Details
| Original language | English |
|---|---|
| Pages (from-to) | 867-912 |
| Number of pages | 46 |
| Journal | Numerische Mathematik |
| Volume | 139 |
| Issue number | 4 |
| Early online date | 20 Feb 2018 |
| Publication status | Published - Aug 2018 |
Abstract
The solution of the wave equation in a polyhedral domain in R3 admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation as equivalent boundary integral equations in time domain, study the regularity properties of their solutions and the numerical approximation. Guided by the theory for elliptic equations, graded meshes are shown to recover the optimal approximation rates known for smooth solutions. Numerical experiments illustrate the theory for screen problems. In particular, we discuss the Dirichlet and Neumann problems, as well as the Dirichlet-to-Neumann operator and applications to the sound emission of tires.
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Numerische Mathematik, Vol. 139, No. 4, 08.2018, p. 867-912.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Boundary elements with mesh refinements for the wave equation
AU - Gimperlein, Heiko
AU - Meyer, Fabian
AU - Özdemir, Ceyhun
AU - Stark, David
AU - Stephan, Ernst P.
PY - 2018/8
Y1 - 2018/8
N2 - The solution of the wave equation in a polyhedral domain in R3 admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation as equivalent boundary integral equations in time domain, study the regularity properties of their solutions and the numerical approximation. Guided by the theory for elliptic equations, graded meshes are shown to recover the optimal approximation rates known for smooth solutions. Numerical experiments illustrate the theory for screen problems. In particular, we discuss the Dirichlet and Neumann problems, as well as the Dirichlet-to-Neumann operator and applications to the sound emission of tires.
AB - The solution of the wave equation in a polyhedral domain in R3 admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation as equivalent boundary integral equations in time domain, study the regularity properties of their solutions and the numerical approximation. Guided by the theory for elliptic equations, graded meshes are shown to recover the optimal approximation rates known for smooth solutions. Numerical experiments illustrate the theory for screen problems. In particular, we discuss the Dirichlet and Neumann problems, as well as the Dirichlet-to-Neumann operator and applications to the sound emission of tires.
UR - http://www.scopus.com/inward/record.url?scp=85041484083&partnerID=8YFLogxK
U2 - 10.1007/s00211-018-0954-6
DO - 10.1007/s00211-018-0954-6
M3 - Article
AN - SCOPUS:85041484083
VL - 139
SP - 867
EP - 912
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 4
ER -