An adaptive isogeometric boundary element method for predicting the effective thermal conductivity of steady state heterogeneity

This work presents an adaptive isogeometric boundary element method (IGBEM) for the calculation of effective thermal conductivity of steady state heterogeneities. Based on the generalized self-consistent scheme (GSCS), some integral equation formulations which only contain the unknown temperatures on the interface are used to calculate the effective thermal conductivity of steady state composites. In our approach, the geometries of the inclusion and original matrix are described using NURBS basis functions. The advantage over currently used methods is that no geometrical errors exist in the analysis process. And the geometry data in the isogeometric GSCS model can be taken directly from CAD programs. In addition, based on the upper bound of the relative error of the Gaussian quadrature formula, an adaptive integration method is used to compute the boundary integrals, which makes the computation of the integrals easier and more efficient at optimal computational cost. The comparisons between the results obtained by the present method and the existing counterparts are carried out and the good agreement can be observed.