带边界约束的网格和曲面生成理论与方法研究
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摘要
本论文在研究带边界约束的网格和曲面生成理论与方法的基础上,给出并讨论了几种网格和卷积曲面的生成方法。
给出了边界形变网格生成方法。该方法先通过边界的四个角点生成初始网格,然后从边界线开始递推计算初始网格到目标网格的形变矩阵,最后将初始网格与形变矩阵相加,即生成给定边界上的目标网格。边界形变方法生成网格速度快,且没有以结点为变量的优化方法那样异常的折线。对于某些复杂边界区域上网格生成质量不佳的问题,可以通过重新定义边界来解决。
提出了可生成弹性网格的应力平衡法。在该方法中,结点坐标很容易由解迭代方程得到。针对某一方向发生压缩形变而导致单元格内部不存在稳定平衡点的问题,用对数函数得到了改进的平衡方程。由改进方程,只要单元格在任意一个方向上有拉伸形变,则存在可迅速收敛的稳定平衡点。在实际网格生成中,由于边界的复杂性,可能存在完全压缩的单元格,建议将整张网格设置为拉伸形变,并给出了参数设置公式。数值实例表明,由(改进)应力平衡方法生成的网格符合在边界线内凹附近网格线较密、外凸附近网格线较为稀疏的物理特性。
给出了由两个方向上带形状参数曲线簇生成网格的方法。随后的定理保证了该方法同样适用于空间网格的生成。讨论了在各种不同边界条件下,形状参数对生成网格的影响。基于相邻网格线间相对位置关系的定理,构造了目标函数来求解最优形状参数。数值实例表明,在这种指标下的最优网格与应力平衡网格具有同样的疏密特征。更重要的是,该方法生成的网格是可调控形状的。
利用指数函数给出了可控密度参数网格生成方法。讨论了该方法中密度参数对各种形状边界网格生成的影响。基于单元格的度量性质,提出了求解最优密度参数的正方形准则。数值实例表明,当两组对边存在一定差异时,最优网格与普通网格存在显著差异。我们提出的两种参数网格中优化变量都仅仅为两个,故算法空间、时间复杂度都很低,更容易收敛。
讨论了基于轮廓线约束的卷积曲面造型方法。首先简单介绍了一种基于元球的隐式曲面造型方法。这个方法使用球或者椭球对轮廓线的进行逼近,并使用超二次曲面作为原始体的扩展元球模型构造曲面。然后我们提出了一种卷积曲面造型方法,使用轮廓线的向内等距曲线形成的二维形体作为骨架构造曲面,该曲面能满足逼近给定的轮廓线的条件。最后,我们介绍了两种方法生成轮廓线的等距曲线,推导出场值解析计算公式并进行误差分析。实验结果表明,使用我们的方法,特别适用于生成扁平模型。
Based on the study about the theories and methods of grid and surface generation with boundary constrains, several methods of grid and convolution surface were presented and discussed.
A method based on boundary deformation for grid generation was presented. Firstly, the initial grid was generated by the four corners of the boundary lines. Then the deformation matrix, between the initial grid and the target grid, could be calculated recursively according to the boundary lines. Finally, the target grid in the domain with boundary constrains generated. The grid was generated very fast by using this method, and there are no such unusual wave curves generated by those optimization methods which using the grid nodes as variables. For the problem of generating poor quality grids on some complex boundary zone by this method, it can be resolved by redefining the boundary.
We proposed a stress balance method to generate elastic grid, where the grid nodes was easy to obtain by solving the iterate equations. For there does stable equilibrium position in the cell for compression deformation in one direction at least, we improved the equilibrium equation by using logarithmic function. Then, there must be an equilibrium position which can be quickly reached in the cells, except those completely compression in two directions. Moreover, in practice, for the complexity of boundary shape, there may exist completely compression cells in zone. It was recommended to set the entire zone as tensile deformation, and the formula of parameter setting was proposed. Numerical experiments showed that the grids generated by (improved) stress balance method meet the physical characteristics of the denser grid curves near the concave boundary and the sparser grid curves near the convex boundary.
A method to generate the grid by the curve clusters with shape parameters in two directions was proposed. The following theorem ensured that the method can also be used in space grid generation. Then, the influence of shape parameters on the grids was discussed by considering a variety of different shape boundaries. Based on the theorem about the relative positions of the adjacent grid curves, an objective function to solve the optimal shape parameters was constructed. Numerical experiments showed that the grid generated by the method and the objective function owns the same density characteristics of the curves. More importantly, the grid generated by the method was shape-controllable.
By using the exponential function, a method to generate density controllable grid is presented. Then we discussed the influence of density parameters on generating the grids with all kinds of shape boundaries. Based on the measurements of cells, a square criteria to obtain the optimal density parameters was proposed. Numerical experiments showed that the optimal grid was significant better than the general, when there exists some difference between the boundary in two direction.
The two methods with parameters listed above both owned the characteristics of the lower algorithm space and the lower algorithm complexity for there only existing two optimal variables in objective functions. Moreover, the methods were easy to converge.
The method to generate the convolution surface constrained with contour curves was discussed. First, a brief introduction of implicit surface modeling based on the metaball. In this method, the contour curves was approximated by the ball or ellipse, and the surface was constructed by the extended metaball model which using the hyper-quadratic as the primitive. Then a modeling method of convolution surface was proposed. In this method, a two-dimensional surface shape formed by inward offset lines of the contour curves was used as the skeleton to construct the surface, which met the condition of approximating the given contour curves. Finally, we introduced two methods to generate the offset lines of the contour curves, and then derived the analytical formula of field value and analyzed its error. Experiments showed that our methods were especially used to generate flat model.
给出了边界形变网格生成方法。该方法先通过边界的四个角点生成初始网格,然后从边界线开始递推计算初始网格到目标网格的形变矩阵,最后将初始网格与形变矩阵相加,即生成给定边界上的目标网格。边界形变方法生成网格速度快,且没有以结点为变量的优化方法那样异常的折线。对于某些复杂边界区域上网格生成质量不佳的问题,可以通过重新定义边界来解决。
提出了可生成弹性网格的应力平衡法。在该方法中,结点坐标很容易由解迭代方程得到。针对某一方向发生压缩形变而导致单元格内部不存在稳定平衡点的问题,用对数函数得到了改进的平衡方程。由改进方程,只要单元格在任意一个方向上有拉伸形变,则存在可迅速收敛的稳定平衡点。在实际网格生成中,由于边界的复杂性,可能存在完全压缩的单元格,建议将整张网格设置为拉伸形变,并给出了参数设置公式。数值实例表明,由(改进)应力平衡方法生成的网格符合在边界线内凹附近网格线较密、外凸附近网格线较为稀疏的物理特性。
给出了由两个方向上带形状参数曲线簇生成网格的方法。随后的定理保证了该方法同样适用于空间网格的生成。讨论了在各种不同边界条件下,形状参数对生成网格的影响。基于相邻网格线间相对位置关系的定理,构造了目标函数来求解最优形状参数。数值实例表明,在这种指标下的最优网格与应力平衡网格具有同样的疏密特征。更重要的是,该方法生成的网格是可调控形状的。
利用指数函数给出了可控密度参数网格生成方法。讨论了该方法中密度参数对各种形状边界网格生成的影响。基于单元格的度量性质,提出了求解最优密度参数的正方形准则。数值实例表明,当两组对边存在一定差异时,最优网格与普通网格存在显著差异。我们提出的两种参数网格中优化变量都仅仅为两个,故算法空间、时间复杂度都很低,更容易收敛。
讨论了基于轮廓线约束的卷积曲面造型方法。首先简单介绍了一种基于元球的隐式曲面造型方法。这个方法使用球或者椭球对轮廓线的进行逼近,并使用超二次曲面作为原始体的扩展元球模型构造曲面。然后我们提出了一种卷积曲面造型方法,使用轮廓线的向内等距曲线形成的二维形体作为骨架构造曲面,该曲面能满足逼近给定的轮廓线的条件。最后,我们介绍了两种方法生成轮廓线的等距曲线,推导出场值解析计算公式并进行误差分析。实验结果表明,使用我们的方法,特别适用于生成扁平模型。
Based on the study about the theories and methods of grid and surface generation with boundary constrains, several methods of grid and convolution surface were presented and discussed.
