A priori pivoting in incomplete Gaussian preconditioning for iterative solution of mixed finite-element formulation of the Navier-Stokes equations

摘要

Mixed finite-element formulations of incompressible Navier-Stokes equations lead to non-positive definite algebraic systems in- appropriate for iterative solution techniques. However, introducing a suitable preconditioner the mixed finite-element equation system becomes positive definite and solvable by iterative solvers. The present work suggests a priori pivoting sequences for parallel and serial implementations of incomplete Gaussian factorization. Tests are performed for the driven cavity problem in two and three dimen- sions