Efficient Solvers for Large-Scale Saddle Point Systems Arising in Feedback Stabilization of Multi-field Flow Problems

Abstract : This article introduces a block preconditioner to solve large-scale block structured saddle point systems using a Krylov-based method. Such saddle point systems arise, e.g., in the Riccati-based feedback stabilization approach for multi-field flow problems as discussed in [2]. Combining well known approximation methods like a least-squares commutator approach for the Navier-Stokes Schur complement, an algebraic multigrid method, and a Chebyshev-Semi-Iteration, an efficient preconditioner is derived and tested for different parameter sets by using a simplified reactor model that describes the spread concentration of a reactive species forced by an incompressible velocity field.
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Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.11-20, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_2〉
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Peter Benner, Jens Saak, Martin Stoll, Heiko Weichelt. Efficient Solvers for Large-Scale Saddle Point Systems Arising in Feedback Stabilization of Multi-field Flow Problems. Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.11-20, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_2〉. 〈hal-01286209〉

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