Laplacian Preconditioning for the Inverse Arnoldi Method. (November 2015)

• Record Type: Journal Article
• Authors: Tuckerman, Laurette S.
• Is Part Of: Communications in computational physics. Volume 18:Number 5(2015:Nov.)
• Page Start: 1336
• Page End: 1351
• Publication Date: 2015-11
• Subjects: 37M20, -- 65F08, -- 65F18, -- 65P10, -- 65P30, -- 76E07; To be provided by author; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.281114.290615a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.