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

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  • Qing Chen
  • Baoqing Liu
  • Qikui Du

Abstract

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.

Suggested Citation

  • Qing Chen & Baoqing Liu & Qikui Du, 2014. "A D-N Alternating Algorithm for Solving 3D Exterior Helmholtz Problems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, July.
    • Handle: RePEc:hin:jnlmpe:418426
    DOI: 10.1155/2014/418426
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