielding a significantly lower memory bandwidth footprint, with a corresponding increase in efficiency on bandwidth limited processors. Additionally, no system matrix must be assembled or stored in memory. We present a GPU parallelization of the matrix-free method including a novel algorithm for resolving hanging-node constraints on the GPU, capable of simulation on adaptively refined grids. For second-order elements and higher in 3D, our GPU implementation of the adaptive algorithm is between 1.8 and 2.3 times faster than an existing optimized CPU version, on comparable hardware. Compared to a matrix-based implementation using CUSPARSE, we get a speedup of 8 and can solve problems 8 times larger in 3D.