Node-by-node FEM

Jarmo Monttinen

I am currently working on an incompressible FEM solver. Basically, the solution methods I am looking into are various CG-methods (problem: pre-conditioning) and an explicit node-by-node solution. For CG and its variants, most of the publications dealing with pre-conditioning are for basic problems (driven cavity, etc) with small number of unknowns. The most effective pre-conditioners seem to require ILU-decomposition, this becomes very difficult for a large system (O(10^6) unknowns) as the original matrix already becomes too large to store in one array. In order to get ILU done, one would need the original matrix.... On the other hand, I am not familiar with papers dealing with explicit FEM solutions of this kind of problems.

My questions here are: 1. do you know of any papers that deal with pre-conditioning for incompressible N-S equations for large problems? 2. do you know of papers with node-by-node solution?

Thank you.

-Jarmo