Department of Mathematics

Boundary Element Methods for Wave Scattering

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Organisers C. Jerez-Hanckes
Place LFW E 13
Time Thursdays 15:15-17:00
Preparation Meeting Thursday 23.09.2010
First Session Thursday 12.10.2010
Contact C. Jerez-Hanckes
Language English
Prerequisites Knowledge of calculus and numerical methods
Description We will discuss theoretical and practical issues concerning the modeling of wave propagation in unbounded domains via of boundary element or Green's function methods. In particular, we will focus on the Helmholtz equation in $\mathbb{R}^{d}$, $d=2,3$ recurring in the modeling of Acoustics, Elasticity and Electromagnetism.
Seminar Details Seminar Details
Presentations O. Jecker Topic #1

F. Weber Topic #2

R. Ruehr Topic #3 and extra material

A. Paganini Topic #4

S. Haug Topic #5

S. Mueller Topic #6
Main References W. McLean. Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, UK, 2000.

S. Sauter and C. Schwab. Randelementmethoden. BG Teubner, Stuttgart, 2004.

O. Steinbach. Numerical approximation methods for elliptic boundary value problems. Springer, New York, 2008.
Bibliography X. Antoine and Y. Boubendir. An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations. International Journal of Computer Mathematics, 85(10):1473--1490, 2008.

R. Beatson and L. Greengard. A short course on fast multipole methods. In M. Ainsworth, K. Levesley, M. Marletta, and W. Light, editors, Wavelets, Multilevel Methods and Elliptic PDEs, Numerical Mathematics and Scientific Computation, pages 1--38. Clarendon Press, Oxford, 1997.

A. de Hoop. The vector integral-equation method for computing three-dimensional magnetic fields. Integral Equations Oper. Theory, 5:458--474, 1982.

L. Greengard, J.-F. Huang, V. Rokhlin, and S. Wandzura. Accelerating fast multipole methods for the Helmholtz equation at low frequencies. IEEE Computational Science and Engineering, 5(3):32--38, 1998.

G. Haase, B. Heise, M. Kuhn, and U. Langer. Adaptive domain decomposition methods for finite and boundary element equations. In W. Wendland, editor, Boundary element topics. Proceedings of the final conference of the priority research programme ``Boundary Element Methods'' 1989-1995 of the German Research Foundation, October 2--4, 1995 in Stuttgart, Germany, pages 121--147. Springer, Berlin, 1997.

R. Hiptmair. Operator preconditioning. Computers and Mathematics with Applications, 52(5):699--706, 2006.

G. Hsiao and W. Wendland. Domain decomposition in boundary element methods. In R. Glowinski, Y. Kuznetsov, G. Meurant, J. Periaux, and O. Widlund, editors,Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 41--49. SIAM Philadelphia, 1991.

C. Johnson and J.C. Nedelec. On the coupling of boundary integral and finite element methods. Math. Comp., 35(152), 1980.

F.-J. Sayas. The validity of Johnson-Nedelec's BEM-FEM coupling on polygonal interfaces. SIAM J. Math. Anal., 47:3451--3463, 2009.

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