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

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Qing Chen ◽  
Baoqing Liu ◽  
Qikui Du
Keyword(s):  
Domain Decomposition Method ◽  
Three Dimensional ◽  
Boundary Element Methods ◽  
The Finite Element Method ◽  
Natural Boundary ◽  
Artificial Boundary ◽  
Nonoverlapping Domain ◽  
Helmholtz Problem ◽  
Nonoverlapping Domain Decomposition ◽  
Dimensional Domain

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.

scholarly journals The Schwartz Alternating Algorithm for Solving 3D Exterior Helmholtz Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Qing Chen ◽  
Baoqing Liu ◽  
Qikui Du
Keyword(s):  
Numerical Experiments ◽  
Domain Decomposition Method ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Natural Boundary ◽  
Helmholtz Problem ◽  
Artificial Boundaries ◽  
Overlapping Domain Decomposition ◽  
Natural Boundary Element Method ◽  
Element Method

Based on the natural boundary reduction, an overlapping domain decomposition method is discussed for solving exterior Helmholtz problem over a three-dimensional (3D) domain. By introducing two different artificial boundaries, the original unbounded domain is divided into a bounded subdomain and a typical unbounded region, and a Schwartz alternating method is presented. The finite element method and natural boundary element method are alternately applied to solve the problems in the bounded subdomain and the typical unbounded subdomain. Moreover, the convergence of the Schwartz alternating algorithm is studied. Finally, some numerical experiments are presented to show the performance of this method.

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