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On the stability of direct time-domain boundary element methods for elastodynamics
- Source :
- Engineering Analysis with Boundary Elements. 96:138-149
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- Numerical stability has been a fundamental challenge in direct time-domain boundary element methods (TD-BEM) for elastodynamics. In this paper, an analytical framework for the evaluation of the critical aspect is presented. By casting a convolution integral-based TD-BEM algorithm in the form of a linear multi-step method with a hybrid amplification matrix and the incorporation of some fundamental characteristics of commonly-used transient Green's functions, a rigorous assessment of the problem is shown to be reducible to a standard spectral analysis in matrix theory by which the stability threshold can be clearly defined. Apt to be relevant to the evaluation of other TD-BEMs, the approach is applied to a regularized time-domain direct boundary element method with optional collocation weights and orders of solution variable projections as illustration. By virtue of the proposed formalism and a systematic parametric study, a proper resolution of the critical aspect for some past schemes as well as the versatility of the generalized TD-BEM algorithm as they pertain to the benchmark finite-domain square-bar and the infinite-domain cavity elastodynamic problems are given as examples.
- Subjects :
- Computer science
Applied Mathematics
General Engineering
010103 numerical & computational mathematics
01 natural sciences
010101 applied mathematics
Computational Mathematics
Matrix (mathematics)
Formalism (philosophy of mathematics)
Applied mathematics
Spectral analysis
Time domain
0101 mathematics
Boundary element method
Analysis
Numerical stability
Parametric statistics
Subjects
Details
- ISSN :
- 09557997
- Volume :
- 96
- Database :
- OpenAIRE
- Journal :
- Engineering Analysis with Boundary Elements
- Accession number :
- edsair.doi...........506744eae810d2ba923e37c6532b7bcd