DescriptionSeveral scientific applications rely on sparse direct solvers for their numerical robustness. However, performance optimization for these solvers remains a challenging task, especially on GPUs. This is due to workloads of small dense matrices that are different in size. Matrix decompositions on such irregular workloads are rarely addressed on GPUs.
This paper addresses irregular workloads of matrix computations on GPUs and shows their impact on a sparse LU solver. We designed an interface for the basic matrix operations supporting problems of different sizes. The interface enables us to develop irrLU-GPU, an LU decomposition on matrices of different sizes. We demonstrate the impact of irrLU-GPU on sparse LU solvers using NVIDIA and AMD GPUs. Experimental results are shown for a sparse direct solver based on multifrontal sparse LU decomposition applied to linear systems arising from the simulation, using finite element discretization on unstructured meshes, of a high frequency indefinite Maxwell problem.