Single and Dual-GPU Generalized Sparse Eigenvalue Solvers for Finding a Few Low-Order Resonances of a Microwave Cavity Using the Finite-Element Method

Abstract

This paper presents two fast generalized eigenvalue solvers for sparse symmetric matrices that arise when electromagnetic cavity resonances are investigated using the higher-order finite element method (FEM). To find a few low-order resonances, the locally optimal block conjugate gradient (LOBPCG) algorithm with null-space deflation is applied. The computations are expedited by using one or two graphical processing units (GPUs) as accelerators. The performance of the solver is tested for single and dual GPU hardware setups, making use of two types of GPU: NVIDIA Kepler K40s and NVIDIA Pascal P100s. The speed of the GPU-accelerated solvers is compared to a multithreaded implementation of the same algorithm using a multicore central processing unit (CPU, Intel Xeon E5-2680 v3 with twelve cores). It was found that, even for the least efficient setups, the GPU-accelerated code is approximately twice as fast as a parallel CPU-only implementation.