An energy method of fundamental solutions for solving the inverse Cauchy problems of the Laplace equation

DOI10.1016/j.camwa.2018.03.038zbMath1417.35230OpenAlexW2796116982MaRDI QIDQ2001353

Chein-Shan Liu, Fajie Wang

Publication date: 3 July 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.03.038

zbMATH Keywords

Laplace equationinverse Cauchy problemmethod of fundamental solutions (MFS)energy regularizationenergy MFS (EMFS)

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Green's functions for elliptic equations (35J08)

Related Items (9)

The regularization B-spline wavelet method for the inverse boundary problem of the Laplace equation from noisy data in an irregular domain ⋮ Localized boundary knot method and its application to large-scale acoustic problems ⋮ Novel meshfree scheme for solving the inverse Cauchy problem of heat conduction ⋮ An energy regularization of the MQ-RBF method for solving the Cauchy problems of diffusion-convection-reaction equations ⋮ Optimal sources in the MFS by minimizing a new merit function: energy gap functional ⋮ Local non-singular knot method for large-scale computation of acoustic problems in complicated geometries ⋮ A homogenization function technique to solve the 3D inverse Cauchy problem of elliptic type equations in a closed walled shell ⋮ Many names of the Trefftz method ⋮ Codes for Distributed Storage

Cites Work

• Unnamed Item
• On choosing the location of the sources in the MFS
• On the choice of source points in the method of fundamental solutions
• A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation
• A new investigation into regularization techniques for the method of fundamental solutions
• The method of fundamental solutions for problems in potential flow
• Some comments on the ill-conditioning of the method of fundamental solutions
• The method of fundamental solutions for elliptic boundary value problems
• A BEM formulation in conjunction with parametric equation approach for three-dimensional Cauchy problems of steady heat conduction
• The collocation points of the fundamental solution method for the potential problem
• Trefftz energy method for solving the Cauchy problem of the Laplace equation
• An equilibrated method of fundamental solutions to choose the best source points for the Laplace equation
• A survey of applications of the MFS to inverse problems
• Multipole fast algorithm for the least-squares approach of the method of fundamental solutions for three-dimensional harmonic problems
• The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium
• Fourier regularization method for solving a Cauchy problem for the Laplace equation

This page was built for publication: An energy method of fundamental solutions for solving the inverse Cauchy problems of the Laplace equation