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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/41406

Title: Application of a modified manifold-based exponentially convergent algorithm to solve elliptic boundary-value problems
Authors: Yung-Wei Chen;Chun-Ming Chang;Chein-Shan Liu;Jiang-Ren Chang
Contributors: 國立臺灣海洋大學:系統工程暨造船學系
Keywords: fictitious time integration method (FTIM);boundary-value problem;finite difference method (FDM)
Date: 2013-05
Issue Date: 2017-02-15T05:56:16Z
Publisher: IMA J Numer Anal
Abstract: Abstract:In this paper, we combine a novel finite difference method (FDM) with a manifold-based exponentially convergent algorithm (MBECA) to solve a nonlinear elliptic boundary-value problem defined in an arbitrary plane domain. It is very difficult to solve nonlinear and geometric complexity problems by conventional FDM. To overcome these problems, the concepts of internal residual and boundary residual in a fictitious rectangular domain are introduced. Besides, by adding a fictitious time coordinate, we avoid the need to treat complex boundary conditions but only use shape functions. Also, it is not necessary to solve an inverse matrix of algebraic equations when by using the MBECA. Moreover, in order to increase the numerical stability of the MBECA, we introduce a group-preserving scheme (GPS) to address fictitious time integration. Given the cone structure of the GPS and MBECA and their manifold properties, we can preserve the manifold path on the cone structure by a weighting factor such that the MBECA must also exhibit a cone construction, Lie algebra and group properties at each fictitious time step. Finally, the accuracy and convergence behaviour of this present method are demonstrated in several examples.
Relation: 34(1),pp.362-389
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/41406
Appears in Collections:[系統工程暨造船學系] 期刊論文

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