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Performant Low-Order Matrix-Free Finite Element Kernels on GPE Architectures

DescriptionNumerical methods such as the Finite Element Method (FEM) have successfully leveraged the computational power of GPU accelerators. However, much of the effort around FEM on GPU’s has been focused on high order discretizations due to their higher arithmetic intensity and order of accuracy. For applications such as the simulation of geologic reservoirs, high levels of heterogeneity results in high-resolution grids characterized by highly discontinuous (cell-wise) material property fields. Additionally, the significant uncertainties typical of geologic reservoirs reduces the benefits of high order accuracy, and low order methods are typically employed. In this study, we present a strategy for implementing highly performant low-order matrix-free FEM operator kernels in the context of the conjugate gradient method. Performance results of the operator kernel are presented and are shown to compare favorably to matrix-based SpMV operators on V100, A100, and MI250X GPUs.

Authors

Randolph Settgast

Lawrence Livermore National Laboratory

William Tobin

Lawrence Livermore National Laboratory

Nicola Castelletto

Lawrence Livermore National Laboratory

Yohann Dudouit

Lawrence Livermore National Laboratory

Sergey Klevtsov

Stanford University

Ben Corbett