scholarly journals Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM

1995 ◽  
Vol 30 (9) ◽  
pp. 9-37 ◽  
Author(s):  
F. Ihlenburg ◽  
I. Babuška
Keyword(s):  
Finite Element ◽  
Helmholtz Equation ◽  
Finite Element Solution ◽  
Wave Number ◽  
Element Solution ◽  
High Wave Number ◽  
High Wave

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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