Effect of Mixed Precision Computing on H-Matrix Vector Multiplication in BEM Analysis

TL;DR

This paper explores how mixed precision computing using FP64 and FP32 can accelerate H-matrix vector multiplication in BEM analysis, reducing computation time while maintaining accuracy.

Contribution

It introduces three novel methods for integrating mixed precision computing into H-matrix vector multiplication and evaluates their effectiveness in BEM simulations.

Findings

Mixed precision methods reduce simulation time.

The methods maintain convergence rates.

Effectiveness confirmed through numerical tests.

Abstract

Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time and space complexity of dense matrix vector multiplication, and hence has been applied to numerous practical problems. In this paper, we aim to accelerate the H-matrix vector multiplication by introducing mixed precision computing, where we employ both binary64 (FP64) and binary32 (FP32) arithmetic operations. We propose three methods to introduce mixed precision computing to H-matrix vector multiplication, and then evaluate them in a boundary element method (BEM) analysis. The numerical tests examine the effects of mixed precision computing, particularly on the required simulation time and rate of convergence of the iterative (BiCG-STAB) linear solver. We confirm the effectiveness of the proposed methods.