Transient Heat Conduction Analysis Using a Boundary Element Method Based on the Convolution Quadrature Method

Abstract

In this work a fast method for the numerical solution of time-domain boundary integral formulations of transient problems governed by the heat equation is presented. In the formulation proposed, the convolution quadrature method is adopted, i.e., the basic integral equation of the time-domain boundary element method is numerically calculated by a quadrature formula whose weights are computed using the Laplace transform of the fundamental solution. In the case that the responses are required at a large number of interior points, it was observed that the convolution performed to calculate them is very time consuming. In this work it is shown that the discrete convolution can be obtained by means of fast Fourier transform techniques, hence reducing considerably the computational complexity. To validate the numerical techniques studied, results for some transient heat conduction examples are presented.