A PRECONDITIONER FOR THE FINITE ELEMENT APPROXIMATION TO THE ARBITRARY LAGRANGIAN-EULERIAN NAVIER-STOKES EQUATIONS

This paper presents an efficient numerical solver for the finite element approximation of the incompressible Navier-Stokes equations within a moving three-dimensional domain. The moving domain is modeled using the arbitrary Lagrangian-Eulerian (ALE) formulation. Applying a finite element approximation leads to the solution of a large sparse system of equations. In this work we look at the application of the Fp preconditioner within GMRES for efficiently solving such systems. Numerical results are presented for tetrahedral and hexahedral elements, and both structured and unstructured meshes. In all cases GMRES convergence rates are seen to be independent of mesh size. Finally, we show an application of this problem for modeling fluid flow within the heart.