Nonsymmetric Black Box multigrid with coarsening by three

The classical Petrov-Galerkin approach to Black Box multigrid for nonsymmetric problems due to Dendy is combined with the recent factor-three-coarsening Black Box algorithm due to Dendy and Moulton, along with a powerful symmetric line Gauss-Seidel smoother, resulting in an e cient and robust multigrid solver. Focusing on the convectiondi usion operator, the algorithm is tested and shown to achieve fast and reliable convergence with both rst-order and second-order accurate upstream discretizations of the convection operator for a wide range of di usion coe cients. The solver also exhibits robust behavior with respect to discontinuous jumps in the di usion coe cient, and performs well for recirculating ows over a wide range of di usion coe cients. The e ciency of the solver is supported by results of an analysis for the case of constant coe cients.