A method based on boundary deformation for grid generation was presented. Firstly, the initial grid was generated by the four corners of the boundary lines. Then the deformation matrix, between the initial grid and the target grid, could be calculated recursively according to the boundary lines. Finally, the target grid in the domain with boundary constrains generated. The grid was generated very fast by using this method, and there are no such unusual wave curves generated by those optimization methods which using the grid nodes as variables. For the problem of generating poor quality grids on some complex boundary zone by this method, it can be resolved by redefining the boundary.
We proposed a stress balance method to generate elastic grid, where the grid nodes was easy to obtain by solving the iterate equations. For there does stable equilibrium position in the cell for compression deformation in one direction at least, we improved the equilibrium equation by using logarithmic function. Then, there must be an equilibrium position which can be quickly reached in the cells, except those completely compression in two directions. Moreover, in practice, for the complexity of boundary shape, there may exist completely compression cells in zone. It was recommended to set the entire zone as tensile deformation, and the formula of parameter setting was proposed. Numerical experiments showed that the grids generated by (improved) stress balance method meet the physical characteristics of the denser grid curves near the concave boundary and the sparser grid curves near the convex boundary.
A method to generate the grid by the curve clusters with shape parameters in two directions was proposed. The following theorem ensured that the method can also be used in space grid generation. Then, the influence of shape parameters on the grids was discussed by considering a variety of different shape boundaries. Based on the theorem about the relative positions of the adjacent grid curves, an objective function to solve the optimal shape parameters was constructed. Numerical experiments showed that the grid generated by the method and the objective function owns the same density characteristics of the curves. More importantly, the grid generated by the method was shape-controllable.
By using the exponential function, a method to generate density controllable grid is presented. Then we discussed the influence of density parameters on generating the grids with all kinds of shape boundaries. Based on the measurements of cells, a square criteria to obtain the optimal density parameters was proposed. Numerical experiments showed that the optimal grid was significant better than the general, when there exists some difference between the boundary in two direction.
The two methods with parameters listed above both owned the characteristics of the lower algorithm space and the lower algorithm complexity for there only existing two optimal variables in objective functions. Moreover, the methods were easy to converge.
The method to generate the convolution surface constrained with contour curves was discussed. First, a brief introduction of implicit surface modeling based on the metaball. In this method, the contour curves was approximated by the ball or ellipse, and the surface was constructed by the extended metaball model which using the hyper-quadratic as the primitive. Then a modeling method of convolution surface was proposed. In this method, a two-dimensional surface shape formed by inward offset lines of the contour curves was used as the skeleton to construct the surface, which met the condition of approximating the given contour curves. Finally, we introduced two methods to generate the offset lines of the contour curves, and then derived the analytical formula of field value and analyzed its error. Experiments showed that our methods were especially used to generate flat model.
引文
[1]朱心雄等著.自由曲线曲面造型技术[M].北京：科学出版社,2000.
[2]FARIN G, HANSFORD D. Discrete Coons patches[J]. Computer Aided Geometric Design,1999,16(7):691-700.
[3]SONI B. Grid Generation:Past, Present and Future[J]. Applied Numerical Mathematics,2000,32:361-369.
[4]KHAMAYSEH A, HAMANN B. Elliptic Grid Generation Using NURBS Surfaces[J]. Computer Aided Geometric Design,1996,13(4):369-386.
[5]MONTERDE J, UGAIL H. A General 4th-order PDE Method to Generate Bezier Surfaces from the Boundary [J]. Computer Aided Geometric Design,2006, 23:208-225.
[6]NEFUSSI G, GILORMINI P. A Simplified Method for The Simulation of Cold-Roll Forming[J]. International Journal of Mechanical Sciences,1993, 35:867-878.
[7]THOMPSON J, SONI B, WEATHERILL N. Handbook of Grid Generation[M]. Washington,D.C:CRC Press,1999.
[8]WANG C, TANG K. Non-self-overlapping Hermite Interpolation Mapping:a Practical Solution for Structured Quadrilateral Meshing [J]. Computer-Aided Design,2005,37:271-283.
[9]YANG D, CHUANG J, HAN Z, et al. Boundary-Conformed Toolpath Generation for Trimmed Free-Form Surfaces via Coons Reparametrization[J]. Journal of Materials Processing Technology,2003,138:138-144.
[10]TINOCO-RUIZ J, BARRERA-SANCHEZ P. Smooth and Convex Grid Generation over General Plane Regions[J]. Mathematics and Computers in Simulation,1998,46:87-102.
[11]CASTILLO J, OTTO J. A Practical Guide to Direct Optimization for Planar Grid-Generation[J]. Computers & Mathematics with Applications,1999,37: 123-156.
[12]CONTI C, MORANDI R, SPITALERI R. An Algebraic Grid Optimization Algorithm Using Condition Numbers [J]. Applied Numerical Mathematics,2006, 56(8):1123-1133.
[13]陈建军.非结构化网格生成及其并行化的若干问题研究[D].杭州：浙江大学,2006.
[14]GEORGALA J, SHAW J. A Discussion on Issues Relating to Multiblock Grid Generation[C]. SCHMIDT W. AGARD Conference Proceedings 464: Applications of Mesh Generation to Complex 3-D Configurations. Loen, Norway:Advisory Group for Aerospace Research and Development,1989.
[15]LISEIKIN V. Grid Generation Methods[M]. Springe Dordrecht Heidelberg London New York:Springer,2009.
[16]BENEK J, BUNING P, STEGER J. A 3-D Chimera Grid Embedding Technique[J].AIAA paper,1985.
[17]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：高等教育出版社,2001.
[18]ABRAHAMSSON L. Orthogonal Grid Generation for Two-Dimensional Ducts[J]. Journal of Computational and Applied Mathematics,1991,34(3): 305-314.
[19]BOURCHTEIN A, BOURCHTEIN L. On Generation of Orthogonal Grids[J]. Applied Mathematics and Computation,2006,173(2):767-781.
[20]BRAKHAGE K, LAMBY P. Application of B-Spline Techniques to the Modeling of Airplane Wings and Numerical Grid Generation [J]. Computer Aided Geometric Design,2008,25(9):738-750.
[21]CASTILLO J, STEINBERG P, S.ANDROACHE. Mathematical Aspects of Variational Grid Generation II[J]. Journal of Computational and Applied Mathematics,1987,20:127-135.
[22]CONTI C, MORANDI R, RABUT C. Locally Tensor Product Functions in Algebraic Grid Optimization[J]. Applied Mathematics and Computation,2008, 197(2):745-754.
[23]DOUGHERTY R, HYMAN J. A Divide-And-Conquer Algorithm for Grid Generation[J]. Applied Numerical Mathematics,1994,14(1-3):125-134.
[24]EGIDI N, MAPONI P. A Robust Direct Variational Approach for Generation of Quadrangular and Triangular Grids on Planar Domains[J]. Mathematics and Computers in Simulation,2007,75(5-6):171-181.
[25]MAKHANOV S, IVANENKO S. Grid Generation as Applied to Optimize Cutting Operations of the Five-Axis Milling Machine [J]. Applied Numerical Mathematics,2003,46(3-4):331-351.
[26]WEN X, INGHAM D, DOMBROWSKI N, et al. The Generation of an Orthogonal Grid by the Use of a Boundary Integral Technique [J]. Engineering Analysis with Boundary Elements,1998,21(3):197-205.
[27]THOMPSON J, WEATHERILL N. Aspects of Numerical Grid Generation: Current Science and Art[J]. AIAA Paper,1993:1029-1070.
