Nested Grid Iteration for Incompressible Viscous Flow and Transport

Benjamin Kirk, University of Texas

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The use of one-way cascadic multigrid strategies (CMG) in the solution of incompressible viscous flow using the finite element method will be discussed. First the basic CMG approach for representative elliptic boundary value problems will be described and theoretical error estimates from approximation theory, desired smoother properties, and arithmetic complexity of the method will be presented. Then the mathematical formulation and the finite element approximation scheme for the class of fluid-thermal problems of interest will be presented. In supporting numerical experiments I examine performance of the algorithm on both serial and distributed parallel systems. The performance of the algorithm with using various smoothers will also be discussed.

Abstract Author(s): Benjamin Kirk, Konstantin Lipnikov, and Graham Carey