Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

DOI10.1080/17415977.2011.590897zbMath1255.65202OpenAlexW2012546820MaRDI QIDQ3111155

B. Tomas Johansson, Johan Helsing

Publication date: 18 January 2012

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: http://publications.aston.ac.uk/id/eprint/20049/

zbMATH Keywords

Cauchy problemLaplace equationalternating methodDirichlet-to-Neumann mapsecond kind boundary integral equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for integral equations (65R32) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems for integral equations (45Q05) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (2)

The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method ⋮ Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM

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