標題: New Solvers for Higher Dimensional Poisson Equations by Reduced B-Splines
作者: Kuo, Hung-Ju
Lin, Wen-Wei
Wang, Chia-Tin
應用數學系
Department of Applied Mathematics
關鍵字: B-spline;divided difference;approximation;numerical experiment
公開日期: 1-三月-2014
摘要: We use higher dimensional B-splines as basis functions to find the approximations for the Dirichlet problem of the Poisson equation in dimension two and three. We utilize the boundary data to remove unnecessary bases. Our method is applicable to more general linear partial differential equations. We provide new basis functions which do not require as many B-splines. The number of new bases coincides with that of the necessary knots. The reducing process uses the boundary conditions to redefine a basis without extra artificial assumptions on knots which are outside the domain. Therefore, more accuracy would be expected from our method. The approximation solutions satisfy the Poisson equation at each mesh point and are solved explicitly using tensor product of matrices. (c) 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 393-405, 2014
URI: http://dx.doi.org/10.1002/num.21814
http://hdl.handle.net/11536/23775
ISSN: 0749-159X
DOI: 10.1002/num.21814
期刊: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume: 30
Issue: 2
起始頁: 393
結束頁: 405
顯示於類別:期刊論文


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