A Time-Space Multi-Level Boundary Element Approach for Time-Dependent Heat Diffusion

Abstract

A new space-time multi-level boundary element method (MLBEM) is developed for transient heat diffusion problems in two-dimensions. This approach extends the MLBEM approach for steady heat diffusion [1] to accommodate fast time convolution algorithm [2]. The space-time MLBEM algorithm developed in this presentation provides fast, accurate and memory efficient numerical solutions for time-dependent heat diffusion problems. Conventional BEM approaches using M boundary elements result in operation counts of order O(M2N2) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(M log MN3/2) for a two-dimensional model problem using the multi-level boundary element algorithm. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach.