Multilevel One-Way Dissection Factorization

Strategies for choosing an eeective 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 ow. When thousands of matrix equations diiering only in their right-hand sides must be solved, a multi-level 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 preconditionediterative methods. In addition, the eeciency at the solution stage is much superior to the iterative competitors. Analysis of the storage and operation counts for the multi-level one-way dissection is presented along with numerical results for unsteady incompressible Navier-Stokes ow on a curvilinear grid. The improvementsin performanceof our new methodsover other competitivemethods are signiicant.