High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems. (11th June 2018)

• Record Type: Journal Article
• Authors: Wang, Yan; Ge, Yongbin
• Other Names: Shotorban Babak Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2018(2018)
• Publication Date: 2018-06-11
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2018/7831731
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : A high-order compact difference scheme for solving the two-dimensional (2D) elliptic problems is proposed by including compact approximations to the leading truncation error terms of the central difference scheme. A multigrid method is employed to overcome the difficulties caused by conventional iterative methods when they are used to solve the linear algebraic system arising from the high-order compact scheme. Numerical experiments are conducted to test the accuracy and efficiency of the present method. The computed results indicate that the present scheme achieves the fourth-order accuracy and the effect of the multigrid method for accelerating the convergence speed is significant.