A D-N Alternating Algorithm for Solving 3D Exterior Helmholtz Problems | Zendy

Qing Chen | Zendy; Baoqing Liu | Zendy; Qikui Du | Zendy

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A D-N Alternating Algorithm for Solving 3D Exterior Helmholtz Problems

Author(s) -

Qing Chen,

Baoqing Liu,

Qikui Du

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/418426

Subject(s) - domain decomposition methods , discretization , mathematics , helmholtz equation , bounded function , domain (mathematical analysis) , finite element method , convergence (economics) , boundary (topology) , schwarz alternating method , dirichlet boundary condition , helmholtz free energy , algorithm , boundary element method , boundary value problem , mathematical analysis , physics , quantum mechanics , economics , thermodynamics , economic growth

The nonoverlapping domain decomposition method, which is based on the natural boundary reduction, is applied to solve the exterior Helmholtz problem over a three-dimensional domain. The basic idea is to introduce a spherical artificial boundary; the original unbounded domain is changed into a bounded subdomain and a typical unbounded region; then, a Dirichlet-Nuemann (D-N) alternating method is presented; the finite element method and natural boundary element methods are alternately applied to solve the problems in the bounded subdomain and the typical unbounded subdomain. The convergence of the D-N alternating algorithm and its discretization are studied. Some numerical experiments are presented to show the performance of this method

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