Mixed Precision Block-Jacobi Preconditioner: Algorithms, Performance Evaluation and Feature Analysis

TL;DR

This paper introduces two mixed precision algorithms for Block-Jacobi preconditioners, demonstrating significant speedups in iterative solvers for complex equations while analyzing convergence behaviors and matrix features.

Contribution

It presents novel fixed and adaptive mixed precision algorithms for Block-Jacobi preconditioning, with comprehensive performance evaluation and feature analysis.

Findings

Speedups of 1.3 to 1.8 times over high precision methods

Mixed precision preconditioners maintain accuracy

Convergence delay observed and analyzed in certain cases

Abstract

In this paper, we propose two mixed precision algorithms for Block-Jacobi preconditioner(BJAC): a fixed low precision strategy and an adaptive precision strategy. We evaluate the performance improvement of the proposed mixed precision BJAC preconditioners combined with the preconditioned conjugate gradient algorithm using problems including diffusion equations and radiation hydrodynamics equations. Numerical results show that, compared to the uniform high precision PCG algorithm, the mixed precision preconditioners can achieve speedups from 1.3 to 1.8 without sacrificing accuracy. Furthermore, we observe the phenomenon of convergence delay in some test cases for the mixed precision preconditioners, and further analyse the matrix features associate with the convergence delay behavior.