A novel interface integral formulation for 3D steady state thermal conduction problem for a medium with non-homogenous inclusions

A novel regularized interface integral equation for three-dimensional steady state heat conduction problems with non-homogeneous inclusions is developed. The proposed formulation only contains the fundamental solution of isotropic matrix. As a result, the fundamental solution of non-homogeneous inclusion, usually very difficult to obtain, is avoided. Domain integrals caused by the contrast of heat conductivities between the inclusions and the matrix are converted into equivalent interface integrals using the radial integration method by expressing the temperature gradient as a series of radial basis functions. Therefore, a pure interface integral equation is obtained and there is no need to discretize the inclusion into finite elements to evaluate the domain integral. For the determination of the flux and temperature, collocation points are distributed inside the inclusion to form a system of linear equations. To eliminate the geometrical errors and study the inclusions with arbitrary geometry, bivariate Non-Uniform Rational B-Splines basis functions are used to depict the boundaries of the inclusions. Numerical results are compared with available analytical solutions or finite element solutions.