A Bermúdez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, p. 87-106
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The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez-Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper, we will improve the former algorithms by means of a generalized duality method with variable parameters and we will present numerical results showing the applicability of the resultant algorithm to solidification processes. Furthermore, we will describe a numerical procedure to choose a constant parameter for the Bermúdez-Moreno algorithm which gives good results when it is applied to solidification processes.

DOI : https://doi.org/10.1051/m2an/2013095
Classification:  74C10,  74D10,  65N30
Keywords: viscoplastic materials, duality methods, solidification process
@article{M2AN_2014__48_1_87_0,
     author = {Barral, P. and Quintela, P. and S\'anchez, M. T.},
     title = {A Berm\'udez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {1},
     year = {2014},
     pages = {87-106},
     doi = {10.1051/m2an/2013095},
     zbl = {1286.74025},
     mrnumber = {3177838},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_1_87_0}
}
Barral, P.; Quintela, P.; Sánchez, M. T. A Bermúdez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, pp. 87-106. doi : 10.1051/m2an/2013095. http://www.numdam.org/item/M2AN_2014__48_1_87_0/

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