The method of fundamental solutions for the two-dimensional inverse Stefan problem

DOI10.1080/17415977.2013.827180zbMath1304.65214OpenAlexW2027826332MaRDI QIDQ5496490

B. Tomas Johansson, Thomas Reeve, Daniel Lesnic

Publication date: 2 February 2015

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

Full work available at URL: https://doi.org/10.1080/17415977.2013.827180

zbMATH Keywords

Tikhonov's regularizationinverse Stefan problemmethod of fundamental solution

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Stefan problems, phase changes, etc. (80A22) Heat equation (35K05) Theoretical approximation in context of PDEs (35A35) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

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Cites Work

• On the choice of source points in the method of fundamental solutions
• Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods
• A method of fundamental solutions for transient heat conduction
• A method of fundamental solutions for the one-dimensional inverse Stefan problem
• Some comments on the ill-conditioning of the method of fundamental solutions
• The method of fundamental solutions for elliptic boundary value problems
• A bidimensional inverse Stefan problem: Identification of boundary value
• The use of fundamental Green's functions for the solution of problems of heat conduction in anisotropic media
• A method of fundamental solutions for two-dimensional heat conduction
• A survey of applications of the MFS to inverse problems
• Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions
• A computational method for inverse free boundary determination problem
• The Numerical Solution of the Inverse Stefan Problem in Two Space Variables
• The Stefan Problem: Comments on its Present State
• The Noncharacteristic Cauchy Problem for a Class of Equations with Time Dependence. II. Multidimensional Problems
• The inverse Stefan problem for the heat equation in two space variables
• The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions
• Method of fundamental solutions: singular value decomposition analysis
• A moving pseudo‐boundary method of fundamental solutions for void detection
• The method of functional equations for the approximate solution of certain boundary value problems
• Parabolic equations in one space variable and the non‐characteristic cauchy problem
• A method for the approximate solution of limiting problems in mathematical physics