[28]THOMPSON J. A Reflection on Grid generation in the 90s:Trends, Needs Influences. In Soni, B.K., Thompson, J.F., Hauser, J., Eiseman, P.R. (eds.), Numerical Grid Generation in CFD[M]. Mississippi:Mississippi State University,1996:1029-1110.
[29]BERN M, PLASSMANN P. Mesh Generation:Chapter 6 in Handbook of Computational Geometry[M]. North Holland:Elsevier B.V.,1999.
[30]TAM T, ARMSTRONG C.2D Finite Element Mesh Generation by Medial Axis Subdivision[J]. Advances in Engineering Software,1991,13:313-344.
[31]BLACKER M, T.D.AND STEPHENSON. Paving:a New Approach to Automated Quadrilateral Mesh Generation[J]. International Journal for Numerical Methods in Engineering,1991,32:811-847.
[32]FIELD D. The Legacy of Automatic Mesh Generation from Solid Modeling[J]. Computer Aided Geometric Design,1995,12:651-673.
[33]OWEN S. A Survey of Unstructured Mesh Generation Technology[C]. Proceedings:7th International Meshing Roundtable. Michigan:Dearborn,1998: 239-267.
[34]LEE K, HUANG M, YU R P, N.J. Grid Generation for General Three-Dimensional Configurations[C]. SMITH R. Proceeding NASA Langley Workshop on Numerical Grid Generation Techniques.1980:355.
[35]RIZK Y, BEN-SHMUEL S. Computation of the Viscous Flow Around the Shuttle Orbiter at Low Supersonic Speeds[J]. AIAA Paper,1985.
[36]SORENSON R. Three-Dimensional Elliptic Grid Generation about Fighter Aircraft for Zonal Finite-Difference Computations [J]. AIAA Paper,1986.
[37]ATTA E, BIRCHELBAW L, HALL K. A Zonal Grid Generation Method for Complex Configurations [J]. AIAA Paper,1987.
[38]BELK D, WHITFIELD D. Three-Dimensional Euler Solutions on Blocked Grids Using an Implicit Two-Pass Algorithms [J]. AIAA Paper,1987.
[39]ANDREWS A. Progress and Challenges in the Application of Artificial Intelligence to Computational Fluid Dynamics[J]. AIAA Paper,1988,26:40-46.
[40]ALLWRIGHT S. Multiblock Topology Specification and Grid Generation for Complete Aircraft Configurations[C]. CHMIDT W. AGARD Conference Proceedings 464:Applications of Mesh Generation to Complex 3-D Configurations. Loen, Norway:Advisory Group for Aerospace Research and Development,1989.
[41]THOMAS P. Composite Three-Dimensional Grids Generated by Elliptic Systems[J]. AIAA Paper,1982,20(9):1195-1202.
[42]ERIKSSON L. Practical Three-Dimensional Mesh Generation Using Transfinite Interpolation. Lecture Series Notes 1983-04,von Karman Institute for Fluid Dynamics, Brussels[J].1983.
[43]RUBBERT P, LEE K. Patched Coordinate Systems. In Thompson, J.F. (ed.),Numerical Grid Generation[M]. Amsterdam:North Holland,1982:235.
[44]ATTA E, VADYAK J. A Grid Interfacing Zonal Algorithm for Three-dimensional Transonic Flows About Aircraft Configurations [J]. AIAA Paper,1982:82-107.
[45]BERGER M, OLIGER J. Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. Manuscript NA-83-02,Stanford University, March[J]. 1983.
[46]BENEK J, STEGER J, DOUGHERTY F. A Flexible Grid Embedding Technique with Application to the Euler Equations[J]. AIAA Paper,1983.
[47]MIKI K, TAKAGI T. A Domain Decomposition and Overlapping Method for the Generation of Three-Dimensional Boundary-Fitted Coordinate Systems [J]. Journal of Computational Physics,1984,53:319-330.
[48]ZHENG Y, LIOU M. A Novel Approach of Three-Dimensional Hybrid Grid Methodology:Part 1.Grid Generation[J]. Computer Methods in Applied Mechanics and Engineering,2003,192:4147-4171.
[49]LIOU M, ZHENG Y. A Novel Approach of Three-Dimensional Hybrid Grid Methodology:Part 2. Flow Solution[J]. Computer Methods in Applied Mechanics and Engineering,2003,192:4173-4193.
[50]ATHANASIADIS A, DECONINCK H. A Folding/Unfolding Algorithm for the Construction of Semi-Structured Layers in Hybrid Grid Generation[J]. Computer Methods in Applied Mechanics and Engineering,2005,194(48-49): 5051-5067.
[51]BOURCHTEIN L, BOURCHTEIN A. On Grid Generation for Numerical Models of Geophysical Fluid Dynamics [J]. Journal of Computational and Applied Mathematics,2008,218(2):317-328.
[52]CHEN T, YANG H. Numerical Construction of Optimal Adaptive Grids in Two Spatial Dimensions[J]. Computers & Mathematics with Applications,2000, 39(12):101-120.
[53]LONG Q, XU X, COLLINS M, et al. Magnetic resonance image processing and structured grid generation of a human abdominal bifurcation[J]. Computer Methods and Programs in Biomedicine,1998,56(3):249-259.
[54]MIKHAIL M. Automatic Grid Generation for Finite Element Models Using the Finite Element Package[J]. Mathematical and Computer Modeling,1990,14: 136-138.
[55]ROACH P. The Generation of Nearly Isotropic Turbulence by Means of Grids[J]. International Journal of Heat and Fluid Flow,1987,8(2):82-92.
[56]SMITH R. Algebraic Grid Generation[J]. Applied Mathematics and Computation, 1982,10-11:137-170.
[57]SOUZA B, MATOS E, FURLAN L, et al. A Simple Two-Dimensional Method for Orthogonal and Nonorthogonal Grid Generation[J]. Computers& Chemical Engineering,2007,31(7):800-807.
[58]SPITALERI R, MICACCHI V. A Multiblock Multigrid Grid Generation Method for Complex Simulations[J], Mathematics and Computers in Simulation,1998, 46(1):1-12.
[59]YU T, SONI B. Application of in Numerical Grid Generation[J]. Computer-Aided Design,1995,27(2):147-157.
[60]ZOCHOWSKI A, HOLNICKI P. Interactive Method of Variational Grid Generation[J]. Journal of Computational and Applied Mathematics,1989,26(3): 281-287.
[61]EGIDI N, MAPONI P. A Class of Network Optimization Methods for Planar Grid Generation[J]. Applied Numerical Mathematics,2005,52:363-379.
[62]THOMPSON J, WARSI Z, MASTIN C. Numerical Grid Generation. Foundations and Applications.[M]. North Holland, Amsterdam,1985.
[63]KNUPP P, STEINBERG S. Fundamentals of Grid Generation[M]. Boca Raton: CRC Press,1993.
[64]EISEMAN P. Grid Generation for Fluid Mechanics Computations [J]. Annual Review of Fluid Mechanics,1985,17(17):487-522.
[65]LISEIKIN V. Techniques for Generating Three-Dimensional Grids in Aerodynamics (Review)[C]. Probl. At. Sci. Tech. Ser. Math. Model. Phys. Process. Russian.1991:31-45.
[66]ALALYKIN G, GODUNOV S, KIREYEVA L, et al. On Solution of One-Dimensional Problems of Gas Dynamics in Moving Grids[M]. Moscow: Nauka,1970.
[67]LISEIKIN V, PETRENKO V. Adaptive Invariant Method for the Numerical Solution of Problems with Boundary and Interior Layers[M]. Novosibirsk: Computer Center SD AS USSR,1989.
[68]LISEIKIN V. Layer Resolving Grids and Transformations for Singular Perturbation Problems[M]. Utrecht:VSP,2001.
[69]ANDERSON D. Adaptive Grid Methods for Partial Differential Equations.In Ghia, K.N., Ghia,U. (eds.),Advances in Grid Generation[M]. Houston:ASME, 1983:1-15.
