Laplacian Preconditioning for the Inverse Arnoldi Method

Laplacian Preconditioning for the Inverse Arnoldi Method

Year:    2015

Communications in Computational Physics, Vol. 18 (2015), Iss. 5 : pp. 1336–1351

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 time step. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.281114.290615a

Communications in Computational Physics, Vol. 18 (2015), Iss. 5 : pp. 1336–1351

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:   

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