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Laplacian Preconditioning for the Inverse Arnoldi Method

Part of: Numerical problems in dynamical systems Hydrodynamic stability Numerical linear algebra Approximation methods and numerical treatment of dynamical systems

Published online by Cambridge University Press:  23 November 2015

Laurette S. Tuckerman
Laurette S. Tuckerman*
Affiliation:
PMMH(UMR 7636 CNRS - ESPCI - UPMC Paris 6 - UPD Paris 7 - ParisTech - PSL), 10 rue Vauquelin, 75005 Paris, France
*
*Corresponding author. Email address:[email protected](L. S. Tuckerman)
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Abstract

Many physical processes are described by elliptic or parabolic partial differential equations. For linear stability problems associated with such equations, the inverse Laplacian provides a very effective preconditioner. In addition, it is also readily available in most scientific calculations in the form of a Poisson solver or an implicit diffusive timestep. We incorporate Laplacian preconditioning into the inverse Arnoldi method, using BiCGSTAB to solve the large linear systems. Two successful implementations are described: spherical Couette flow described by the Navier-Stokes equations and Bose-Einstein condensation described by the nonlinear Schrödinger equation.

Keywords

To be provided by author

MSC classification

Secondary: 37M20: Computational methods for bifurcation problems 65F08: Preconditioners for iterative methods 65F18: Inverse eigenvalue problems 65P10: Hamiltonian systems including symplectic integrators 65P30: Bifurcation problems 76E07: Rotation
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 5 , November 2015 , pp. 1336 - 1351
Copyright
Copyright © Global-Science Press 2015 

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