Block Conjugate Gradient Method with Multilevel Preconditioning and GPU Acceleration for FEM Problems in Electromagnetics
In this paper a GPU-accelerated block conjugate gradient solver with multilevel preconditioning is presented for solving large system of sparse equations with multiple right hand-sides (RHSs) which arise in the finite-element analysis of electromagnetic problems. We demonstrate that blocking reduces the time to solution significantly and allows for better utilization of the computing power of GPUs, especially when the system matrix is complex-valued. We show that, for a complex-valued sparse matrix with over 1.2 million unknowns and sixteen righthand-sides, the block version of the preconditioned conjugategradient method using a single NVIDIA Tesla P100 accelerator is almost three times faster than a nonblocked version. Numerical tests have also shown that a CPU-only nonblocked complex implementation is unlikely to benefit much from blocking. Compared to an optimized CPU-only solver using an Intel Xeon E5-2680 v3 with twelve cores, the nonblocked GPU-accelerated version was 4.5 times faster, while the blocked version was 12.4 times faster.
Adam Dziekoński, Michał Mrozowski. (2018). Block Conjugate Gradient Method with Multilevel Preconditioning and GPU Acceleration for FEM Problems in Electromagnetics, 17(6), 1039-1042. https://doi.org/10.1109/lawp.2018.2830124
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