[70]THOMPSON J. A Survey of Dynamically-Adaptive Grids in the Numerical Solution of Partial Differential Equations[J]. AIAA Paper,1984:84-106.
[71]EISEMAN P. Adaptive Grid Generation [J]. Computer Methods in Applied Mechanics and Engineering,1987,64(64):321-376.
[72]HAWKEN D, GOTTLIEB J, HANSEN J. Review of Some Adaptive Node-Movement Techniques in Finite-Element and Finite-Difference Solutions of Partial Differential Equations[J]. Journal of Computational Physics,1991, 95(95):254-302.
[73]LISEIKIN V. Construction of structured adaptive grids—a review[J]. Computational Mathematics and Mathematical Physics,1996,36(1):1-32.
[74]BAKER T. Mesh Adaptation Strategies for Problems in Fluid Dynamics[J]. Finite Elements in Analysis and Design-Special Issue:Adaptive Meshing Part 2, 1997,25:243-273.
[75]HEDSTROM G, RODRIGUE C. Adaptive-Grid Methods for Time-Dependent Partial Differential Equations. Lect. Notes Math.[M]. Berlin:Springer,1982.
[76]ERIKSSON L. Generation of Boundary-Conforming Grids Around Wingbody Configurations Using Transfinite Interpolation[J]. AIAA Paper,1982,20: 1313-1320.
[77]陶文铨.数值传热学(第2版)[M].西安：西安交通大学出版社,2004.
[78]陶文铨.计算传热学的近代进展[M].北京：科学出版社,2000.
[79]FARRASHKHALVAT M, MILES J. Basic Structured Grid Generation:With an introduction to unstructured grid generation[M]. Oxford:Butterworth-Heineman, 2003.
[80]金隽.网格生成算法研究和软件实现[D].上海：复旦大学,2008.
[81]张永华.叶轮机CFD网格生成[D].南京：南京航空航天大学,2007.
[82]刘厚林,董亮,王勇,et al流体机械CFD中得网格生成方法进展[J].流体机械,2010,38(4)：32-37.
[83]WINSLOW A. Numerical Solution of the Quasilinear Poisson Equation in a Nonuniform Triangle Mesh[J]. Journal of Computational Physics,1967,2:149-172.
[84]THOMPSONB J, THAMES F, MASTIN C. Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate System for Field Containing any Number of Arbitrary Two Dimensional Bodies[J]. Journal of Computational Physics,1974, 15(3):299-319.
[85]NAKAMURA S. Marching Grid Generation Using Parabolic Partial Differential Equations[J]. In:Thompson J F (eds.). Numerical Grid Generation. New York: Elsevier.,1982:79-105.
[86]BRACKBILL J, SDNMAN J. Adaptive Zoning for Singular Problems in Two Dimensions [J]. Journal of Computational Physics,1982,46:342-368.
[87]于明.二维自适应结构网格的变分生成方法[J].计算物理,2004,21(1)：27-34.
[88]康红文,谷湘潜,柳崇健.自适应网格技术中的权函数问题研究[J].力学学报,2002,34(5)：790-795.
[89]THACKER W. A Brief Review of Techniques for Generating Irregular Computational Grids[J]. International Journal for Numerical Methods in Engineering,1980,15(9):1335-1341.
[90]HO-LE K. Finite element mesh generation methods:a review and classification[J]. Computer-aided design,1988,20:27-38.
[91]SHEPHARD M, GRICE K, LOT J, et al. Trends in Automatic Three-Dimensional Mesh Generation[J]. Computers & Structures,1988,30(1/2): 421-429.
[92]BAKER T. Prospects and Expectations for Unstructured Methods[J]. Computational Fluid Dynamic Solutions,1995:273-287.
[93]CAREY G. Computational Grids:Generation, Adaptation and Solution Strategies[M]. London:Taylor and Francis,1997.
[94]GEORGE P, BOROUCHAKI H. Delaunay Triangulation and Meshing[M]. Paris: Hermes,1998.
[95]KRUG LJAKOVA L, NELEDOVA A, TISHKIN V, et al. Unstructured Adaptive Grids for Problems of Mathematical Physics (Survey)[J]. Matematicheskoe modelirovanie,1998,10(3):93-116.
[96]刘二勇.冲压成形有限元模拟自适应三角形网格剖分方法的研究与实现[D].上海：上海交通大学,2007.
[97]李新星.基于DUSE的数字—数值一体化核心技术研究及其应用[D].上海：同济大学，2007.
[98]李来纪.基于注射成型模拟系统的表面网格技术研究[D].武汉：华中科技大学,2007.
[99]李寒清.结冰机翼自适应非结构化网格生成及流场分析[D].上海：复旦大学,2010.
[100]DELAUNAY B. Sur La Sphere Vide. Bull. Acad. Sci. USSR VII:Class Sci. Mat. Nat[J].1934,6:793-800.
[101]DELAUNAY B. Petersburg School of Number Theory [M]. Moscow:Akad. Sci. USSR,1947.
[102]VORONOI G. Nouvelles Applications des Parameters Countinus a la Theorie des Formes Quadratiques.Deuxieme Memoire:Recherches Sur La Parallelloedres Primitifs[J]. Journal fur die Reine und Angewandte Mathematik (Crelles Journal),1908,134:198-287.
[103]BAKER T. Automatic Mesh Generation for Complex Three-Dimensional Region Using a Constrained Delaunay Triangulation[J]. Engineering with Computers,1989,5(3-4):161-175.
[104]关振群,宋超,顾元宪等.有限元网格生成方法研究的新进展[J].计算机辅助设计与图形学学报,2003,15(1)：1-14.
[105]袁友伟.自适应非结构化网格生成及优化技术研究[D].武汉：武汉理工大学,2007.
[106]单菊林.自适应有限元网格生成算法研究与应用[D].大连：大连理工大学,2007.
[107]赵建.自适应有限元在注塑成型数值模拟中的应用[D].郑州：郑州大学,2006.
[108]LOHNER R. Matching Semi-Structured and Unstructured Grids for Navier-Stokes Calculations[J].AIAA Paper,1993.
[109]PIRZADEH S. Recent Progress in Unstructured Grid Generation[J]. AIAA Paper,1992.
[110]PARTHASARATHY V, KALLINDERIS Y. Directional Viscous Multigrid Using Adaptive Prismatic Meshes[J]. AIAA Paper,1995,33(1):69-78.
[111]宋超.非结构化自适应有限元网格生成的AFT方法[D].大连：大连理工大学，2004.
[112]LOHNER R. Some Useful Data Structures for the Generation of Unstructured Grids[J]. Communications in Applied Numerical Methods,1988,4:123-135.
[113]SHEPHARD M, GUERTNONI F, FLAHERTY J, et al. Finite Octree Mesh Generation for Automated Adaptive Three-Dimensional Flow Analysis In Sengupta, S., Hauser, J., Eiseman, P.R., Thompson, J.F. (eds.),Numerical Grid Generation in Computational Fluid Mechanics[M]. Swansea:Pineridge,1988: 709-718.
[114]SCHNEIDERS R, BUNTEN R. Automatic Generation of Hexahedral Finite Element Meshes [J]. Computer Aided Geometric Design,1995,12(7):693.
[115]刘含波.基于散乱点云数据的隐式曲面重建研究[D].哈尔滨：哈尔滨工业大学,2009.
[116]BLOOMENTHAL J, WYVILL B. Interactive Techniques for Implicit Modeling[J]. Computer Graphics,1990,24(2):109-116.
[117]BLOOMENTHAL J, SHOEMAKE K. Convolution Surfaces[C]. ACM. In: Proceedings of SIGGRAPH. New York,1991:251-256.
[118]SAVCHENKO V, PASKO A, OKUNEV O, et al. Function Representation of Solids Reconstructed from Scattered Surface Points and Contours[J]. Computer Graphics Forum,1995,14(4):181-188.
