Lower bounds for three-dimensional nonoverlapping domain decomposition algorithms

2003 ◽  
Vol 93 (3) ◽  
pp. 445-470 ◽  
Author(s):  
Susanne C. Brenner ◽  
Qingmi He
Keyword(s):  
Domain Decomposition ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Decomposition Algorithms ◽  
Nonoverlapping Domain ◽  
Nonoverlapping Domain Decomposition

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.

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