Multigrid methods

Abstract

In [2], Yaveneh et al. consider the classic Petrov-Galerkin for black box multigrid for nonsymmetric problems with factor-of-three coarsening. With symmetric line Gauss-Seidel as a smoother, the algorithm achieves fast and reliable convergence for both first-order and second-order discretizations of the convection operator for a wide range of diffusion coefficients.In [3], Emams reports on experiences with aggregation AMG relying on Krylov acceleration as preconditioners for linear systems in general purpose fluid flow simulation. In benchmarks that reflect the requirements for industrial situations, the performance of recently published algorithms for semi-definite problems is shown to be very attractive except for proposed variants that occasionally fail for nonsymmetric problems; modifications are suggested to lead to reliable solvers for these situations.In [4], Reps et al. analyze the Krylov convergence rate of a Helmholtz problem preconditioned with multigrid, which is applied to the Helmholtz problem formulated on a complex contour and uses polynomial smoothers at each level. For a one-dimensional model, it is shown that the Krylov