Multiscale seamless-domain method for nonperiodic fields: linear heat conduction analysis

TL;DR

This paper introduces and validates a multiscale seamless-domain method (SDM) for linear heat conduction analysis in nonperiodic fields, demonstrating high accuracy and computational efficiency comparable to existing methods.

Contribution

The paper extends the SDM to nonperiodic fields and compares its performance with finite difference and domain decomposition methods.

Findings

SDM achieves accuracy comparable to DDM with less than 0.02% error.

SDM reduces computational time to 13% of finite difference method.

SDM is effective for nonperiodic heat conduction problems.

Abstract

A multiscale numerical solver called the seamless-domain method (SDM) is used in linear heat conduction analysis of nonperiodic simulated fields. The practical feasibility of the SDM has been verified for use with periodic fields but has not previously been verified for use with nonperiodic fields. In this paper, we illustrate the mathematical framework of the SDM and the associated error factors in detail. We then analyze a homogeneous temperature field using the SDM, the standard finite difference method, and the conventional domain decomposition method (DDM) to compare the convergence properties of these methods. In addition, to compare their computational accuracies and time requirements, we also simulated a nonperiodic temperature field with a nonuniform thermal conductivity distribution using the three methods. The accuracy of the SDM is very high and is approximately equivalent to that of the DDM. The mean temperature error is less than 0.02% of the maximum temperature in the simulated field. The total central processing unit (CPU) times required for the analyses using the most efficient SDM model and the DDM model represent 13% and 17% of that of the finite difference model, respectively.