A Fast Solver for Convection Diffusion Equations Based on Nested Dissection with Incomplete Elimination

We present an approach for the efficient parallel solution of convection diffusion equations. Based on iterative nested dissection techniques [1] we extended these existing iterative algorithms to a solver based on nested dissection with incomplete elimination of the unknowns. Our elimination strategy is derived from physical properties of the convection diffusion equation, but is independent of the actual discretized operator. The resulting algorithm has a memory requirement that grows linearly with the number of unknowns. This also holds for the computational cost of the setup of the nested dissection structure and the individual relaxation cycles. We present numerical examples that indicate that the number of iterations needed to solve a convection diffusion equation grows only slightly with the number of unknowns, but is widely independent of the type and strength of the convection field.