Grid solution of problem with unilateral constraints

Abstract : The present study deals with the solution of a problem, defined in a three-dimensional domain, arising in fluid mechanics. Such problem is modelled with unilateral constraints on the boundary. Then, the problem to solve consists in minimizing a functional in a closed convex set. The characterization of the solution leads to solve a time-dependent variational inequality. An implicit scheme is used for the discretization of the time-dependent part of the operator and so we have to solve a sequence of stationary elliptic problems. For the solution of each stationary problem, an equivalent form of a minimization problem is formulated as the solution of a multivalued equation, obtained by the perturbation of the previous stationary elliptic operator by a diagonal monotone maximal multivalued operator. The spatial discretization of such problem by appropriate scheme leads to the solution of large scale algebraic systems. According to the size of these systems, parallel iterative asynchronous and synchronous methods are carried out on distributed architectures; in the present study, methods without and with overlapping like Schwarz alternating methods are considered. The convergence of the parallel iterative algorithms is analysed by contraction approaches. Finally, the parallel experiments are presented.
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https://hal.archives-ouvertes.fr/hal-01450772
Contributeur : Ming Chau <>
Soumis le : mardi 31 janvier 2017 - 13:17:03
Dernière modification le : mercredi 12 septembre 2018 - 17:46:03

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Ming Chau, Laouar Abdelhamid, Thierry Garcia, Pierre Spiteri. Grid solution of problem with unilateral constraints. Numerical Algorithms, Springer Verlag, 2017, 75 (4), pp.879-908. 〈https://www.springer.com/〉. 〈10.1007/s11075-016-0224-6〉. 〈hal-01450772〉

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