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Multigrid and sparse-grid schemes for elliptic control problems with random coefficients

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Computing and Visualization in Science

Abstract

A multigrid and sparse-grid computational approach to solving nonlinear elliptic optimal control problems with random coefficients is presented. The proposed scheme combines multigrid methods with sparse-grids collocation techniques. Within this framework the influence of randomness of problem’s coefficients on the control provided by the optimal control theory is investigated. Numerical results of computation of stochastic optimal control solutions and formulation of mean control functions are presented.

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Authors and Affiliations

  1. Università degli Studi del Sannio, Dipartimento e Facoltà di Ingegneria, Palazzo Dell’Aquila Bosco Lucarelli, Corso Garibaldi 107, 82100, Benevento, Italy

    A. Borzì

  2. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstr. 36, 8010, Graz, Austria

    A. Borzì

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  1. A. Borzì
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Correspondence to A. Borzì.

Additional information

Supported in part by the Austrian Science Fund FWF project P18136-N13 “Quantum optimal control of semiconductor nanostructures” and F3205-N18 “Fast Multigrid Methods for Inverse Problems”.

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Borzì, A. Multigrid and sparse-grid schemes for elliptic control problems with random coefficients. Comput. Visual Sci. 13, 153–160 (2010). https://doi.org/10.1007/s00791-010-0134-4

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  • DOI: https://doi.org/10.1007/s00791-010-0134-4

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