APPLICATION OF CONJUGATE-GRADIENT METHODS TO TIDAL SIMULATION

A harmonic decomposition technique is applied to the shallow water equ ations to yield a complex, nonsymmetric, nonlinear, Helmholtz type pro blem for the sea surface and an accompanying complex, nonlinear diagon al problem for the velocities. The equation for the sea surface is lin earized using successive approximation and then discretized with linea r, triangular finite elements. The study focuses on applying iterative methods to solve the resulting complex linear systems. The comparativ e evaluation includes both standard iterative methods for the real sub systems and complex versions of the well known Bi-Conjugate Gradient a nd Bi-Conjugate Gradient Squared methods. Several Incomplete LU type p reconditioners are discussed, and the effects of node ordering, reject ion strategy, domain geometry and Coriolis parameter (affecting asymme try) are investigated. Implementation details for the complex case are discussed. Performance studies are presented and comparisons made wit h a frontal solver.