Details
| Original language | English |
|---|---|
| Pages (from-to) | 145-174 |
| Number of pages | 30 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 356 |
| Early online date | 23 Jul 2019 |
| Publication status | Published - 1 Nov 2019 |
Abstract
Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.
Keywords
- Approximation properties, Asymptotic expansion, Boundary element method, hp methods, Wave equation
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 356, 01.11.2019, p. 145-174.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - hp-version time domain boundary elements for the wave equation on quasi-uniform meshes
AU - Gimperlein, Heiko
AU - Özdemir, Ceyhun
AU - Stark, David
AU - Stephan, Ernst Peter
N1 - Funding information: We thank two anonymous reviewers for detailed comments, which have significantly improved this manuscript. H.G. acknowledges support by ERC Advanced Grant HARG 268105 and the EPSRC Impact Acceleration Account. C. Ö. was supported by the Avicenna foundation.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.
AB - Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.
KW - Approximation properties
KW - Asymptotic expansion
KW - Boundary element method
KW - hp methods
KW - Wave equation
UR - http://www.scopus.com/inward/record.url?scp=85069697558&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1811.01595
DO - 10.48550/arXiv.1811.01595
M3 - Article
AN - SCOPUS:85069697558
VL - 356
SP - 145
EP - 174
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -