Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Transparent Boundary Conditions for the Helmholtz Equation in Some Ramified

Summary: Transparent Boundary Conditions for the
Helmholtz Equation in Some Ramified
Domains with a Fractal Boundary
Yves Achdou a,b,1
Christophe Sabot c
Nicoletta Tchou d,1
aUFR Math´ematiques, Universit´e Paris 7, Case 7012, 75251 Paris Cedex 05,
bLaboratoire Jacques-Louis Lions, Universit´e Paris 6, 75252 Paris Cedex 05.
c CNRS, UMPA, UMR 5669, 46, Allee d'Italie, F-69364 Lyon Cedex 07, France,
dIRMAR, Universit´e de Rennes 1, Rennes, France,
The paper addresses a class of boundary value problems in some self-similar ram-
ified domains, with the Laplace or Helmholtz equations. Much stress is placed on
transparent boundary conditions which allow the solutions to be computed in sub-
domains. 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


Source: Achdou, Yves - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6


Collections: Mathematics