High-order compact solvers for the three-dimensional Poisson equation
G. Sutmann, B. Steffen.
Journal of Computational and Applied Mathematics, 187, 142-170, (2006)
New compact approximation schemes for the Laplace operator of fourth- and sixth-order are proposed. The schemes are based on a Padé approximation of the Taylor expansion for the discretized Laplace operator. The new schemes are compared with other finite difference approximations in several benchmark problems. It is found that the new schemes exhibit a very good performance and are highly accurate. Especially on large grids they outperform non compact schemes.
Keyword(s): Poisson equation; compact solvers; Iterative solvers; Padé approximation