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Analysis of three-dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method. (English) Zbl 1416.80006
Summary: In this paper, an advanced boundary element method (BEM) is developed for solving three-dimensional (3D) anisotropic heat conduction problems in thin-walled structures. The troublesome nearly singular integrals, which are crucial in the applications of the BEM to thin structures, are calculated efficiently by using a nonlinear coordinate transformation method. For the test problems studied, promising BEM results with only a small number of boundary elements have been obtained when the thickness of the structure is in the orders of micro-scales $$(10^{-6})$$, which is sufficient for modeling most thin-walled structures as used in, for example, smart materials and thin layered coating systems. The advantages, disadvantages as well as potential applications of the proposed method, as compared with the finite element method (FEM), are also discussed.

##### MSC:
 80M15 Boundary element methods applied to problems in thermodynamics and heat transfer 65N38 Boundary element methods for boundary value problems involving PDEs
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