[119]WYVILL B, GALIN E, GUY A. Extending the CSG Tree:Warping Blending and Boolean Operations in an Implicit Surface Modeling System[J]. Computer Graphics Forum,1999,18(2):149-158.
[120]BLINN J. A Generalization of Algebraic Surface Drawing[J]. ACM Transactions on Graphics,1982, 1(3):235-256.
[121]NISHIMURA H, HIRAI M, KAWAI T, et al. Object Modeling by distribution function and a method of image generation(In Japanese, translated into English by Fujuwara, T.)[J]. The Transactions of the Institute of Electronics and Communication Engineers of Japan,1985, J68-D(4):718-725.
[122]WYVILL G, MCPHEETERS C, WYVILL B. Data structure for soft objects[J]. The Visual Computer,1986,2(4):227-234.
[123]FREY P, GEORGE P. Mesh Generation:Application to Finite Elements[M]. Hermes:Oxford,2000.
[124]KNUPP P, ROBIDOUX N. A Framework for Variational Grid Generation: Conditioning the Jacobean Matrix With Matrix Norms[J]. SIAM Journal on Scientific Computing,2000,21:2029-2047.
[125]SPITALERI R. Full-FAS Multigrid Grid Generation Algorithms [J]. Applied Numerical Mathematics,2000,32:483-494.
[126]ZHANG Y, JIA Y, WANG S.2D Nearly Orthogonal Mesh Generation with Controls on Distortion Function[J]. Journal of Computational Physics,2006, 218:549-571.
[127]ITO Y, SHIH A, ERUKALA A. Parallel Unstructured Mesh Generation by an Advancing Front Method[J]. Mathematics and Computers in Simulation,2007, 75:200-209.
[128]BARRERA-SANCHEZ P, FLORES G, DOMINGUEZ-MOTA F. Some Experiences on Orthogonal Grid Generation[J]. Applied Numerical Mathematics,2002,40:179-190.
[129]BERTSEKAS D. Linear Network Optimization[M]. Cambridge:MIT Press, 1991.
[130]BOWYER A. Computing Dirichlet Tessallations[J]. The Computer Journal, 1981,24(2):162-166.
[131]LAWSON C. Software for C1 Surface Interpolation[J]. Mathematical Software, 1977:161-194.
[132]PERAIRE J, VAHDATI P, MORGAN K. Adaptive Remeshing for Pressible flow Computations [J]. Journal of Computational Physics,1987,72:449-466.
[133]WATSON D. Computing the N-Dimensional Delaunay Tessellation with Application to Voronoi Polytopes[J]. The Computer Journal,1981,24:161-172.
[134]WATHERILLN. Mixed Structured-Unstructured Meshes for Aerodynamic flow Simulation[J]. The Aeronautical Journal,1990,84:111-123.
[135]ZIENKIEWICZ O, PHILLIPS D. An Automatic Mesh Generation Scheme for Plane and Curved Surfaces by Isoparametric Coordinates [J]. International Journal for Numerical Methods in Engineering,1971,3:519-528.
[136]EGIDIN, MAPONI P. A Linearly Constrained Optimization Problem for Planar Grid Generation[J]. Applied Numerical Mathematics,2005,55(3):283-294.
[137]CASTILLO J, OTTO J. A Generalized Length Strategy for Direct Optimization in Planar Grid generation[J]. Mathematics and Computers in Simulation,1997, 44:441-456.
[138]LIU S, JIN X, WANG C, et al. Ellipsoidal-blob Approximation of 3D Models and Its Applications[J]. Computers & Graphics,2007,31(2):243-251.
[139]JIN X, TAI C, ZHANG H. Implicit Modeling from Polygon Soup Using Convolution[J]. The Visual Computer,2009,25(3):279-288.
[140]TAI C, ZHANG H, FONG J. Prototype Modeling from Sketched Silhouettes Based on Convolution Surfaces [J]. Computer Graphics Forum,2004,23(1): 71-84.
[141]LIU S, JIN X, LIN J, et al. Extended metaball modeling techniques based on 2D silhouette curves [J]. Journal of software, Accepted(In Chinese).
[142]刘圣军.基于几何的水和云彩动画特效模拟[D].浙江：浙江大学,2007.
[143]MURAKAMI S, ICHIHARA H. On a 3D Display Method by Metaball Technique[J]. Journal of the Electronics Communication,1987, J70-D(8): 1607-1615.
[144]RAN JAN V, FOURNIER A. Matching and Interpolation of Shapes using Unions of Circles[J]. Computer Graphics Forum,1996,15(3):129-142.
[145]LEE D. Medial Axis Transformation of a Planar Shape[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1982,4(4):363-369.
[146]SHEWCHUK J. Triangle:Engineering a 2D Quality Mesh Generator and Delaunay Triangulator[C]. First Workshop on Applied Computational Geometry..[S.l.]:[s.n.],1996:124-133.
[147]SUN L, JIN X, FENG J, et al.3D Metaball Modeling Technique Based on 2D Silhouette Curves[J]. Journal of System Simulation,2003,15:96-98.
[148]BISCHOFF S, KOBBELT L. Ellipsoid Decomposition of 3D-models. In: Proceedings of International Symposium on 3D Data Processing, Visualization, and Transmission[M]. New York:IEEE Computer Society Press,2002: 480-488.
[149]JU T, LOSASSO F, SCHAEFER S, et al. Dual contouring of hermite data[J]. ACM Transactions on Graphics (TOG).Proceedings of ACM SIGGRAPH,2002, 21(339-346).
[150]BLOOMENTHAL J. Polygonization of Implicit Surfaces[J]. Computer Aided Geometric Design,1988,5(4):341-355.
[2]FARIN G, HANSFORD D. Discrete Coons patches[J]. Computer Aided Geometric Design,1999,16(7):691-700.
[3]SONI B. Grid Generation:Past, Present and Future[J]. Applied Numerical Mathematics,2000,32:361-369.
[4]KHAMAYSEH A, HAMANN B. Elliptic Grid Generation Using NURBS Surfaces[J]. Computer Aided Geometric Design,1996,13(4):369-386.
[5]MONTERDE J, UGAIL H. A General 4th-order PDE Method to Generate Bezier Surfaces from the Boundary [J]. Computer Aided Geometric Design,2006, 23:208-225.
[6]NEFUSSI G, GILORMINI P. A Simplified Method for The Simulation of Cold-Roll Forming[J]. International Journal of Mechanical Sciences,1993, 35:867-878.
[7]THOMPSON J, SONI B, WEATHERILL N. Handbook of Grid Generation[M]. Washington,D.C:CRC Press,1999.
[8]WANG C, TANG K. Non-self-overlapping Hermite Interpolation Mapping:a Practical Solution for Structured Quadrilateral Meshing [J]. Computer-Aided Design,2005,37:271-283.
[9]YANG D, CHUANG J, HAN Z, et al. Boundary-Conformed Toolpath Generation for Trimmed Free-Form Surfaces via Coons Reparametrization[J]. Journal of Materials Processing Technology,2003,138:138-144.
[10]TINOCO-RUIZ J, BARRERA-SANCHEZ P. Smooth and Convex Grid Generation over General Plane Regions[J]. Mathematics and Computers in Simulation,1998,46:87-102.
[11]CASTILLO J, OTTO J. A Practical Guide to Direct Optimization for Planar Grid-Generation[J]. Computers & Mathematics with Applications,1999,37: 123-156.
[12]CONTI C, MORANDI R, SPITALERI R. An Algebraic Grid Optimization Algorithm Using Condition Numbers [J]. Applied Numerical Mathematics,2006, 56(8):1123-1133.
[13]陈建军.非结构化网格生成及其并行化的若干问题研究[D].杭州：浙江大学,2006.
[14]GEORGALA J, SHAW J. A Discussion on Issues Relating to Multiblock Grid Generation[C]. SCHMIDT W. AGARD Conference Proceedings 464: Applications of Mesh Generation to Complex 3-D Configurations. Loen, Norway:Advisory Group for Aerospace Research and Development,1989.
