The Fourier-Bessel method for solving the Cauchy problem connected with the Helmholtz equation

DOI10.1016/j.cam.2016.07.023zbMath1382.65366OpenAlexW2487723384MaRDI QIDQ730534

Deyue Zhang, Feng Liu, Xu Zhou, Ming-Hui Liu

Publication date: 28 December 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.07.023

zbMATH Keywords

Cauchy problemHelmholtz equationtruncated SVDFourier-Bessel expansionno meshing

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items (6)

Analysis of Dirichlet-Robin iterations for solving the Cauchy problem for elliptic equations ⋮ A direct imaging method for the exterior and interior inverse scattering problems ⋮ The Fourier–Bessel method for the inverse scattering problem of cavities ⋮ Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain ⋮ A Fourier-Bessel method with a regularization strategy for the boundary value problems of the Helmholtz equation ⋮ A class of homotopy with regularization for nonlinear ill-posed problems in Hilbert space

Cites Work

• A potential function method for the Cauchy problem of elliptic operators
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• The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
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• An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation
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• Operator adapted spectral element methods. I: Harmonic and generalized harmonic polynomials
• A meshless method for some inverse problems associated with the Helmholtz equation
• Numerical method for inverse scattering in two-layered background in near-field optics
• Increased stability in the continuation of solutions to the Helmholtz equation
• Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation
• The stability for the Cauchy problem for elliptic equations
• Optimal Choice of a Truncation Level for the Truncated SVD Solution of Linear First Kind Integral Equations When Data are Noisy
• A GSVD formulation of a domain decomposition method forplanar eigenvalue problems
• Inverse problems for partial differential equations
• An introduction to the mathematical theory of inverse problems

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