Modified multigrid for 3D elliptic equations with cross-derivatives

摘要

A portable Fortran code that solves the general nonseparable three-dimensional linear elliptic partial differential equation (PDE) with cross-derivative terms on a rectangular region is described. Boundary conditions can be any combination of periodic, specified, or mixed derivative. A multigrid scheme, modified to handle complexities introduced by cross-derivative terms and nonnormal derivative components in boundary conditions, is utilized. Successful application is illustrated with an analytically prescribed abstract example and simulation of an idealized geophysical fluid flow.