A High Order ADI Method For Separable Genneralized Helmholty Equations

We present a multilevel high order ADI method for separable generalized Helmholtz equations. The discretization method we use is a 1-D fourth order compact nite di erence applied to each directional component of the Laplace operator, resulting a discrete system e ciently solvable by ADI methods. We apply this high order di erence scheme to all levels of grids, and then starting from the coarsest grid, solve the discretized equation with an ADI method at each grid level, with solution from the previous grid level as the initial guess. The multilevel procedure stops as the ADI nishes its iterations on the nest grid. Analytical and experimental results show that the proposed method is highly accurate and e cient while remains as algorithmically and data-structurally simple as the single grid ADI method.