A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

Authors:
Y. Boubendir;X. Antoine;C. Geuzaine
Affiliations:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, NJIT, Univ. Heights. 323 Dr. M.L. King Jr. Blvd, Newark, NJ 07102, USA;Institut Elie Cartan Nancy (IECN), Nancy University, INRIA Corida Team, B.P. 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France;University of Liège, Department of Electrical Engineering and Computer Science, Montefiore Institute, B28, B-4000 Liège, Belgium
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions.