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Front. Inform. Technol. Electron. Eng.  2010, Vol. 11 Issue (12): 998-1008    DOI: 10.1631/jzus.C0910732
    
A numerical local orthogonal transform method for stratified waveguides
Peng Li, Wei-zhou Zhong, Guo-sheng Li, Zhi-hua Chen
School of Economics and Finance, Xi\'an Jiaotong University, Xi\'an 710061, China, Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450045, China, Department of Mathematics, Zhongyuan University of Technology, Zhengzhou 450007, China, Science Department, Zhijiang College of Zhejiang University of Technology, Hangzhou 310027, China
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Abstract  Flattening of the interfaces is necessary in computing wave propagation along stratified waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure.

Key wordsHelmholtz equation      Local orthogonal transform      Dirichlet-to-Neumann (DtN) reformulation      Marching method      Internal interface     
Received: 29 November 2009      Published: 09 December 2010
CLC:  O29  
  O42  
Cite this article:

Peng Li, Wei-zhou Zhong, Guo-sheng Li, Zhi-hua Chen. A numerical local orthogonal transform method for stratified waveguides. Front. Inform. Technol. Electron. Eng., 2010, 11(12): 998-1008.

URL:

http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C0910732     OR     http://www.zjujournals.com/xueshu/fitee/Y2010/V11/I12/998


A numerical local orthogonal transform method for stratified waveguides

Flattening of the interfaces is necessary in computing wave propagation along stratified waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure.

关键词: Helmholtz equation,  Local orthogonal transform,  Dirichlet-to-Neumann (DtN) reformulation,  Marching method,  Internal interface 
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