Table of Content

Open Access iconOpen Access

ARTICLE

An Alternating Iterative MFS Algorithm for the Cauchy Problem in Two-Dimensional Anisotropic Heat Conduction

LiviuMarin 1

Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, Sector 1, P.O.Box 1-863, 010141 Bucharest, Romania. Telephone/Fax: +40-(0)21-3126736. E-mails: marin.liviu@gmail.com; liviu@imsar.bu.edu.ro

Computers, Materials & Continua 2009, 12(1), 71-100. https://doi.org/10.3970/cmc.2009.012.071

Abstract

In this paper, the alternating iterative algorithm originally proposed by Kozlov, Maz'ya and Fomin (1991) is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The iterative MFS algorithm is tested for Cauchy problems related to heat conduction in two-dimensional anisotropic solids to confirm the numerical convergence, stability and accuracy of the method.

Keywords


Cite This Article

APA Style
LiviuMarin, (2009). An alternating iterative MFS algorithm for the cauchy problem in two-dimensional anisotropic heat conduction. Computers, Materials & Continua, 12(1), 71-100. https://doi.org/10.3970/cmc.2009.012.071
Vancouver Style
LiviuMarin . An alternating iterative MFS algorithm for the cauchy problem in two-dimensional anisotropic heat conduction. Comput Mater Contin. 2009;12(1):71-100 https://doi.org/10.3970/cmc.2009.012.071
IEEE Style
LiviuMarin, “An Alternating Iterative MFS Algorithm for the Cauchy Problem in Two-Dimensional Anisotropic Heat Conduction,” Comput. Mater. Contin., vol. 12, no. 1, pp. 71-100, 2009. https://doi.org/10.3970/cmc.2009.012.071



cc Copyright © 2009 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 1991

    View

  • 1584

    Download

  • 0

    Like

Share Link