Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

DOI10.1515/jiip-2015-0053zbMath1351.35257OpenAlexW2552073824MaRDI QIDQ2520114

B. Tomas Johansson, Ihor Borachok, R. S. Chapko

Publication date: 13 December 2016

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://publications.aston.ac.uk/id/eprint/29649/1/Elliptic_3_dimensional_Cauchy_problem_by_the_alternating_method_and_boundary_integral_equations.pdf

zbMATH Keywords

integral equationCauchy problemLaplace equationalternating method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Ill-posed problems for PDEs (35R25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

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• An analysis of inverse source problems with final time measured output data for the heat conduction equation: A semigroup approach
• Boundary integral equations
• Identification of sound-soft 3D obstacles from phaseless data
• An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation
• Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in \(\mathbb R^3\)
• A high-order algorithm for obstacle scattering in three dimensions
• On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach
• Direct and iteration methods for solving inverse and ill-posed problems
• Integral equations for inverse problems in corrosion detection from partial Cauchy data
• On the Alternating Method for Cauchy Problems and Its Finite Element Discretisation
• Finite element methods for coefficient identification in an elliptic equation
• A Direct Integral Equation Method for a Cauchy Problem for the Laplace Equation in 3-Dimensional Semi-Infinite Domains
• On the Numerical Solution of the Laplace Equation withComplete and Incomplete Cauchy Data Using IntegralEquations
• A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation
• A New Spectral Boundary Integral Collocation Method for Three-Dimensional Potential Problems
• Optimizational method for solving the Cauchy problem for an elliptic equation
• A direct boundary integral equation method for the numerical construction of harmonic functions in three-dimensional layered domains containing a cavity
• An alternating iterative procedure for the Cauchy problem for the Helmholtz equation