Title of Paper:The coupled method of multi-domain BEM and element differential method for solving multi-scale problems

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Date of Publication:2020-04-01

Journal:ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

Included Journals:EI、SCIE

Volume:113

Page Number:145-155

ISSN No.:0955-7997

Key Words:Multi-Domain Boundary Element Method; Element Differential Method; Multi-Scale Problem; Heat Conduction, Elasticity

Abstract:In this paper, the element differential method (EDM), a new numerical method proposed recently, is coupled with the multi-domain boundary element method (MDBEM), an improved Boundary Element Method (BEM), for solving general multi-scale heat conduction and elasticity problems. The basic algebraic equations in MDBEM are formulated in terms of displacements/temperatures and surface tractions/heat fluxes, which are the same as those in EDM. Therefore, when coupling these two methods, we don't need to transform the variables such as the equivalent nodal forces into the surface tractions as done in the Finite Element Method (FEM). The key task in the proposed coupled method is to use the displacement/temperature consistency conditions and the surface traction/heat flux equilibrium equations at interface nodes to eliminate all BEM nodes except for those on the interfaces, rather than to iterate. After elimination, the coefficient matrix we get is sparse although a small part is dense. The coupled method inherits the advantages of EDM in flexibility and computational efficiency, and the advantage of BEM in the robustness of treating multi-scale problems. Three numerical examples of general heat conduction and mechanical problems are given to demonstrate the correctness and efficiency of this coupled method.