Heterogeneous Heat Conduction Problems by an Improved Element-Free Galerkin Method

Abstract

In this article an improved element-free Galerkin method is proposed to solve heat conduction problems with heterogeneous media. Because the method almost possesses interpolation property, the implementation of essential boundary condition is as simple as that in the finite-element method. In order to validate the proposed method, several heat conduction problems with different degrees of heterogeneity are presented. In these test problems, we focus on the influence of nodal distribution to the proposed method for heat conduction problems with heterogeneous media. It is shown that, for different degrees of heterogeneity, regardless of matter whether the node is located on the interface, accurate solutions can be obtained by the proposed method for heterogeneous heat conduction problems without a source term.

Acknowledgments

Support from the Natural Sciences Foundation of China (No. 11102101, No. 11171181), the Academic Mainstay Foundation of Hubei Province of China (No. T201103, No. Q20111208), and the Science Foundation of China Three Gorges University (No. KJ2009B058) are fully acknowledged.