Multilevel one-way dissection factorization

Strategies for choosing an effective solver for a large sparse matrix equat ion are governed by the particular application. In this article, the contex t is the numerical solution of unsteady incompressible Navier Stokes ow. Wh en thousands of matrix equations differing only in their right-hand sides m ust be solved, a multilevel one-way dissection scheme is an attractive choi ce. This method has the property that large parts of the matrix factors are not stored; they are (implicitly) regenerated as needed during the solutio n process. The resulting storage requirement is competitive with those of p reconditioned iterative methods. In addition, the efficiency at the solutio n stage is much superior to the iterative competitors. Analysis of the storage and operation counts for the multilevel one-way dis section is presented along with numerical results for unsteady incompressib le Navier Stokes ow on a curvilinear grid. The improvements in performance of our new methods over other competitive methods are significant.