A new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods (BEM) for transient diffusion. This approach, which is based upon the multi-level multi-integration concepts of Brandt and Lubrecht, provides a fast, accurate and memory efficient time domain method for this entire class of problems. Conventional BEM approaches result in operation counts of order O(N2) 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(N3/2) for a couple of two-dimensional model problems using the multi-level convolution BEM. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach.
A Fast Time Convolution Algorithm for Unsteady Heat Diffusion Problems
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Wang, CH, Grigoriev, MM, & Dargush, GF. "A Fast Time Convolution Algorithm for Unsteady Heat Diffusion Problems." Proceedings of the ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. Volume 2, Parts A and B. Charlotte, North Carolina, USA. July 11–15, 2004. pp. 641-651. ASME. https://doi.org/10.1115/HT-FED2004-56322
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