Grid solution of problem with unilateral constraints

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...

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Bibliographic Details
Published in:Numerical algorithms 2017-08, Vol.75 (4), p.879-908
Main Authors: Chau, M., Laouar, A., Garcia, T., Spiteri, P.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Constraint modelling
Convexity
Decomposition
Discretization
Distributed, Parallel, and Cluster Computing
Fluid mechanics
Iterative algorithms
Iterative methods
Mathematical analysis
Mathematical models
Mathematical problems
Modeling and Simulation
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Partial differential equations
Theory of Computation
Time dependence
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-016-0224-6