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Hierarchical matrix preconditioners for the Oseen equations

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Computing and Visualization in Science

Abstract

Hierarchical matrices provide a technique for the data-sparse approximation and matrix arithmetic of large, fully populated matrices. In particular, approximate inverses as well as approximate LU factorizations of finite element stiffness matrices may be computed and stored in nearly optimal complexity. In this paper, we develop efficient \(\mathcal{H}\)-matrix preconditioners for the Oseen equations. In particular, \(\mathcal{H}\)-matrices will provide efficient preconditioners for the auxiliary (scalar) discrete convection–diffusion and pressure Schur complement problems. We will provide various numerical tests comparing the resulting preconditioners with each other.

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Authors and Affiliations

  1. Tennessee Technological University, Box 5054, Cookeville, TN, 38505, USA

    Sabine Le Borne

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  1. Sabine Le Borne
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Correspondence to Sabine Le Borne.

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Communicated by C. Oosterlee.

This work was supported in part by the US Department of Energy under Grant No. DE-FG02-04ER25649 and in part by the National Science Foundation under grant No. DMS-0408950.

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Le Borne, S. Hierarchical matrix preconditioners for the Oseen equations. Comput. Visual Sci. 11, 147–157 (2008). https://doi.org/10.1007/s00791-007-0065-x

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  • DOI: https://doi.org/10.1007/s00791-007-0065-x

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