Parallel computation of incompressible flows in materials processing: Numerical experiments in diagonal preconditioning

Massively parallel computing is enabling dramatic advances in the simulation of three-dimensional flows in materials processing systems. This study focuses on the efficiency and robustness of parallel algorithms applied to such systems. Specifically, various diagonal preconditioning schemes are tested for the iterative solution of the linear equations arising from Newton's method applied to finite element discretizations. Two finite element discretizations are considered - the classical Galerkin and the Galerkin/least-squares method. Results show that the choice of preconditioning method can greatly influence the rate of convergence, but that no type worked uniformly well in all cases.