TY - JOUR

T1 - Domain decomposition method and nodal finite element for solving Helmholtz equation

AU - Bendali, Abderrahmane

AU - Boubendir, Yassine

PY - 2004/8/1

Y1 - 2004/8/1

N2 - The utilization of a non-overlapping domain decomposition method, in the framework of a resolution by finite elements, requires a particular treatment of the degrees of freedom shared by more than two subdomains. This is the case, for example, when solving a Laplace or Helmholtz equation by means of a conformal nodal finite element method. For convenience, such degrees of freedom will be called 'cross-points'. We describe here an approach permitting such a treatment. In contrast to a domain decomposition method in the strict sense, our approach requires a post-processing completing each iteration, which consists of solving a system whose size is the number of cross-points. We prove that the algorithm cannot break down and that it converges.

AB - The utilization of a non-overlapping domain decomposition method, in the framework of a resolution by finite elements, requires a particular treatment of the degrees of freedom shared by more than two subdomains. This is the case, for example, when solving a Laplace or Helmholtz equation by means of a conformal nodal finite element method. For convenience, such degrees of freedom will be called 'cross-points'. We describe here an approach permitting such a treatment. In contrast to a domain decomposition method in the strict sense, our approach requires a post-processing completing each iteration, which consists of solving a system whose size is the number of cross-points. We prove that the algorithm cannot break down and that it converges.

UR - http://www.scopus.com/inward/record.url?scp=4043085095&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4043085095&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2004.06.002

DO - 10.1016/j.crma.2004.06.002

M3 - Article

AN - SCOPUS:4043085095

SN - 1631-073X

VL - 339

SP - 229

EP - 234

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 3

ER -