Preconditioned Solver Performance with Compressed Banded Data Format in Three-Dimensional Convective Heat Transfer Simulations

ABSTRACT

A new data storage format called compressed banded data (CBD) is developed for sparse banded matrices generated by hybrid finite-element/volume methods in numerical heat transfer. The platform of the new CBD structure permits dynamic switching between various solvers. The performance of various Krylov techniques, including GMRES(m) (Generalized Minimal RESidual), Bi-CGSTAB (Bi-Conjugate Gradient STABilized), Bi-CG (Bi-Conjugate Gradient), CG (Conjugate Gradient), and CGS (Conjugate Gradient Squared) with an ILU(0) preconditioner, are compared in three test problems. The performance of each preconditioned iterative solver is compared with a direct solver, particularly in terms of memory storage requirements. It is shown that the new CBD format provides useful benefits with respect to both reduction of storage requirements and CPU runtime.

Support of this research by the Natural Sciences and Engineering Research Council of Canada and a University of Manitoba Graduate Fellowship (E. O. B. Ogedengbe) are gratefully acknowledged.