A Bermúdez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 87-106.

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 : 10.1051/m2an/2013095
Classification : 74C10, 74D10, 65N30
Mots clés : viscoplastic materials, duality methods, solidification process
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     title = {A {Berm\'udez-Moreno} algorithm adapted to solve a viscoplastic problem in alloy solidification processes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {87--106},
     publisher = {EDP-Sciences},
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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 , Tome 48 (2014) no. 1, pp. 87-106. doi : 10.1051/m2an/2013095. http://www.numdam.org/articles/10.1051/m2an/2013095/

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