The Schur complement method as a fast parallel solver for elliptic partial differential equations in oceanography (Q2760367)

The method is described in the context of ice-ocean model BRIOS (Bremerhaven Regional Ice-Ocean Simulation System). After an introduction, hydrostatic primitive equations (a set of three-dimensional time-dependent nonlinear coupled PDEs) are presented and further modified by the introduction of a vertically integrated stream function. The stream function solves the Laplace or, after a transformation of coordinate system, a two-dimensional elliptic PDE with highly variable anisotropic coefficients on a regular rectangular grid. The latter equation is a part of an explicit time-stepping scheme in BRIOS. The equation is solved in parallel by means of domain decomposition approach which gives rise to the application of Schur complement method. It uses a direct solver and an explicitly inverted Schur complement matrix, as the direct approach turns out to be advantageous in problems BRIOS solves. Two solvers are presented and, together with other BRIOS features, are tested and discussed.