Developments in numerical methods for transient scattering problems

2007 ◽  
pp. 236-249
Author(s):  
Patrick Joly
Keyword(s):  
Numerical Methods ◽  
Scattering Problems ◽  
Transient Scattering

Scattering Problems: Numerical Methods (FEM, Multiple Scattering)

2017 ◽  
pp. 171-208
Author(s):  
Didier Felbacq ◽  
Frédéric Zolla ◽  
André Nicolet
Keyword(s):  
Numerical Methods ◽  
Multiple Scattering ◽  
Scattering Problems

scholarly journals Numerical methods for scattering problems in periodic waveguides

2021 ◽  
Author(s):  
Ruming Zhang
Keyword(s):  
Numerical Methods ◽  
Periodic Solutions ◽  
Error Estimation ◽  
Standard Error ◽  
Contour Integral ◽  
Scattering Problems ◽  
Small Circle ◽  
Standard Error Estimation ◽  
Numerical Solver ◽  
Definition Of

AbstractIn this paper, we propose new numerical methods for scattering problems in periodic waveguides. Based on [20], the “physically meaningful” solution, which is obtained via the Limiting Absorption Principle (LAP) and is called an LAP solution, is written as an integral of quasi-periodic solutions on a contour. The definition of the contour depends both on the wavenumber and the periodic structure. The contour integral is then written as the combination of finite propagation modes and a contour integral on a small circle. Numerical methods are developed and based on the two representations. Compared with other numerical methods, we do not need the LAP process during numerical approximations, thus a standard error estimation is easily carried out. Based on this method, we also develop a numerical solver for halfguide problems. The method is based on the result that any LAP solution of a halfguide problem can be extended to the LAP solution of a fullguide problem. At the end of this paper, we also give some numerical results to show the efficiency of our numerical methods.

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