Numerical simulation of ac conduction in three-dimensional heterogeneous materials

Abstract

Three-dimensional wavelet transformations and a finite-volume method are combined to develop an efficient method for computing the effective frequency-dependent conductivity of three-dimensional (3D) disordered materials at low temperatures. Such computations have, in the past, been beset by numerical difficulties arising from the local conductivities $g(\mathbf{r})$ varying over many orders of magnitude. A disordered matrerial is modeled by a 3D lattice, and it is assumed that conduction is thermally activated, so that $g(\mathbf{r})$ is related to the activation energies which are distributed according to a probability distribution function (PDF). Five distinct PDF's are used and, depending on the form of the PDF, the corresponding $g(\mathbf{r})$ varies over 3--17 orders of magnitude. The ac conduction is simulated over 10 orders of magnitude variations in the frequency. The speedup in the computations is up to four orders of magnitude.