Performance dependence of GPU accelerated sparse linear system solvers on the finite element mesh structure in micromagnetic simulations

In this work, the relation between the sparsity patterns of sparse matrices created through FEM descretization of a Possion’s equation problem and the performance of sparse linear system solvers working on them has been investigated. Six representative mesh geometries from the realm of micromagnetic simulations are selected and scaled in resolution and thus also in the number of unknowns in the sparse linear system, to look into the scaling behaviour of the solvers. Various concrete solver implementations are benchmarked against these specimens on three different hardware platforms: CPU, consumer GPU and professional GPU. To gain further insight these benchmarks are also conducted on the same specimen represented in reduced (single) floating point precision. As a microbenchmark the performance of sparse matrix vector multiplications on the different platforms is recorded and put into relation to the solvers overall performance. By characterizing the specimen matrices through the mean distance of each nonzero element to its nearest nonzero neighbor, a novel metric is introduced which can accurately distinguish between matrices with fundamentally different sparsity patterns. A modern solver configuration is identified which offers significant performance gains compared to legacy implementations across all specimen. It is found that the sparse matrix characterization metric can be applied to judge on which matrices the use of a more expensive professional GPU will have the highest return on investment. In the same way, this discriminator can also be applied to choose an appropriate sparse matrix vector multiplication routine for a specific matrix