GPU-Accelerated LOBPCG Method with Inexact Null-Space Filtering for Solving Generalized Eigenvalue Problems in Computational Electromagnetics Analysis with Higher-Order FEM

Abstract

This paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact null-space filtering approach to find eigenvalues in electromagnetics analysis with higher-order FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from the Intel MKL on the Intel Xeon (E5-2680 v3, 12 threads) central processing unit (CPU) executed in parallel mode. Compared to the CPU reference implementation based on the Intel MKL functions, the proposed GPU-based LOBPCG method with inexact null-space filtering allowed us to achieve up to 2.9-fold acceleration.