A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation. (26th April 2010)

• Record Type: Journal Article
• Authors: Kyei, Yaw; Roop, John Paul; Tang, Guoqing
• Other Names: He Yin Nian Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2010(2010)
• Publication Date: 2010-04-26
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2010/352174
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson's equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson's equation on a compact stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.