检索结果-南通市图书馆

Addition formulae, Backlund transformations, periodic solutions, and quadrilateral equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Frontiers of Mathematics in China 2019年第1期14卷 203-223页

作者： Danda ZHANG Da-jun ZHANG School of Mathematics and Statistics Ningbo University Ningbo 315211 China Department of Mathematics Shanghai University Shanghai 200444 China

Addition formulae of trigonometric and elliptic functions are used to generate Backlund transformations together with their connecting quadrilateral equations. As a result, we obtain the periodic solutions for a numbe... 详细信息

关键词： Addition formulae trigonometric functions elliptic functions Backlund transformation quadrilateral equations

THE DESIGN OF BEZIER SURFACE THROUGH QUINTIC BEZIER ASYM PTOTIC quadrilateral

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2019年第5期37卷 721-738页

作者： Hui Wang Chungang Zhu Caiyun Li School of Mathematical Sciences Dalian University of TechnologyDalian 116024China School of Mathematical and Physical Sciences Dalian University of TechnologyPanjin 124221China

The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bezier asymptotic quadrilateral interpolated by a smooth Bezier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bezier surfaces is compatible with the CAD systems.

关键词： Asymptotic curves Bezier surface Interpolation quadrilateral

C1-Conforming quadrilateral Spectral Element Method for Fourth-Order Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2019年第3期1卷 403-434页

作者： Huiyuan Li Weikun Shan Zhimin Zhang State Key Laboratory of Computer Science/Laboratory of Parallel Computing Institute of SoftwareChinese Academy of SciencesBeijing 100190China School of Science Henan University of TechnologyZhengzhou 450001HenanChina Beijing Computational Science Research Center Beijing 100193China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

This paper is devoted to Professor Benyu Guo's open question on the C1-conforming quadrilateral spectral element method for fourth-order equations which has been endeavored for years. Starting with generalized Jacobi polynomials on the reference square, we construct the C1-conforming basis functions using the bilinear mapping from the reference square onto each quadrilateral element which fall into three categories-interior modes, edge modes, and vertex modes. In contrast to the triangular element, compulsively compensatory requirements on the global C1-continuity should be imposed for edge and vertex mode basis functions such that their normal derivatives on each common edge are reduced from rational functions to polynomials, which depend on only parameters of the common edge. It is amazing that the C1-conforming basis functions on each quadrilateral element contain polynomials in primitive variables, the completeness is then guaranteed and further confirmed by the numerical results on the Petrov-Galerkin spectral method for the non-homogeneous boundary value problem of fourth-order equations on an arbitrary quadrilateral. Finally, a C1-conforming quadrilateral spectral element method is proposed for the biharmonic eigenvalue problem, and numerical experiments demonstrate the effectiveness and efficiency of our spectral element method.

关键词： quadrilateral spectral element method Fourth-order equations Mapped polynomials C1-conforming basis Polynomial inclusion Completeness

FINITE ELEMENT ERROR EXPANSION FOR NONUNIFORM quadrilateral MESHES

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Systems Science and Mathematical Sciences 1989年第3期2卷 275-282页

作者：林群 Institute of Systems ScienceAcademia SinicaBeijingChina

An error expansion for isoparametric bilinear finite element approximation isestablished with some kind of nonuniform quadrilateral mesh constructed in the followingway:We first decompose the considered polygonal domain into several fixed convex macro-quadrilaterals and then link up some equi-proportionate points of the opposite edges in eachmacro-quadrilateral and form a quadrilateral mesh which may not be uniform and so isuseful in the adaptive refinement.

关键词： Finite elements nonuniform quadrilateral mesh error expansion a posterior error estimate Richardson extrapolation

Tilings of the Sphere by Congruent quadrilaterals I:Edge Combination a^(2)bc

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2024年第5期45卷 733-766页

作者： Yixi LIAO Pinren QIAN Erxiao WANG Yingyun XU School of Mathematical Sciences Zhejiang Normal UniversityJinhua 321004ZhejiangChina

Edge-to-edge tilings of the sphere by congruent a^(2)bc-quadrilaterals are classified as 3 classes:(1)A 1-parameter family of quadrilateral subdivisions of the octahedron with24 tiles,and a flip modification for one special parameter;(2)a 2-parameter family of 2-layer earth map tilings with 2n tiles for each n≥3;(3)a 3-layer earth map tiling with 8n tiles for each n≥2,and two flip modifications for each odd *** authors also describe the moduli of parameterized tilings and provide the full geometric data for all tilings.

