Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities

2021 ◽  
Author(s):  
Evan North ◽  
Semyon Tsynkov ◽  
Eli Turkel
Keyword(s):  
Helmholtz Equation ◽  
Domain Decomposition ◽  
Strong Material ◽  
Material Discontinuities

An optimized Schwarz method with relaxation for the Helmholtz equation: the negative impact of overlap

2019 ◽  
Vol 53 (1) ◽  
pp. 249-268
Author(s):  
Yongxiang Liu ◽  
Xuejun Xu
Keyword(s):  
Convergence Rate ◽  
Helmholtz Equation ◽  
Domain Decomposition ◽  
Negative Impact ◽  
Mesh Size ◽  
Careful Analysis ◽  
Numerical Results ◽  
Wave Number ◽  
Convergence Behavior ◽  
Schwarz Method

In this paper we study how the overlapping size influences the convergence rate of an optimized Schwarz domain decomposition (DD) method with relaxation in the two subdomain case for the Helmholtz equation. Through choosing suitable parameters, we find that the convergence rate is independent of the wave number k and mesh size h, but sensitively depends on the overlapping size. Furthermore, by careful analysis, we obtain that the convergence behavior deteriorates with the increase of the overlapping size. Numerical results which confirm our theory are given.

scholarly journals A robust domain decomposition method for the Helmholtz equation with high wave number

2016 ◽  
Vol 50 (3) ◽  
pp. 921-944 ◽  
Author(s):  
Wenbin Chen ◽  
Yongxiang Liu ◽  
Xuejun Xu
Keyword(s):  
Helmholtz Equation ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Mesh Size ◽  
Relaxation Parameter ◽  
Point Of View ◽  
Wave Number ◽  
Theoretical Point ◽  
High Wave Number ◽  
High Wave

In this paper we present a robust Robin−Robin domain decomposition (DD) method for the Helmholtz equation with high wave number. Through choosing suitable Robin parameters on different subdomains and introducing a new relaxation parameter, we prove that the new DD method is robust, which means the convergence rate is independent of the wave number k for kh = constant and the mesh size h for fixed k. To the best of our knowledge, from the theoretical point of view, this is a first attempt to design a robust DD method for the Helmholtz equation with high wave number in the literature. Numerical results which confirm our theory are given.

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