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Compression of time‐generated matrices in two‐dimensional time‐domain elastodynamic BEM analysis
Author(s) -
Soares D.,
Mansur W. J.
Publication year - 2004
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.1111
Subject(s) - time domain , interpolation (computer graphics) , lagrange polynomial , algorithm , convolution (computer science) , chebyshev polynomials , mathematics , domain (mathematical analysis) , linear interpolation , process (computing) , computer science , mathematical analysis , computer graphics (images) , polynomial , machine learning , artificial neural network , operating system , animation , computer vision
This paper describes a new scheme to improve the efficiency of time‐domain BEM algorithms. The discussion is focused on the two‐dimensional elastodynamic formulation, however, the ideas presented apply equally to any step‐by‐step convolution based algorithm whose kernels decay with time increase. The algorithm presented interpolates the time‐domain matrices generated along the time‐stepping process, for time‐steps sufficiently far from the current time. Two interpolation procedures are considered here (a large number of alternative approaches is possible): Chebyshev–Lagrange polynomials and linear. A criterion to indicate the discrete time at which interpolation should start is proposed. Two numerical examples and conclusions are presented at the end of the paper. Copyright © 2004 John Wiley & Sons, Ltd.