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Achdou, Yves; Sabot, Christophe; Tchou, Nicoletta

Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary. (English) Zbl 1109.65096

J. Comput. Phys. 220, No. 2, 712-739 (2007).
Summary: The paper addresses a class of boundary value problems in some self-similar ramified domains, with the Laplace or Helmholtz equations. Much stress is placed on transparent boundary conditions which allow the solutions to be computed in subdomains. A self similar finite element method is proposed and tested. It can be used for numerically computing the spectrum of the Laplace operator with Neumann boundary conditions, as well as the eigenmodes. The eigenmodes are normalized by means of a perturbation method and the spectral decomposition of a compactly supported function is carried out. Finally, a numerical method for the wave equation is addressed.

Cited in 10 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs

Keywords:

domains with fractal boundaries; Laplace equation; numerical examples; finite element method; perturbation method; spectral decomposition; wave equation
PDFBibTeX XMLCite
\textit{Y. Achdou} et al., J. Comput. Phys. 220, No. 2, 712--739 (2007; Zbl 1109.65096)
Full Text: DOI

References:

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