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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| Veröffentlicht in: | Numerical algorithms 2017-08, Vol.75 (4), p.879-908 |
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| container_title | Numerical algorithms |
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| creator | Chau, M. Laouar, A. Garcia, T. Spiteri, P. |
| description | 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. |
| doi_str_mv | 10.1007/s11075-016-0224-6 |
| format | Article |
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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. 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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.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computer Science</subject><subject>Constraint modelling</subject><subject>Convexity</subject><subject>Decomposition</subject><subject>Discretization</subject><subject>Distributed, Parallel, and Cluster Computing</subject><subject>Fluid mechanics</subject><subject>Iterative algorithms</subject><subject>Iterative methods</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematical problems</subject><subject>Modeling and Simulation</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Optimization</subject><subject>Original Paper</subject><subject>Partial differential equations</subject><subject>Theory of Computation</subject><subject>Time dependence</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kMFKxDAQhoMouK4-gLeCJw_RmbRJmuOy6K6w4EXPIW1St0u3WZNW8e3NUtGTpxmG7_8YfkKuEe4QQN5HRJCcAgoKjBVUnJAZcsmoYoKfph1QUsxVeU4uYtwBpBSTM1KsQmuz6LtxaH2f-SY7BF91bp99tsM2G_u2M4MLpstq38chmLYf4iU5a0wX3dXPnJPXx4eX5ZpunldPy8WG1gWDgVZS5S63Tkhbqsqiyq1BcI7n1kqHlSg5uMJAlRCjLPJKNqI2zKmcNRxYPie3k3drOn0I7d6EL-1Nq9eLjT7eAAsOUrIPTOzNxKb_30cXB73zY-jTe5opLAuVCjoacaLq4GMMrvnVIuhjkXoqMpmFPhapRcqwKRMT27-58Gf-P_QN6sR0lw</recordid><startdate>20170801</startdate><enddate>20170801</enddate><creator>Chau, M.</creator><creator>Laouar, A.</creator><creator>Garcia, T.</creator><creator>Spiteri, P.</creator><general>Springer US</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-1875-7020</orcidid></search><sort><creationdate>20170801</creationdate><title>Grid solution of problem with unilateral constraints</title><author>Chau, M. ; 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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. 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| 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 |
| title | Grid solution of problem with unilateral constraints |
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