Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

DOI10.1080/17415971003624322zbMath1190.65147OpenAlexW2158984931MaRDI QIDQ3565079

B. Tomas Johansson, Johan Helsing

Publication date: 27 May 2010

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/20051/

zbMATH Keywords

Fredholm integral equationsregularizationCauchy problemnumerical examplesharmonic functionLaplace equationill-posed problemNyström methodalternating methodNyström discretizationsecond kind boundary integral equation

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38)

Related Items (14)

An a posteriori truncation method for some Cauchy problems associated with Helmholtz-type equations ⋮ A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source ⋮ A local regularization scheme of Cauchy problem for the Laplace equation on a doubly connected domain ⋮ On the discretization of Laplace's equation with Neumann boundary conditions on polygonal domains ⋮ A boundary integral equation method for numerical solution of parabolic and hyperbolic Cauchy problems ⋮ Recovery of harmonic functions from partial boundary data respecting internal pointwise values ⋮ An order optimal regularization method for the Cauchy problem of a Laplace equation in an annulus domain ⋮ Calculation of the heat flux near the liquid-gas-solid contact line ⋮ Numerical analytic continuation on bounded domains ⋮ On the Numerical Solution of Elliptic Partial Differential Equations on Polygonal Domains ⋮ A coupled complex boundary method for the Cauchy problem ⋮ Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations ⋮ On the use of an integral equation approach for the numerical solution of a Cauchy problem for Laplace equation in a doubly connected planar domain ⋮ On the Alternating Method for Cauchy Problems and Its Finite Element Discretisation

Cites Work

• Integral equation methods for elliptic problems with boundary conditions of mixed type
• An alternating method for an inverse Cauchy problem
• Relaxation procedures for an iterative algorithm for solving the Cauchy problem for the Laplace equation
• A MANN ITERATIVE REGULARIZATION METHOD FOR ELLIPTIC CAUCHY PROBLEMS
• Uniqueness in the Cauchy Problem for Partial Differential Equations
• Solving Cauchy problems by minimizing an energy-like functional
• Iterative methods for solving a nonlinear boundary inverse problem in glaciology
• The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• Convergence of an Alternating Method to Solve the Cauchy Problem for Poisson's Equation
• Cortical mapping by Laplace–Cauchy transmission using a boundary element method
• An alternating method for the stationary Stokes system
• Boundary element method for the Cauchy problem in linear elasticity.

This page was built for publication: Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques