Error analysis for the operator marching method applied to range dependent waveguides
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Peng Li
Abstract
The relations between stability and accuracy of the operator marching method (OMM) are usually conflicting in waveguides with strong range dependence. To explain this phenomenon, this study intends to present an error estimate for the OMM in range dependent waveguides. We utilize “approximation level” to measure truncation error for a marching method in various range step sizes. Then, the error estimate is developed to analyze the performances of the OMM. Through an error analysis, we verify the following features of the OMM: (i) it is valid to apply the OMM in slowly varying waveguides with very large range step sizes; (ii) the OMM may blow up suddenly when the range dependence is strong and the step size is extremely small in the same time. We also develop a three-number set to describe the stability and accuracy level of a general marching method for computing wave propagation in a waveguide. In the end, extensive numerical experiments are implemented to verify the correctness of the error analysis.
Funding source: Xi’an Jiaotong University
Award Identifier / Grant number: NCET-08-0450
Award Identifier / Grant number: 985 II
Funding statement: Supported by NCET-08-0450 and 985 II of Xi’an Jiaotong University.
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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- A finite element method for the inverse problem of boundary data recovery in an oxygen balance model
- On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation
- Application of the factorization method to retrieve a crack from near field data
- Solution to a class of inverse problems for a system of loaded ordinary differential equations with integral conditions
- The variational formulation of an inverse problem for multidimensional nonlinear time-dependent Schrödinger equation
- Integral identity for a class of ill-posed problems generated by a parabolic equation
- A meshless method to the solution of an ill-posed problem
- About an inverse problem for a free boundary compressible problem in hydrodynamic lubrication
- Error analysis for the operator marching method applied to range dependent waveguides
Artikel in diesem Heft
- Frontmatter
- A finite element method for the inverse problem of boundary data recovery in an oxygen balance model
- On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation
- Application of the factorization method to retrieve a crack from near field data
- Solution to a class of inverse problems for a system of loaded ordinary differential equations with integral conditions
- The variational formulation of an inverse problem for multidimensional nonlinear time-dependent Schrödinger equation
- Integral identity for a class of ill-posed problems generated by a parabolic equation
- A meshless method to the solution of an ill-posed problem
- About an inverse problem for a free boundary compressible problem in hydrodynamic lubrication
- Error analysis for the operator marching method applied to range dependent waveguides
