Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains

This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these multiscale problems are successfully obtained based on multiscale asymptotic analysis. Then, the error analysis of SOTS solutions in the pointwise sense is given to illustrate the importance of developing the SOTS solutions. Furthermore, the error estimate for the SOTS approximate solutions in the integral sense is presented. In addition, a SOTS numerical algorithm is proposed to effectively solve these problems based on finite element method (FEM). Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed. In this paper, a unified two-scale computational framework is established for heat conduction problems of composite structures with diverse periodic configurations in different subdomains.