scholarly journals A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation

2021 ◽  
Vol 29 (2) ◽  
pp. 357-398
Author(s):  
Wei Leng & Lili Ju
Keyword(s):  
Helmholtz Equation ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method

Complex Trapped Modes of the Helmholtz Equation in Cross, S, and U Bends

2015 ◽  
Vol 07 (02) ◽  
pp. 1550024
Author(s):  
C. Y. Wang
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Domain Decomposition ◽  
Eigenfunction Expansion ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Local Effect ◽  
Trapped Modes ◽  
Simply Supported ◽  
Quantum Waveguides

The Helmholtz equation with zero boundary conditions is important in the vibration of membranes, simply-supported plates, and electromagnetic and quantum waveguides. Trapped modes, with a lowered frequency and limited local effect, may exist for infinite strips with local bends or enlargements. Infinite strips with a cross bulge, with an S bend and with a U bend are studied using an efficient eigenfunction expansion and domain decomposition method. As the bulge become larger, more trapped modes with more complexity appear. Some geometries do not support trapped modes at all. These results are new.

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