Finite Difference preconditioning for compact scheme discretizations of the Poisson equation with variable coefficients

[摘要] The finite difference preconditioning for higher-order compact scheme discretizations of non separable Poisson's equation is investigated. An eigenvalue analysis of a one-dimensional problem is detailed for compact schemes up to the tenth-order. The analysis concludes that the spectrum is bounded irrespective of the mesh size and the continuous variable coefficient. Hence, combined to a multigrid method, the preconditioned Richardson method shows a convergence rate which is independent from the mesh size and the variable coefficient. Several numerical experiments, including the simulation of a flow with large density variations, confirm that the spectrum of the preconditioned operator remains bounded. (C) 2020 Elsevier B.V. All rights reserved.

[发布日期] 2020-12-01

[关键词] Compact schemes;Poisson's equation;Preconditioned Richardson method