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Domain Decomposition and Model Reduction of Systems with Local Nonlinearities

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • K. Sun

    (Rice University, Department of Computational and Applied Mathematics, MS-134)

  • R. Glowinski

    (University of Houston, Department of Mathematics)

  • M. Heinkenschloss

    (Rice University, Department of Computational and Applied Mathematics, MS-134)

  • D. C. Sorensen

    (Rice University, Department of Computational and Applied Mathematics, MS-134)

Abstract

The goal of this paper is to combine balanced truncation model reduction and domain decomposition to derive reduced order models with guaranteed error bounds for systems of discretized partial differential equations (PDEs) with a spatially localized nonlinearities. Domain decomposition techniques are used to divide the problem into linear subproblems and small nonlinear subproblems. Balanced truncation is applied to the linear subproblems with inputs and outputs determined by the original in- and outputs as well as the interface conditions between the sub-problems. The potential of this approach is demonstrated for a model problem.

Suggested Citation

  • K. Sun & R. Glowinski & M. Heinkenschloss & D. C. Sorensen, 2008. "Domain Decomposition and Model Reduction of Systems with Local Nonlinearities," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 389-396, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_46
    DOI: 10.1007/978-3-540-69777-0_46
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