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Numerical methods such as the Finite Element Method (FEM) have beensuccessfully adapted to utilize the computational power of GPU accelerators.However, much of the effort around applying FEM to GPU's has been focused onhigh-order FEM due to higher arithmetic intensity and order of accuracy. Forapplications such as the simulation of subsurface processes, high levels ofheterogeneity results in high-resolution grids characterized by highlydiscontinuous (cell-wise) material property fields. Moreover, due to thesignificant uncertainties in the characterization of the domain of interest,e.g. geologic reservoirs, the benefits of high order accuracy are reduced, andlow-order methods are typically employed. In this study, we present a strategyfor implementing highly performant low-order matrix-free FEM operator kernelsin the context of the conjugate gradient (CG) method. Performance results ofmatrix-free Laplace and isotropic elasticity operator kernels are presented andare shown to compare favorably to matrix-based SpMV operators on V100, A100,and MI250X GPUs.

Performant low-order matrix-free finite element kernels on GPU architectures