High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

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 ite...

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Main Authors: Yan Wang, Yongbin Ge
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2018/7831731
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spelling doaj-57bcecf00b514192bf01a646acbaa50a2020-11-25T00:46:36ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/78317317831731High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic ProblemsYan Wang0Yongbin Ge1School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, ChinaSchool of Mathematics and Statistics, Ningxia University, Yinchuan 750021, ChinaA 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.http://dx.doi.org/10.1155/2018/7831731
collection DOAJ
language English
format Article
sources DOAJ
author Yan Wang
Yongbin Ge
spellingShingle Yan Wang
Yongbin Ge
High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems
Mathematical Problems in Engineering
author_facet Yan Wang
Yongbin Ge
author_sort Yan Wang
title High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems
title_short High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems
title_full High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems
title_fullStr High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems
title_full_unstemmed High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems
title_sort high-order compact difference scheme and multigrid method for solving the 2d elliptic problems
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2018-01-01
description 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.
url http://dx.doi.org/10.1155/2018/7831731
work_keys_str_mv AT yanwang highordercompactdifferenceschemeandmultigridmethodforsolvingthe2dellipticproblems
AT yongbinge highordercompactdifferenceschemeandmultigridmethodforsolvingthe2dellipticproblems
_version_ 1725264274674155520

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