A regularization method for the approximate particular solution of nonhomogeneous Cauchy problems of elliptic partial differential equations with variable coefficients

DOI10.1016/j.enganabound.2011.08.006zbMath1245.65150OpenAlexW1981042810MaRDI QIDQ444835

J. Herrera, H. S. Yoon

Publication date: 24 August 2012

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2011.08.006

zbMATH Keywords

regularizationCauchy problemradial basis functionmethod of approximate particular solutions

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items

Fast method of approximate particular solutions using Chebyshev interpolation, Application of the Trefftz method, on the basis of Stroh formalism, to solve the inverse Cauchy problems of anisotropic elasticity in multiply connected domains, Method of particular solutions for solving PDEs of the second and fourth orders with variable coefficients, Solution of Cauchy Problems by the Multiple Scale Method of Particular Solutions Using Polynomial Basis Functions, Collocation Methods for Cauchy Problems of Elliptic Operators via Conditional Stabilities, The method of approximate fundamental solutions (MAFS) for elliptic equations of general type with variable coefficients

Uses Software

• Regularization tools

Cites Work

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• Inverse source identification by Green's function
• An iterative method for solving the Cauchy problem for elliptic equations
• Bounds in the Cauchy problem for the Laplace equation
• On separation of minimal Riesz energy points on spheres in Euclidean spaces
• The role of the multiquadric shape parameters in solving elliptic partial differential equations
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions
• A least-squares preconditioner for radial basis functions collocation methods
• Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators
• The boundary element method for nonlinear problems
• Heritage and early history of the boundary element method
• Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
• Boundary-value problems for linear PDEs with variable coefficients
• The method of particular solutions for solving scalar wave equations
• The identification of a Robin coefficient by a conjugate gradient method
• Inverse source identification for Poisson equation
• A computational method for inverse free boundary determination problem
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• Unique continuation on a line for harmonic functions
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
• Stability for an inverse boundary problem of determining a part of a boundary
• The use of monotonicity for choosing the regularization parameter in ill-posed problems
• Direct solution of ill-posed boundary value problems by radial basis function collocation method