| Title:
|
Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D (English) |
| Author:
|
Zapletal, Jan |
| Author:
|
Bouchala, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
5 |
| Year:
|
2014 |
| Pages:
|
527-542 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations on these results. (English) |
| Keyword:
|
boundary element method |
| Keyword:
|
Galerkin discretization |
| Keyword:
|
Helmholtz equation |
| Keyword:
|
hypersingular boundary integral equation |
| MSC:
|
65N38 |
| idZBL:
|
Zbl 06391449 |
| idMR:
|
MR3255794 |
| DOI:
|
10.1007/s10492-014-0070-6 |
| . |
| Date available:
|
2014-09-29T08:58:37Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143929 |
| . |
| Reference:
|
[1] Grigorieff, R. D., Sloan, I. H.: Galerkin approximation with quadrature for the screen problem in $\mathbb{R}^3$.J. Integral Equations Appl. 9 (1997), 293-319. MR 1614302, 10.1216/jiea/1181076026 |
| Reference:
|
[2] Mauersberger, D., Sloan, I. H.: A simplified approach to the semi-discrete Galerkin method for the single-layer equation for a plate.M. Bonnet, et al. Mathematical Aspects of Boundary Element Methods Minisymposium during the IABEM 98 conference France, 1998, Chapman Hall, Boca Raton. Notes Math. 414 178-190 (2000). Zbl 0937.65142, MR 1719844 |
| Reference:
|
[3] McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations.Cambridge University Press Cambridge (2000). Zbl 0948.35001, MR 1742312 |
| Reference:
|
[4] Nédélec, J.-C.: Acoustic and Electromagnetic Equations. Integral Representations for Harmonic Problems.Applied Mathematical Sciences 144 Springer, New York (2001). Zbl 0981.35002, MR 1822275, 10.1007/978-1-4757-4393-7_3 |
| Reference:
|
[5] Of, G., Steinbach, O., Wendland, W. L.: The fast multipole method for the symmetric boundary integral formulation.IMA J. Numer. Anal. 26 (2006), 272-296. Zbl 1101.65114, MR 2218634, 10.1093/imanum/dri033 |
| Reference:
|
[6] Rjasanow, S., Steinbach, O.: The Fast Solution of Boundary Integral Equations.Mathematical and Analytical Techniques with Applications to Engineering Springer, New York (2007). Zbl 1119.65119, MR 2310663 |
| Reference:
|
[7] Sauter, S., Schwab, C.: Boundary Element Methods.Springer Series in Computational Mathematics 39 Springer, Berlin (2011). Zbl 1215.65183, MR 2743235, 10.1007/978-3-540-68093-2 |
| Reference:
|
[8] Zapletal, J.: The Boundary Element Method for the Helmholtz Equation in 3D.MSc. thesis, Department of Applied Mathematics, VŠB-TU, Ostrava (2011). |
| . |
