Design of Parallel BEM Analyses Framework for SIMD Processors

Abstract

Parallel Boundary Element Method (BEM) analyses are typically conducted using a purpose-built software framework called BEM-BB. This framework requires a user-defined function program that calculates the i-th row and the j-th column of the coefficient matrix arising from the convolution integral term in the fundamental BEM equation. Owing to this feature, the framework can encapsulate MPI and OpenMP hybrid parallelization with \(\mathcal {H}\)-matrix approximation. Therefore, users can focus on implementing a fundamental solution or a Green’s function, which is the most important element in BEM and depends on the targeted physical phenomenon, as a user-defined function. However, the framework does not consider single instruction multiple data (SIMD) vectorization, which is important for high-performance computing and is supported by the majority of existing processors. Performing SIMD vectorization of a user-defined function is difficult because SIMD exploits instruction-level parallelization and is closely associated with the user-defined function. In this paper, a conceptual framework for enhancing SIMD vectorization is proposed. The proposed framework is evaluated using two BEM problems, namely, static electric field analysis with a perfect conductor and static electric field analysis with a dielectric, on Intel Broadwell (BDW) processor and Intel Xeon Phi Knights Landing (KNL) processor. It offers good vectorization performance with limited SIMD knowledge, as can be verified from the numerical results obtained herein. Specifically, in perfect conductor analyses conducted using the \(\mathcal {H}\)-matrix, the framework achieved performance improvements of 2.22x and 4.34x compared to the original BEM-BB framework for the BDW processor and KNL, respectively.