Volume 18, Issue 5
Laplacian Preconditioning for the Inverse Arnoldi Method

Laurette S. Tuckerman

Commun. Comput. Phys., 18 (2015), pp. 1336-1351.

Published online: 2018-04

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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 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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@Article{CiCP-18-1336, author = {}, title = {Laplacian Preconditioning for the Inverse Arnoldi Method}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.281114.290615a}, url = {http://global-sci.org/intro/article_detail/cicp/11071.html} }
TY - JOUR T1 - Laplacian Preconditioning for the Inverse Arnoldi Method JO - Communications in Computational Physics VL - 5 SP - 1336 EP - 1351 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.281114.290615a UR - https://global-sci.org/intro/article_detail/cicp/11071.html KW - AB -

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.

Laurette S. Tuckerman. (2020). Laplacian Preconditioning for the Inverse Arnoldi Method. Communications in Computational Physics. 18 (5). 1336-1351. doi:10.4208/cicp.281114.290615a
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