A Robust Two-Level Incomplete Factorization for (Navier–)Stokes Saddle Point Matrices

Fred W. Wubs; Jonas Thies

doi:10.1137/100789439

A Robust Two-Level Incomplete Factorization for (Navier–)Stokes Saddle Point Matrices

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/100789439 ◽

2011 ◽

Vol 32 (4) ◽

pp. 1475-1499 ◽

Cited By ~ 4

Author(s):

Fred W. Wubs ◽

Jonas Thies

Keyword(s):

Saddle Point ◽

Navier Stokes ◽

Incomplete Factorization ◽

Saddle Point Matrices

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On the eigenvalues of the saddle point matrices discretized from Navier–Stokes equations

Numerical Algorithms ◽

10.1007/s11075-017-0427-5 ◽

2017 ◽

Vol 79 (1) ◽

pp. 41-64 ◽

Cited By ~ 1

Author(s):

Na Huang ◽

Chang-Feng Ma

Keyword(s):

Saddle Point ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Saddle Point Matrices

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Threshold incomplete factorization constraint preconditioners for saddle-point matrices

Linear Algebra and its Applications ◽

10.1016/j.laa.2018.01.034 ◽

2018 ◽

Vol 545 ◽

pp. 76-107 ◽

Cited By ~ 1

Author(s):

Sangye Lungten ◽

Wil H.A. Schilders ◽

Joseph M.L. Maubach

Keyword(s):

Saddle Point ◽

Incomplete Factorization ◽

Saddle Point Matrices

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ILU Preconditioners for Nonsymmetric Saddle-Point Matrices with Application to the Incompressible Navier--Stokes Equations

SIAM Journal on Scientific Computing ◽

10.1137/15m1012311 ◽

2015 ◽

Vol 37 (5) ◽

pp. A2171-A2197 ◽

Cited By ~ 16

Author(s):

Igor N. Konshin ◽

Maxim A. Olshanskii ◽

Yuri V. Vassilevski

Keyword(s):

Saddle Point ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Saddle Point Matrices

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Preconditioners for regularized saddle point matrices

Journal of Numerical Mathematics ◽

10.1515/jnum.2011.005 ◽

2011 ◽

Vol 19 (2) ◽

Cited By ~ 2

Author(s):

O. Axelsson

Keyword(s):

Saddle Point ◽

Saddle Point Matrices

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A Note on the Eigenvalues of Saddle Point Matrices

2008 International Conference on Intelligent Computation Technology and Automation (ICICTA) ◽

10.1109/icicta.2008.33 ◽

2008 ◽

Author(s):

Zheng Li ◽

Tie Zhang ◽

Changjun Li

Keyword(s):

Saddle Point ◽

Saddle Point Matrices

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General finite-volume framework for saddle-point problems of various physics

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2021-0029 ◽

2021 ◽

Vol 36 (6) ◽

pp. 359-379

Author(s):

Kirill M. Terekhov

Keyword(s):

Saddle Point ◽

Finite Volume ◽

Navier Stokes ◽

Saddle Point Problems ◽

Surface Integral ◽

Matrix Coefficients ◽

Gauss Theorem ◽

Stability Issue ◽

Incompressible Elasticity ◽

Vector Flux

Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.

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