[15]LISEIKIN V. Grid Generation Methods[M]. Springe Dordrecht Heidelberg London New York:Springer,2009.
[16]BENEK J, BUNING P, STEGER J. A 3-D Chimera Grid Embedding Technique[J].AIAA paper,1985.
[17]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：高等教育出版社,2001.
[18]ABRAHAMSSON L. Orthogonal Grid Generation for Two-Dimensional Ducts[J]. Journal of Computational and Applied Mathematics,1991,34(3): 305-314.
[19]BOURCHTEIN A, BOURCHTEIN L. On Generation of Orthogonal Grids[J]. Applied Mathematics and Computation,2006,173(2):767-781.
[20]BRAKHAGE K, LAMBY P. Application of B-Spline Techniques to the Modeling of Airplane Wings and Numerical Grid Generation [J]. Computer Aided Geometric Design,2008,25(9):738-750.
[21]CASTILLO J, STEINBERG P, S.ANDROACHE. Mathematical Aspects of Variational Grid Generation II[J]. Journal of Computational and Applied Mathematics,1987,20:127-135.
[22]CONTI C, MORANDI R, RABUT C. Locally Tensor Product Functions in Algebraic Grid Optimization[J]. Applied Mathematics and Computation,2008, 197(2):745-754.
[23]DOUGHERTY R, HYMAN J. A Divide-And-Conquer Algorithm for Grid Generation[J]. Applied Numerical Mathematics,1994,14(1-3):125-134.
[24]EGIDI N, MAPONI P. A Robust Direct Variational Approach for Generation of Quadrangular and Triangular Grids on Planar Domains[J]. Mathematics and Computers in Simulation,2007,75(5-6):171-181.
[25]MAKHANOV S, IVANENKO S. Grid Generation as Applied to Optimize Cutting Operations of the Five-Axis Milling Machine [J]. Applied Numerical Mathematics,2003,46(3-4):331-351.
[26]WEN X, INGHAM D, DOMBROWSKI N, et al. The Generation of an Orthogonal Grid by the Use of a Boundary Integral Technique [J]. Engineering Analysis with Boundary Elements,1998,21(3):197-205.
[27]THOMPSON J, WEATHERILL N. Aspects of Numerical Grid Generation: Current Science and Art[J]. AIAA Paper,1993:1029-1070.
[28]THOMPSON J. A Reflection on Grid generation in the 90s:Trends, Needs Influences. In Soni, B.K., Thompson, J.F., Hauser, J., Eiseman, P.R. (eds.), Numerical Grid Generation in CFD[M]. Mississippi:Mississippi State University,1996:1029-1110.
[29]BERN M, PLASSMANN P. Mesh Generation:Chapter 6 in Handbook of Computational Geometry[M]. North Holland:Elsevier B.V.,1999.
[30]TAM T, ARMSTRONG C.2D Finite Element Mesh Generation by Medial Axis Subdivision[J]. Advances in Engineering Software,1991,13:313-344.
[31]BLACKER M, T.D.AND STEPHENSON. Paving:a New Approach to Automated Quadrilateral Mesh Generation[J]. International Journal for Numerical Methods in Engineering,1991,32:811-847.
[32]FIELD D. The Legacy of Automatic Mesh Generation from Solid Modeling[J]. Computer Aided Geometric Design,1995,12:651-673.
[33]OWEN S. A Survey of Unstructured Mesh Generation Technology[C]. Proceedings:7th International Meshing Roundtable. Michigan:Dearborn,1998: 239-267.
[34]LEE K, HUANG M, YU R P, N.J. Grid Generation for General Three-Dimensional Configurations[C]. SMITH R. Proceeding NASA Langley Workshop on Numerical Grid Generation Techniques.1980:355.
[35]RIZK Y, BEN-SHMUEL S. Computation of the Viscous Flow Around the Shuttle Orbiter at Low Supersonic Speeds[J]. AIAA Paper,1985.
[36]SORENSON R. Three-Dimensional Elliptic Grid Generation about Fighter Aircraft for Zonal Finite-Difference Computations [J]. AIAA Paper,1986.
[37]ATTA E, BIRCHELBAW L, HALL K. A Zonal Grid Generation Method for Complex Configurations [J]. AIAA Paper,1987.
[38]BELK D, WHITFIELD D. Three-Dimensional Euler Solutions on Blocked Grids Using an Implicit Two-Pass Algorithms [J]. AIAA Paper,1987.
[39]ANDREWS A. Progress and Challenges in the Application of Artificial Intelligence to Computational Fluid Dynamics[J]. AIAA Paper,1988,26:40-46.
[40]ALLWRIGHT S. Multiblock Topology Specification and Grid Generation for Complete Aircraft Configurations[C]. CHMIDT W. AGARD Conference Proceedings 464:Applications of Mesh Generation to Complex 3-D Configurations. Loen, Norway:Advisory Group for Aerospace Research and Development,1989.
[41]THOMAS P. Composite Three-Dimensional Grids Generated by Elliptic Systems[J]. AIAA Paper,1982,20(9):1195-1202.
[42]ERIKSSON L. Practical Three-Dimensional Mesh Generation Using Transfinite Interpolation. Lecture Series Notes 1983-04,von Karman Institute for Fluid Dynamics, Brussels[J].1983.
[43]RUBBERT P, LEE K. Patched Coordinate Systems. In Thompson, J.F. (ed.),Numerical Grid Generation[M]. Amsterdam:North Holland,1982:235.
[44]ATTA E, VADYAK J. A Grid Interfacing Zonal Algorithm for Three-dimensional Transonic Flows About Aircraft Configurations [J]. AIAA Paper,1982:82-107.
[45]BERGER M, OLIGER J. Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. Manuscript NA-83-02,Stanford University, March[J]. 1983.
[46]BENEK J, STEGER J, DOUGHERTY F. A Flexible Grid Embedding Technique with Application to the Euler Equations[J]. AIAA Paper,1983.
[47]MIKI K, TAKAGI T. A Domain Decomposition and Overlapping Method for the Generation of Three-Dimensional Boundary-Fitted Coordinate Systems [J]. Journal of Computational Physics,1984,53:319-330.
[48]ZHENG Y, LIOU M. A Novel Approach of Three-Dimensional Hybrid Grid Methodology:Part 1.Grid Generation[J]. Computer Methods in Applied Mechanics and Engineering,2003,192:4147-4171.
[49]LIOU M, ZHENG Y. A Novel Approach of Three-Dimensional Hybrid Grid Methodology:Part 2. Flow Solution[J]. Computer Methods in Applied Mechanics and Engineering,2003,192:4173-4193.
[50]ATHANASIADIS A, DECONINCK H. A Folding/Unfolding Algorithm for the Construction of Semi-Structured Layers in Hybrid Grid Generation[J]. Computer Methods in Applied Mechanics and Engineering,2005,194(48-49): 5051-5067.
[51]BOURCHTEIN L, BOURCHTEIN A. On Grid Generation for Numerical Models of Geophysical Fluid Dynamics [J]. Journal of Computational and Applied Mathematics,2008,218(2):317-328.
[52]CHEN T, YANG H. Numerical Construction of Optimal Adaptive Grids in Two Spatial Dimensions[J]. Computers & Mathematics with Applications,2000, 39(12):101-120.
[53]LONG Q, XU X, COLLINS M, et al. Magnetic resonance image processing and structured grid generation of a human abdominal bifurcation[J]. Computer Methods and Programs in Biomedicine,1998,56(3):249-259.
[54]MIKHAIL M. Automatic Grid Generation for Finite Element Models Using the Finite Element Package[J]. Mathematical and Computer Modeling,1990,14: 136-138.
[55]ROACH P. The Generation of Nearly Isotropic Turbulence by Means of Grids[J]. International Journal of Heat and Fluid Flow,1987,8(2):82-92.
[56]SMITH R. Algebraic Grid Generation[J]. Applied Mathematics and Computation, 1982,10-11:137-170.