关键词： Spherical tiling quadrilateral Classification Earth map tiling Subdivision

On 2-Factors with Prescribed Properties in a Bipartite Graph

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2006年第4期22卷 1115-1120页

作者： Jin YAN Gui Zhen LIU School of Mathematics and Systems Science Shandong University Jinan 250100 P. R. China

Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjectured that for any k independent edges e1,……, ek of G, G has a 2-factor with k cycles C1, C2, ……, Ck with respect to {e1, e2,……, ek} such that k - 1 of them are quadrilaterals. In this paper, we prove this conjecture.

关键词： Bipartite graph Vertex-disjoint quadrilateral 2-Factor

Random heterogeneous microstructure construction of composites via fractal geometry

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2019年第10期40卷 1413-1428页

作者： Siwen WANG Zhansheng GUO Department of Mathematics College of Sciences Shanghai University Shanghai 200444 China Shanghai Institute of Applied Mathematics and Mechanics School of Mechanics and Engineering Science Shanghai University Shanghai 200072 China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China

The microstructures of a composite determine its macroscopic properties. In this study, microstructures with particles of arbitrary shapes and sizes are constructed by using several developed fractal geometry algorithms implemented in MATLAB. A two-dimensional (2D) quadrilateral fractal geometry algorithm is developed based on the modified Sierpinski carpet algorithm. Square-, rectangle-, circle-, and ellipse-based microstructure constructions are special cases of the 2D quadrilateral fractal geometry algorithm. Moreover, a three-dimensional (3D) random hexahedron geometry algorithm is developed according to the Menger sponge algorithm. Cube-and sphere-based mi-crostructure constructions are special cases of the 3D hexahedron fractal geometry algo-rithm. The polydispersities of fractal shapes and random fractal sub-units demonstrate significant enhancements compared to those obtained by the original algorithms. In ad-dition, the 2D and 3D algorithms mentioned in this article can be combined according to the actual microstructures. The verification results also demonstrate the practicability of these algorithms. The developed algorithms open up new avenues for the constructions of microstructures, which can be embedded into commercial finite element method soft-wares.

关键词： microstructure fractal geometry algorithm arbitrary shape and size ar-bitrary quadrilateral arbitrary hexahedron

WENO Schemes for Mixed-Element Unstructured Meshes

在线全文

学校读者我要写书评

暂无评论

Communications in Computational Physics 2010年第8期8卷 585-609页

作者： V.A.Titarev P.Tsoutsanis D.Drikakis Fluid Mechanics and Computational Sciences Group Aerospace Sciences DepartmentCranfield UniversityCranfieldMK430ALUK

The paper extends weighted essentially non-oscillatory(WENO)schemes to two-dimensional quadrilateral and mixed-element unstructured *** key element of the proposed methods is a reconstruction procedure suitable for arbitrarilyshaped *** resulting schemes achieve the designed uniformly high-order of accuracy and compute discontinuous solutions without spurious oscillations at interfaces between cells of two different types.

关键词： WENO unstructured mixed-element triangular quadrilateral finite volume

FINITE ELEMENT ERROR EXPANSIONS FOR THE EIGENVALUE APPROXIMATION TO THE MULTIGROUP DIFFUSION EQUATIONS

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Systems Science and Mathematical Sciences 1991年第3期4卷 225-235页

作者：丁彦恒林群 Institute of Mathematics Academia SinicaBeijing 100080China Institute of Systems Science Academia SinicaBeijing 100080China

Asymptotic expansions for the finite element approximation to the eigenvalues of the mult-igroup diffusion equations on Ω(?)R^n(n=2,3)of reactor theory are given,firstly for a piecewiseuniform triangulation,then for nonuniform quadrilateral meshes,and finally for nonuniformhexahedral *** effect of certain classes of numerical integrations is *** applicationsof the expansions,several extrapolation formulas and a posteriori error estimates are obtained.

关键词： multigroup diffusion equations finite element quadrature error expansion quadrilateral hexahedron extrapolation a posteriori error estimate