Multilevel One-Way Dissection Factorization

Strategies for choosing an effective solver for a large sparse matrix equation are governed by the particular application. In this article, the context is the numerical solution of unsteady incompressible Navier--Stokes flow. When thousands of matrix equations differing only in their right-hand sides must be solved, a multilevel one-way dissection scheme is an attractive choice. This method has the property that large parts of the matrix factors are not stored; they are (implicitly) regenerated as needed during the solution process. The resulting storage requirement is competitive with those of preconditioned iterative methods. In addition, the efficiency at the solution stage is much superior to the iterative competitors.Analysis of the storage and operation counts for the multilevel one-way dissection is presented along with numerical results for unsteady incompressible Navier--Stokes flow on a curvilinear grid. The improvements in performance of our new methods over other competitive methods are signif...