[57]SOUZA B, MATOS E, FURLAN L, et al. A Simple Two-Dimensional Method for Orthogonal and Nonorthogonal Grid Generation[J]. Computers& Chemical Engineering,2007,31(7):800-807.
[58]SPITALERI R, MICACCHI V. A Multiblock Multigrid Grid Generation Method for Complex Simulations[J], Mathematics and Computers in Simulation,1998, 46(1):1-12.
[59]YU T, SONI B. Application of in Numerical Grid Generation[J]. Computer-Aided Design,1995,27(2):147-157.
[60]ZOCHOWSKI A, HOLNICKI P. Interactive Method of Variational Grid Generation[J]. Journal of Computational and Applied Mathematics,1989,26(3): 281-287.
[61]EGIDI N, MAPONI P. A Class of Network Optimization Methods for Planar Grid Generation[J]. Applied Numerical Mathematics,2005,52:363-379.
[62]THOMPSON J, WARSI Z, MASTIN C. Numerical Grid Generation. Foundations and Applications.[M]. North Holland, Amsterdam,1985.
[63]KNUPP P, STEINBERG S. Fundamentals of Grid Generation[M]. Boca Raton: CRC Press,1993.
[64]EISEMAN P. Grid Generation for Fluid Mechanics Computations [J]. Annual Review of Fluid Mechanics,1985,17(17):487-522.
[65]LISEIKIN V. Techniques for Generating Three-Dimensional Grids in Aerodynamics (Review)[C]. Probl. At. Sci. Tech. Ser. Math. Model. Phys. Process. Russian.1991:31-45.
[66]ALALYKIN G, GODUNOV S, KIREYEVA L, et al. On Solution of One-Dimensional Problems of Gas Dynamics in Moving Grids[M]. Moscow: Nauka,1970.
[67]LISEIKIN V, PETRENKO V. Adaptive Invariant Method for the Numerical Solution of Problems with Boundary and Interior Layers[M]. Novosibirsk: Computer Center SD AS USSR,1989.
[68]LISEIKIN V. Layer Resolving Grids and Transformations for Singular Perturbation Problems[M]. Utrecht:VSP,2001.
[69]ANDERSON D. Adaptive Grid Methods for Partial Differential Equations.In Ghia, K.N., Ghia,U. (eds.),Advances in Grid Generation[M]. Houston:ASME, 1983:1-15.
[70]THOMPSON J. A Survey of Dynamically-Adaptive Grids in the Numerical Solution of Partial Differential Equations[J]. AIAA Paper,1984:84-106.
[71]EISEMAN P. Adaptive Grid Generation [J]. Computer Methods in Applied Mechanics and Engineering,1987,64(64):321-376.
[72]HAWKEN D, GOTTLIEB J, HANSEN J. Review of Some Adaptive Node-Movement Techniques in Finite-Element and Finite-Difference Solutions of Partial Differential Equations[J]. Journal of Computational Physics,1991, 95(95):254-302.
[73]LISEIKIN V. Construction of structured adaptive grids—a review[J]. Computational Mathematics and Mathematical Physics,1996,36(1):1-32.
[74]BAKER T. Mesh Adaptation Strategies for Problems in Fluid Dynamics[J]. Finite Elements in Analysis and Design-Special Issue:Adaptive Meshing Part 2, 1997,25:243-273.
[75]HEDSTROM G, RODRIGUE C. Adaptive-Grid Methods for Time-Dependent Partial Differential Equations. Lect. Notes Math.[M]. Berlin:Springer,1982.
[76]ERIKSSON L. Generation of Boundary-Conforming Grids Around Wingbody Configurations Using Transfinite Interpolation[J]. AIAA Paper,1982,20: 1313-1320.
[77]陶文铨.数值传热学(第2版)[M].西安：西安交通大学出版社,2004.
[78]陶文铨.计算传热学的近代进展[M].北京：科学出版社,2000.
[79]FARRASHKHALVAT M, MILES J. Basic Structured Grid Generation:With an introduction to unstructured grid generation[M]. Oxford:Butterworth-Heineman, 2003.
[80]金隽.网格生成算法研究和软件实现[D].上海：复旦大学,2008.
[81]张永华.叶轮机CFD网格生成[D].南京：南京航空航天大学,2007.
[82]刘厚林,董亮,王勇,et al流体机械CFD中得网格生成方法进展[J].流体机械,2010,38(4)：32-37.
[83]WINSLOW A. Numerical Solution of the Quasilinear Poisson Equation in a Nonuniform Triangle Mesh[J]. Journal of Computational Physics,1967,2:149-172.
[84]THOMPSONB J, THAMES F, MASTIN C. Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate System for Field Containing any Number of Arbitrary Two Dimensional Bodies[J]. Journal of Computational Physics,1974, 15(3):299-319.
[85]NAKAMURA S. Marching Grid Generation Using Parabolic Partial Differential Equations[J]. In:Thompson J F (eds.). Numerical Grid Generation. New York: Elsevier.,1982:79-105.
[86]BRACKBILL J, SDNMAN J. Adaptive Zoning for Singular Problems in Two Dimensions [J]. Journal of Computational Physics,1982,46:342-368.
[87]于明.二维自适应结构网格的变分生成方法[J].计算物理,2004,21(1)：27-34.
[88]康红文,谷湘潜,柳崇健.自适应网格技术中的权函数问题研究[J].力学学报,2002,34(5)：790-795.
[89]THACKER W. A Brief Review of Techniques for Generating Irregular Computational Grids[J]. International Journal for Numerical Methods in Engineering,1980,15(9):1335-1341.
[90]HO-LE K. Finite element mesh generation methods:a review and classification[J]. Computer-aided design,1988,20:27-38.
[91]SHEPHARD M, GRICE K, LOT J, et al. Trends in Automatic Three-Dimensional Mesh Generation[J]. Computers & Structures,1988,30(1/2): 421-429.
[92]BAKER T. Prospects and Expectations for Unstructured Methods[J]. Computational Fluid Dynamic Solutions,1995:273-287.
[93]CAREY G. Computational Grids:Generation, Adaptation and Solution Strategies[M]. London:Taylor and Francis,1997.
[94]GEORGE P, BOROUCHAKI H. Delaunay Triangulation and Meshing[M]. Paris: Hermes,1998.
[95]KRUG LJAKOVA L, NELEDOVA A, TISHKIN V, et al. Unstructured Adaptive Grids for Problems of Mathematical Physics (Survey)[J]. Matematicheskoe modelirovanie,1998,10(3):93-116.
[96]刘二勇.冲压成形有限元模拟自适应三角形网格剖分方法的研究与实现[D].上海：上海交通大学,2007.
[97]李新星.基于DUSE的数字—数值一体化核心技术研究及其应用[D].上海：同济大学，2007.
[98]李来纪.基于注射成型模拟系统的表面网格技术研究[D].武汉：华中科技大学,2007.
[99]李寒清.结冰机翼自适应非结构化网格生成及流场分析[D].上海：复旦大学,2010.
[100]DELAUNAY B. Sur La Sphere Vide. Bull. Acad. Sci. USSR VII:Class Sci. Mat. Nat[J].1934,6:793-800.
[101]DELAUNAY B. Petersburg School of Number Theory [M]. Moscow:Akad. Sci. USSR,1947.
[102]VORONOI G. Nouvelles Applications des Parameters Countinus a la Theorie des Formes Quadratiques.Deuxieme Memoire:Recherches Sur La Parallelloedres Primitifs[J]. Journal fur die Reine und Angewandte Mathematik (Crelles Journal),1908,134:198-287.
[103]BAKER T. Automatic Mesh Generation for Complex Three-Dimensional Region Using a Constrained Delaunay Triangulation[J]. Engineering with Computers,1989,5(3-4):161-175.
[104]关振群,宋超,顾元宪等.有限元网格生成方法研究的新进展[J].计算机辅助设计与图形学学报,2003,15(1)：1-14.
