Convergence estimation and characteristic analysis of a two-level iterative algorithm for the discretized three-temperature energy linear systems

TL;DR

This paper analyzes the convergence properties of a two-level iterative method for solving discretized three-temperature energy systems, providing theoretical bounds and insights into factors affecting its efficiency.

Contribution

It offers a detailed convergence analysis of the PCTL algorithm based on AMG theory and identifies key algebraic features influencing its performance.

Findings

Provided an upper bound on the convergence factor of PCTL

Identified diagonal dominance and coupling strength as key factors affecting convergence

Theoretical analysis supports practical application and optimization of the algorithm

Abstract

For solving the discretized three-temperature energy linear systems, Xu et al. proposed a physical-variable based coarsening two-level iterative method (PCTL algorithm) in 2009 and verified its efficiency by numerical experiments in practical applications. In this paper, we study in detail the specific convergence property of the PCTL algorithm based on the theory of algebraic multigrid method (AMG),and give a reasonable upper bound on the convergence factor, which provides a theoretical guarantee for the PCTL algorithm. Moreover, we also analyse the algebraic features that affect the convergence of the PCTL algorithm, such as diagonal dominance and coupling strength, hoping provides theoretical guidance for the applications and algorithm optimization of the PCTL algorithm.