An efficient tangent scheme for solving phase-change problems
type: Item
instance of: scholarly article
title: An efficient tangent scheme for solving phase-change problems
zbMATH Open document ID: 0631.73100
DOI: 10.1016/0045-7825(88)90060-6
author: Luis A. Crivelli
author: Mario A. Storti
author: S. R. Idelsohn
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: Using weak formulations and finite elements to solve heat-conduction problems with phase change finally leads to the solution, at each time step, of a nonlinear system of equations in the nodal temperatures. The Newton-Raphson scheme is an effective procedure to cope with this type of problems; however, the choice of a good appoximation to the tangent matrix is critical when the latent heat is comparatively large. In this work we derive an exact expression fo the tangent matrix and analyze the behavior of its terms for different values of the physical parameters of the system. We demonstrate that this method has good convergence properties. In fact, the rate of convergence is quadratic when the trial approximation is sufficiently close to the solution. Finally, several numerical examples are given.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74S99
zbMATH DE Number: 4026990
zbMATH Keywords: fixed domain method
zbMATH Keywords: weak formulations
zbMATH Keywords: finite elements
zbMATH Keywords: heat-conduction problems
zbMATH Keywords: phase change
zbMATH Keywords: nonlinear system of equations
zbMATH Keywords: Newton-Raphson scheme
zbMATH Keywords: appoximation to the tangent matrix
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90060-6
OpenAlex ID: W2007125314
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description: scientific article; zbMATH DE number 4026990