[105]袁友伟.自适应非结构化网格生成及优化技术研究[D].武汉：武汉理工大学,2007.
[106]单菊林.自适应有限元网格生成算法研究与应用[D].大连：大连理工大学,2007.
[107]赵建.自适应有限元在注塑成型数值模拟中的应用[D].郑州：郑州大学,2006.
[108]LOHNER R. Matching Semi-Structured and Unstructured Grids for Navier-Stokes Calculations[J].AIAA Paper,1993.
[109]PIRZADEH S. Recent Progress in Unstructured Grid Generation[J]. AIAA Paper,1992.
[110]PARTHASARATHY V, KALLINDERIS Y. Directional Viscous Multigrid Using Adaptive Prismatic Meshes[J]. AIAA Paper,1995,33(1):69-78.
[111]宋超.非结构化自适应有限元网格生成的AFT方法[D].大连：大连理工大学，2004.
[112]LOHNER R. Some Useful Data Structures for the Generation of Unstructured Grids[J]. Communications in Applied Numerical Methods,1988,4:123-135.
[113]SHEPHARD M, GUERTNONI F, FLAHERTY J, et al. Finite Octree Mesh Generation for Automated Adaptive Three-Dimensional Flow Analysis In Sengupta, S., Hauser, J., Eiseman, P.R., Thompson, J.F. (eds.),Numerical Grid Generation in Computational Fluid Mechanics[M]. Swansea:Pineridge,1988: 709-718.
[114]SCHNEIDERS R, BUNTEN R. Automatic Generation of Hexahedral Finite Element Meshes [J]. Computer Aided Geometric Design,1995,12(7):693.
[115]刘含波.基于散乱点云数据的隐式曲面重建研究[D].哈尔滨：哈尔滨工业大学,2009.
[116]BLOOMENTHAL J, WYVILL B. Interactive Techniques for Implicit Modeling[J]. Computer Graphics,1990,24(2):109-116.
[117]BLOOMENTHAL J, SHOEMAKE K. Convolution Surfaces[C]. ACM. In: Proceedings of SIGGRAPH. New York,1991:251-256.
[118]SAVCHENKO V, PASKO A, OKUNEV O, et al. Function Representation of Solids Reconstructed from Scattered Surface Points and Contours[J]. Computer Graphics Forum,1995,14(4):181-188.
[119]WYVILL B, GALIN E, GUY A. Extending the CSG Tree:Warping Blending and Boolean Operations in an Implicit Surface Modeling System[J]. Computer Graphics Forum,1999,18(2):149-158.
[120]BLINN J. A Generalization of Algebraic Surface Drawing[J]. ACM Transactions on Graphics,1982, 1(3):235-256.
[121]NISHIMURA H, HIRAI M, KAWAI T, et al. Object Modeling by distribution function and a method of image generation(In Japanese, translated into English by Fujuwara, T.)[J]. The Transactions of the Institute of Electronics and Communication Engineers of Japan,1985, J68-D(4):718-725.
[122]WYVILL G, MCPHEETERS C, WYVILL B. Data structure for soft objects[J]. The Visual Computer,1986,2(4):227-234.
[123]FREY P, GEORGE P. Mesh Generation:Application to Finite Elements[M]. Hermes:Oxford,2000.
[124]KNUPP P, ROBIDOUX N. A Framework for Variational Grid Generation: Conditioning the Jacobean Matrix With Matrix Norms[J]. SIAM Journal on Scientific Computing,2000,21:2029-2047.
[125]SPITALERI R. Full-FAS Multigrid Grid Generation Algorithms [J]. Applied Numerical Mathematics,2000,32:483-494.
[126]ZHANG Y, JIA Y, WANG S.2D Nearly Orthogonal Mesh Generation with Controls on Distortion Function[J]. Journal of Computational Physics,2006, 218:549-571.
[127]ITO Y, SHIH A, ERUKALA A. Parallel Unstructured Mesh Generation by an Advancing Front Method[J]. Mathematics and Computers in Simulation,2007, 75:200-209.
[128]BARRERA-SANCHEZ P, FLORES G, DOMINGUEZ-MOTA F. Some Experiences on Orthogonal Grid Generation[J]. Applied Numerical Mathematics,2002,40:179-190.
[129]BERTSEKAS D. Linear Network Optimization[M]. Cambridge:MIT Press, 1991.
[130]BOWYER A. Computing Dirichlet Tessallations[J]. The Computer Journal, 1981,24(2):162-166.
[131]LAWSON C. Software for C1 Surface Interpolation[J]. Mathematical Software, 1977:161-194.
[132]PERAIRE J, VAHDATI P, MORGAN K. Adaptive Remeshing for Pressible flow Computations [J]. Journal of Computational Physics,1987,72:449-466.
[133]WATSON D. Computing the N-Dimensional Delaunay Tessellation with Application to Voronoi Polytopes[J]. The Computer Journal,1981,24:161-172.
[134]WATHERILLN. Mixed Structured-Unstructured Meshes for Aerodynamic flow Simulation[J]. The Aeronautical Journal,1990,84:111-123.
[135]ZIENKIEWICZ O, PHILLIPS D. An Automatic Mesh Generation Scheme for Plane and Curved Surfaces by Isoparametric Coordinates [J]. International Journal for Numerical Methods in Engineering,1971,3:519-528.
[136]EGIDIN, MAPONI P. A Linearly Constrained Optimization Problem for Planar Grid Generation[J]. Applied Numerical Mathematics,2005,55(3):283-294.
[137]CASTILLO J, OTTO J. A Generalized Length Strategy for Direct Optimization in Planar Grid generation[J]. Mathematics and Computers in Simulation,1997, 44:441-456.
[138]LIU S, JIN X, WANG C, et al. Ellipsoidal-blob Approximation of 3D Models and Its Applications[J]. Computers & Graphics,2007,31(2):243-251.
[139]JIN X, TAI C, ZHANG H. Implicit Modeling from Polygon Soup Using Convolution[J]. The Visual Computer,2009,25(3):279-288.
[140]TAI C, ZHANG H, FONG J. Prototype Modeling from Sketched Silhouettes Based on Convolution Surfaces [J]. Computer Graphics Forum,2004,23(1): 71-84.
[141]LIU S, JIN X, LIN J, et al. Extended metaball modeling techniques based on 2D silhouette curves [J]. Journal of software, Accepted(In Chinese).
[142]刘圣军.基于几何的水和云彩动画特效模拟[D].浙江：浙江大学,2007.
[143]MURAKAMI S, ICHIHARA H. On a 3D Display Method by Metaball Technique[J]. Journal of the Electronics Communication,1987, J70-D(8): 1607-1615.
[144]RAN JAN V, FOURNIER A. Matching and Interpolation of Shapes using Unions of Circles[J]. Computer Graphics Forum,1996,15(3):129-142.
[145]LEE D. Medial Axis Transformation of a Planar Shape[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1982,4(4):363-369.
[146]SHEWCHUK J. Triangle:Engineering a 2D Quality Mesh Generator and Delaunay Triangulator[C]. First Workshop on Applied Computational Geometry..[S.l.]:[s.n.],1996:124-133.
[147]SUN L, JIN X, FENG J, et al.3D Metaball Modeling Technique Based on 2D Silhouette Curves[J]. Journal of System Simulation,2003,15:96-98.
[148]BISCHOFF S, KOBBELT L. Ellipsoid Decomposition of 3D-models. In: Proceedings of International Symposium on 3D Data Processing, Visualization, and Transmission[M]. New York:IEEE Computer Society Press,2002: 480-488.
[149]JU T, LOSASSO F, SCHAEFER S, et al. Dual contouring of hermite data[J]. ACM Transactions on Graphics (TOG).Proceedings of ACM SIGGRAPH,2002, 21(339-346).
[150]BLOOMENTHAL J. Polygonization of Implicit Surfaces[J]. Computer Aided Geometric Design,1988,5(4):341-355.