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

10/30/2019
by   Rise Ooi, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/05/2017

Tuning Technique for Multiple Precision Dense Matrix Multiplication using Prediction of Computational Time

Although reliable long precision floating-point arithmetic libraries suc...
research
02/21/2019

GPU Acceleration of Real-Time Control Loops

Extreme Ultraviolet (EUV) photolithography is seen as the key enabler fo...
research
12/31/2021

Fast ultrametric matrix-vector multiplication

We study the properties of ultrametric matrices aiming to design methods...
research
05/26/2022

Single-pass Nyström approximation in mixed precision

Low rank matrix approximations appear in a number of scientific computin...
research
07/08/2022

Log-CCDM: Distribution Matching via Multiplication-free Arithmetic Coding

Recent years have seen renewed attention to arithmetic coding (AC). This...
research
09/12/2023

Ensemble Mask Networks

Can an ℝ^n→ℝ^n feedforward network learn matrix-vector multiplication? T...
research
12/12/2018

Application of the Fast Multipole Fully Coupled Poroelastic Displacement Discontinuity Method to Hydraulic Fracturing Problems

In this study, a fast multipole method (FMM) is used to decrease the com...

Please sign up or login with your details

Forgot password? Click here to reset