Laplacian Preconditioning for the Inverse Arnoldi Method (Communications in Computational Physics, 2020)
Many physical processes are described by elliptic or parabolic partial differentialequations. For linear stability problems associated with such equations, theinverse Laplacian provides a very effective preconditioner. In addition, it is also readilyavailable in most scientific calculations in the form of a Poisson solver or an implicitdiffusive time step. We incorporate Laplacian preconditioning into the inverse Arnoldimethod, using BiCGSTAB to solve the large linear systems. Two successful implementationsare described: spherical Couette flow described by the Navier-Stokes equationsand Bose-Einstein condensation described by the nonlinear Schrödinger equation.