TY - JOUR T1 - Laplacian Preconditioning for the Inverse Arnoldi Method AU - Laurette S. Tuckerman 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.