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In this paper, a boundary-volume based Lippmann Schwinger integral equation for numerical homogenization problems of heterogeneous conductive materials is formulated. The method can solve problems with arbitrary contrast ratio and imperfect interface behavior. In the formulation, the interior temperature gradient within each homogeneous phase is connected to the material dissimilarity quantities at all boundaries between different phases. The Kapitza interface model can also be included in the formulation. Using Fourier discretization, the basic iteration schemes and Bi-Conjugate Gradient Stabilized schemes based on the new formulation converge very fast. Comparison with standard Finite Element Method is also presented and confirm the accuracy of the method.

Fast Fourier Transform; Numerical homogenization method; Infinite contrast; Kapitza resistance model