Design of a parallel hybrid direct/iterative solver for CFD problems

Jonas Thies, Fred Wubs

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    We discuss the parallel implementation of a hybrid direct/iterative solver for a special class of saddle point matrices arising from the discretization of the steady Navier-Stokes equations on an Arakawa C-grid, the F-matrices. The two-level method described here has the following properties: (i) it is very robust, even hat comparatively high Reynolds Numbers; (ii) a single parameter controls fill and convergence, making the method straightforward to use; (iii) the convergence rate is independent of the number of unknowns; (iv) it can be implemented on distributed memory machines in a natural way; (v) the matrix on the second level has the same structure and numerical properties as the original problem, so the method can be applied recursively. The implementation focusses on generality, modularity, code reuse and recursiveness. The solver is implemented using building blocks of the Trilinos libraries. We show its performance on a parallel computer for the Navier-Stokes equations.
    Original languageEnglish
    Title of host publicationEPRINTS-BOOK-TITLE
    PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
    Number of pages8
    ISBN (Print)9781457721632
    Publication statusPublished - 2011

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