Premium
A fast multi‐level convolution boundary element method for transient diffusion problems
Author(s) -
Wang C.H.,
Grigoriev M. M.,
Dargush G. F.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1253
Subject(s) - boundary element method , convolution (computer science) , transient (computer programming) , boundary (topology) , diffusion , time domain , overlap–add method , domain (mathematical analysis) , computer science , mathematics , boundary value problem , element (criminal law) , algorithm , mathematical optimization , finite element method , mathematical analysis , engineering , fourier transform , physics , artificial intelligence , structural engineering , fourier analysis , artificial neural network , fractional fourier transform , law , political science , computer vision , thermodynamics , operating system
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 ( N 2 ) 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 ( N 3/2 ) for three 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. Copyright © 2005 John Wiley & Sons, Ltd.