A Robust Two-Level Incomplete Factorization for (Navier–)Stokes Saddle Point Matrices
نویسندگان
چکیده
منابع مشابه
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method introduced here has the following properties: (i) it is very robust, even close to the point where the solution becomes unstable; (ii) a single parameter contr...
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We consider the application of the conjugate gradient method to the solution of large symmetric, indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerica...
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Mastronardi and Van Dooren [this journal, 34 (2013) pp. 173–196] recently introduced the block antitriangular (“Batman”) decomposition for symmetric indefinite matrices. Here we show the simplification of this factorisation for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated in...
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The factorization method presented in this paper takes advantage of the special structures and properties of saddle point matrices. A variant of Gaussian elimination equivalent to the Cholesky’s factorization is suggested and implemented for factorizing the saddle point matrices block-wise with small blocks of order 1 and 2. The Gaussian elimination applied to these small blocks on block level ...
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Limited-memory incomplete Cholesky factorizations can provide robust preconditioners for sparse symmetric positive-definite linear systems. In this paper, the focus is on extending the approach to sparse symmetric indefinite systems in saddle-point form. A limited-memory signed incomplete Cholesky factorization of the form LDL is proposed, where the diagonal matrix D has entries ±1. The main ad...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2011
ISSN: 0895-4798,1095-7162
DOI: 10.1137/100789439