Overview and recent advances in natural neighbour galerkin methods

[1]  Stefano Berton,et al.  Simulation of shrinkage induced cracking in cement composite overlays , 2004 .

[2]  Elías Cueto,et al.  Natural element meshless simulation of flows involving short fiber suspensions , 2003 .

[3]  N. Sukumar,et al.  Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids , 2003 .

[4]  Elías Cueto,et al.  On the imposition of essential boundary conditions in natural neighbour Galerkin methods , 2003 .

[5]  Francisco Chinesta,et al.  Thermomechanical Cutting Model Discretisation. Eulerian or Lagrangian, Mesh or Meshless? , 2004 .

[6]  Elías Cueto,et al.  Modelling three‐dimensional piece‐wise homogeneous domains using the α‐shape‐based natural element method , 2002 .

[7]  Kokichi Sugihara,et al.  Improving continuity of Voronoi-based interpolation over Delaunay spheres , 2002, Comput. Geom..

[8]  Jiun-Shyan Chen,et al.  Non‐linear version of stabilized conforming nodal integration for Galerkin mesh‐free methods , 2002 .

[9]  Wing Kam Liu,et al.  Meshfree and particle methods and their applications , 2002 .

[10]  Jean-Daniel Boissonnat,et al.  Natural neighbor coordinates of points on a surface , 2001, Comput. Geom..

[11]  N. Aluru,et al.  Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation , 2001 .

[12]  N. B. Petrovskaya,et al.  Modification of A Finite Volume Scheme for Laplace's Equation , 2001, SIAM J. Sci. Comput..

[13]  K. Bathe,et al.  Towards an efficient meshless computational technique: the method of finite spheres , 2001 .

[14]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[15]  B. Moran,et al.  Natural neighbour Galerkin methods , 2001 .

[16]  N. Sukumar,et al.  Sibson and non-Sibsonian interpolants for elliptic partial differential equations , 2001 .

[17]  B.,et al.  Natural Neighbor Galerkin Methods , 2001 .

[18]  W. P. Jones,et al.  Analysis of the cell-centred finite volume method for the diffusion equation , 2000 .

[19]  Jerzy Pamin,et al.  Dispersion analysis and element‐free Galerkin solutions of second‐ and fourth‐order gradient‐enhanced damage models , 2000 .

[20]  Manuel Doblaré,et al.  Imposing essential boundary conditions in the natural element method by means of density-scaled?-shapes , 2000 .

[21]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[22]  M. Doblaré,et al.  The alpha-shapes-based natural element method , 2000 .

[23]  Antonio Huerta,et al.  Enrichment and coupling of the finite element and meshless methods , 2000 .

[24]  Santiago Falcón,et al.  Penalty functions in constrained variational principles for element free Galerkin method , 2000 .

[25]  Kokichi Sugihara,et al.  Voronoi-based interpolation with higher continuity , 2000, SCG '00.

[26]  Jean-Daniel Boissonnat,et al.  Smooth surface reconstruction via natural neighbour interpolation of distance functions , 2000, SCG '00.

[27]  Jonathan Richard Shewchuk,et al.  Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations , 2000, SCG '00.

[28]  K. Bathe,et al.  The method of finite spheres , 2000 .

[29]  Andrei Yu. Semenov,et al.  Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive isolines generation , 2000 .

[30]  Piotr Breitkopf,et al.  Double grid diffuse collocation method , 2000 .

[31]  N. Aluru.  A point collocation method based on reproducing kernel approximations , 2000 .

[32]  R. Lewis,et al.  Finite element simulation of metal casting , 2000 .

[33]  Satya N. Atluri,et al.  New concepts in meshless methods , 2000 .

[34]  Kokichi Sugihara,et al.  Two Generalizations of an Interpolant Based on Voronoi Diagrams , 1999, Int. J. Shape Model..

[35]  Hyun Gyu Kim,et al.  A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods , 1999 .

[36]  Ted Belytschko,et al.  Numerical integration of the Galerkin weak form in meshfree methods , 1999 .

[37]  R. Sibson,et al.  Scaling random walks on arbitrary sets , 1999, Mathematical Proceedings of the Cambridge Philosophical Society.

[38]  Kokichi Sugihara,et al.  Surface interpolation based on new local coordinates , 1999, Comput. Aided Des..

[39]  T. Belytschko,et al.  THE NATURAL ELEMENT METHOD IN SOLID MECHANICS , 1998 .

[40]  J. Bolander,et al.  Fracture analyses using spring networks with random geometry , 1998 .

[41]  Marek Teichmann,et al.  Surface reconstruction with anisotropic density-scaled alpha shapes , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[42]  Marshall W. Bern,et al.  A new Voronoi-based surface reconstruction algorithm , 1998, SIGGRAPH.

[43]  Ilya D. Mishev,et al.  FINITE VOLUME METHODS ON VORONOI MESHES , 1998 .

[44]  David Eppstein,et al.  The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction , 1998, Graph. Model. Image Process..

[45]  S. Mukherjee,et al.  THE BOUNDARY NODE METHOD FOR POTENTIAL PROBLEMS , 1997 .

[46]  V. D. Ivanov,et al.  The non-Sibsonian interpolation : A new method of interpolation of the values of a function on an arbitrary set of points , 1997 .

[47]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

[48]  E. Oñate,et al.  A stabilized finite point method for analysis of fluid mechanics problems , 1996 .

