Two-grid algorithms for linear and nonlinear elliptic problems based on HSS iteration method
In this paper, based on the idea of Hermitian/skew-Hermitian splitting(HSS) iteration method, we present several two-grid (two level) algorithms for solving a large class of linear and nonlinear second-order elliptic boundary value problems. These algorithms reduce the nonsymmetric linear system or nonlinear system on the fine-grid space to two linear (one symmetric positive definite and one shifted skew-symmetric) systems on the fine-grid space and the original system on a coarse-grid space. Under certain conditions, these algorithms have a convergence property similar to that of the two-grid algorithms proposed by Xu. It is shown, both theoretically and numerically, that our algorithms perform well for some convection-diffusion problems.
two-grid algorithm hss iteration method convection-diffusion problems finite element