• 论文 • 上一篇    下一篇

Powell-Sabin(Ⅱ)型加密三角剖分下的二元三次一阶光滑样条函数空间

谌孙康,刘焕文,   

  1. 广西民族大学数学与计算机科学学院,广西民族大学数学与计算机科学学院 南宁 530006 云南省蒙自县红河学院数学系661100,南宁 530006
  • 出版日期:2008-01-14 发布日期:2008-01-14

谌孙康,刘焕文,. Powell-Sabin(Ⅱ)型加密三角剖分下的二元三次一阶光滑样条函数空间[J]. 计算数学, 2008, 30(1): 49-58.

BIVARIATE C~1 CUBIC SPLINE SPACE OVER POWELL-SABIN'S TYPE (Ⅱ) REFINEMENT

  1. Chen Sunkang Liu Huanwen (Department of Mathematics and Computer Science,Guangxi University for Nationalities,Nanning 530006,China)
  • Online:2008-01-14 Published:2008-01-14
利用B网方法和最小决定集技术,构造了Powell-Sabin(Ⅱ)型加密三角剖分Δ_(PS2)下二元三次C~1样条函数空间的一个最小决定集,给出了该空间的维数和一组具有局部支集的对偶基.
In this paper,by using the B-net method and the technique of minimal determining set, the dimension of bivariate C~1 cubic spline space S_3~1(Δ_(PS2)) over the Powell-Sabin's type (Ⅱ) refinement is determined and a locally supported dual basis is constructed.
()

[1]Strang G.Piecewise polynomials and the finite elements Method
[J].Bull.Amer.Math.Soc.,1973, 79:736-740.
[2]Morgan J,Scott R.A nodal basis for C piecewise polynomials of degree n(?)5
[J].Math.Comp., 1975,29:736-740.
[3]王仁宏.多元齿的结构与插值
[J].数学学报,1975,18:91-106.
[4]Chui C K,Wang R H.Multivariate spline spaces
[J].J.Math.Anal.Appl.,1983,47:131-142.
[5]Schumaker L L.On the dimension of spaces of piecewise polynomials in two variables,in:Multi- variable Approx.Theory (eds.Schempp,Zeller),Birkhauser,Basel,1979,396-412.
[6]Alfeld P,Schumaker L L.The dimension of spline spaces of smoothness r for d(?)4r+1
[J]. Construct.Approx.,1987,3:189-197.
[7]王仁宏和卢旭光.二元样条空间的维数
[J].中国科学,1988,A6:585-594.
[8]Hong D.Spaces of bivariate spline functions over triangulations
[J].Approx.Theory and Appl., 1991,7:56-75.
[9]Alfeld P,Piper B,Schumaker L L.An explicit basis for C~1 quartic bivariate spline
[J].Siam J. Numer.Anal.,1987,24:891-911.
[10]Morgan J,Scott R.The dimension of piecewise polynomial
[M].Manuscript,1975.
[11]王仁宏,许志强.分片代数曲线Bezout数的估计.中国科学
[J].2003,33:185-192.
[12]Ye M D.Some problems for the bivariate C~1-cubic splines
[J].J.Approx.Theory Appl.,1988,4: 1-11.
[13]Liu H W.The dimension of cubic spline space over stratified triangulation
[J].J.Math.Res.& Exp.,1996,16:199-208.
[14]刘焕文.二元样条的积分表示及分层三角剖分下二次样条空间的维数
[J].数学学报,1994,37:534-543.
[15]Liu H W,Hong D.The bivariate C~1 cubic spline space over even stratified triangulations
[J].J. Comput.Anal.Appl.,2002,4:19-35.
[16]Lai M J.Scattered data interpolation and approximation by using bivariate C~1 piecewise cubic polynomials
[J].Comp.Aided Geom.Design,1996,13:81-88.
[17]Liu H W,Hong D.An explicit local basis for C~1 cubic spline spaces over a triangulated quadran- gulation
[J].J.Comput.Appl.Math.,2003,155:187-200.
[18]Ciarlet P G.Sur Lélement de Clough et Tocher
[J].Rev.Francaise Auto.Int.Rech.Oper.,1974, 8:19-27.
[19]Percell P.On cubic and quartic Clough-Tocher finite elements
[J].SIAM J.Numer.Anal.,1976, 13:100-103.
[20]Powell M J D,Sabin M A.Piecewise quadratic approximation on triangles
[J].ACM Trans.Math. Software,1977,3:316-325.
[21]Sablonniere P.Composite finite elements of class C~2,in:Topics in Multivariate Approximation
[M], C.K.Chui,L.L.Schumaker and F.I.Utreras (ed.),Academic Press,New York,1987,207-217.
[22]Lai M J.On C~2 quintic spline functions over triangulation of Powell-Sabin's type
[J].J.Comput. Appl.Math.,1996,73:135-155.
[23]Liu H W,Chen S K,Chen Y P.Bivariate C~1 cubic spline space over Powell-Sabin's type-1 refinement
[J].Journal of Information and Computational Science,2007,4:151-160.
[24]王仁宏等.多元样条及其应用
[M].北京:科学出版社,1994.
No related articles found!
阅读次数
全文


摘要