[49]  Oden,et al.  An h-p adaptive method using clouds , 1996 .

[50]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[51]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[52]  M. Sambridge,et al.  Geophysical parametrization and interpolation of irregular data using natural neighbours , 1995 .

[53]  Ted Belytschko,et al.  Analysis of thin plates by the element-free Galerkin method , 1995 .

[54]  M. Ortiz,et al.  Modelling and simulation of high-speed machining , 1995 .

[55]  J. W. Thomas.  Numerical Partial Differential Equations: Finite Difference Methods , 1995 .

[56]  Jean Braun,et al.  A numerical method for solving partial differential equations on highly irregular evolving grids , 1995, Nature.

[57]  Brian Moran,et al.  A computational model for nucleation of solid-solid phase transformations , 1995 .

[58]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[59]  Somnath Ghosh,et al.  Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method , 1995 .

[60]  Steven J. Owen,et al.  Plume Characterization with Natural Neighbor Interpolation , 1995 .

[61]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[62]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[63]  A. Jagota,et al.  Spring-network and finite-element models for elasticity and fracture , 1994 .

[64]  D. Sulsky,et al.  A particle method for history-dependent materials , 1993 .

[65]  Bruce R. Piper.  Properties of Local Coordinates Based on Dirichlet Tesselations , 1993, Geometric Modelling.

[66]  John C. Davis,et al.  Contouring: A Guide to the Analysis and Display of Spatial Data , 1992 .

[67]  B. Nayroles,et al.  Generalizing the finite element method: Diffuse approximation and diffuse elements , 1992 .

[68]  Raimund Seidel,et al.  On the difficulty of triangulating three-dimensional Nonconvex Polyhedra , 1992, Discret. Comput. Geom..

[69]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[70]  Gerald E. Farin,et al.  Surfaces over Dirichlet tessellations , 1990, Comput. Aided Geom. Des..

[71]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[72]  Tony DeRose,et al.  A multisided generalization of Bézier surfaces , 1989, TOGS.

[73]  Bernard Chazelle,et al.  Triangulating a non-convex polytype , 1989, SCG '89.

[74]  A. Weiser,et al.  On convergence of block-centered finite differences for elliptic-problems , 1988 .

[75]  Beale,et al.  Elastic fracture in random materials. , 1988, Physical review. B, Condensed matter.

[76]  John D. Radke,et al.  On the Shape of a Set of Points , 1988 .

[77]  Joseph J Monaghan,et al.  An introduction to SPH , 1987 .

[78]  Thomas A. Manteuffel,et al.  The numerical solution of second-order boundary value problems on nonuniform meshes , 1986 .

[79]  Andrew B. White,et al.  Supra-convergent schemes on irregular grids , 1986 .

[80]  C. D. Boor,et al.  B-Form Basics. , 1986 .

[81]  Gerald Farin,et al.  Triangular Bernstein-Bézier patches , 1986, Comput. Aided Geom. Des..

[82]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[83]  R. Friedberg,et al.  Vector algebra on a lattice , 1984 .

[84]  Charles A. Hall,et al.  The maximum principle for bilinear elements , 1984 .

[85]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[86]  Jean B. Lasserre,et al.  An analytical expression and an algorithm for the volume of a convex polyhedron inRn , 1983 .

[87]  Norman H. Christ,et al.  Gauge theory on a random lattice , 1982 .

[88]  Norman H. Christ,et al.  Weights of links and plaquettes in a random lattice , 1982 .

[89]  Norman H. Christ,et al.  Random Lattice Field Theory: General Formulation , 1982 .

[90]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[91]  R. Sibson,et al.  A brief description of natural neighbor interpolation , 1981 .

[92]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[93]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[94]  T. Liszka,et al.  The finite difference method at arbitrary irregular grids and its application in applied mechanics , 1980 .

[95]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[96]  R. Sibson.  A vector identity for the Dirichlet tessellation , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[97]  C. Lawson.  Software for C1 Surface Interpolation , 1977 .

[98]  T. Narasimhan,et al.  AN INTEGRATED FINITE DIFFERENCE METHOD FOR ANALYZING FLUID FLOW IN POROUS MEDIA , 1976 .

[99]  D. Griffin,et al.  Finite-Element Analysis , 1975 .

[100]  V. Girault,et al.  Theory of a Finite Difference Method on Irregular Networks , 1974 .

[101]  P. S. Jensen.  FINITE DIFFERENCE TECHNIQUES FOR VARIABLE GRIDS , 1972 .

[102]  Bruce M. Irons,et al.  EXPERIENCE WITH THE PATCH TEST FOR CONVERGENCE OF FINITE ELEMENTS , 1972 .

[103]  Günter Ewald,et al.  Geometry: an introduction , 1971 .

[104]  G. C. Shephard,et al.  Convex Polytopes , 1969, The Mathematical Gazette.

[105]  Bruce M. Irons,et al.  A conforming quartic triangular element for plate bending , 1969 .

[106]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[107]  B. M. Fraeijs de Veubeke,et al.  A conforming finite element for plate bending , 1968 .

[108]  L. Herrmann.  Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem , 1965 .

[109]  A. A. Samarskii,et al.  Homogeneous difference schemes on non-uniform nets☆ , 1963 .

[110]  E. Schönhardt,et al.  Über die Zerlegung von Dreieckspolyedern in Tetraeder , 1928 .