% mesh generation bibliography
%
% This is a bibliography on mesh generation and related topics. It is
% not an exhaustive bibliography, by any means, but an attempt to collect
% references to the best work on unstructured mesh generation, in 2-D and
% 3-D, particularly papers on:
%
% * good control over the shape, size, and orientation of elements
% (typically triangles or tetrahedra),
% * anisotropic mesh generation,
% * automatic mesh generation for complex boundary geometry,
% * approximation theory (error of a given mesh approximating a known function),
% * adaptive meshing: refinement & coarsening,
% * mesh improvement: smoothing,
% * high quality mesh generation,
% * definition of "mesh quality"
%
% We do not cover the following much: structured mesh (grid) generation,
% quadrilateral or hexahedral meshes, element types, solvers.
%
% Many of the papers describe mesh generators tailored to one of the
% following applications:
%
% * finite element methods (FEM),
% * computational fluid dynamics (CFD),
% * viscous flow,
% * aerodynamics,
% * multigrid,
% * triangulation,
% * computational geometry,
% * computer graphics,
% * computer aided geometric design,
% * and surface meshing.
%
% We have included URL's to papers or software, where known.
% Please send corrections to Heckbert's email address below.
%
% For more web info on mesh generation, see
% http://www.cs.cmu.edu/~ph/mesh.html
%
% Paul Heckbert - http://www.cs.cmu.edu/~ph
% and Frank Bossen - http://ltswww.epfl.ch/~bossen.html
% Nov 1996
@STRING{heckbert_email = "Paul Heckbert, ph@cs.cmu.edu"}
@STRING{bossen_email = "Frank Bossen, bossen@ltssg7.epfl.ch"}
@ARTICLE{Hansbo95,
AUTHOR = {Peter Hansbo},
TITLE = {Generalized {Laplacian} Smoothing of Unstructured Grids},
JOURNAL = {Comm. Numer. Meth. Eng.},
VOLUME = 11,
YEAR = 1995,
PAGES = {455-464},
}
@ARTICLE{Moller95,
AUTHOR = {Peter M\"oller and Peter Hansbo},
TITLE = {On Advancing Front Mesh Generation in Three Dimensions},
JOURNAL = {Intl. J. Numer. Meth. Eng.},
VOLUME = 38,
PAGES = {3551--3569},
YEAR = 1995,
}
@ARTICLE{Golias94,
AUTHOR = {N.A. Golias and T.D. Tsiboukis},
TITLE = {An Approach to Refining Three-Dimensional Tetrahedral Meshes
Based on {Delaunay} Transformations},
JOURNAL = {Intl. J. Numer. Meth. Eng.},
VOLUME = 37,
PAGES = {793--812},
YEAR = 1994,
}
@ARTICLE{Zienkiewicz91adaptivity,
AUTHOR = {O.C. Zienkiewicz and J.Z. Zhu},
TITLE = {Adaptivity and Mesh Generation},
JOURNAL = {Intl. J. Numer. Meth. Eng.},
VOLUME = 32,
PAGES = {783--810},
YEAR = 1991,
}
@ARTICLE{Peraire87,
AUTHOR = {J. Peraire and M. Vahdati and K. Morgan and
O.C. Zienkiewicz},
TITLE = {Adaptive Remeshing for Compressible Flow Computations},
JOURNAL = {J. of Computational Physics},
VOLUME = 72,
PAGES = {449--466},
YEAR = 1987,
}
@ARTICLE{Peraire92,
AUTHOR = {J. Peraire and J. Peir\'o},
TITLE = {Adaptive Remeshing for Three-Dimensional
Compressible Flow Computations},
JOURNAL = {J. of Computational Physics},
VOLUME = 103,
PAGES = {269--285},
YEAR = 1992,
}
@TECHREPORT{Vallet90,
AUTHOR = {Marie-Gabrielle Vallet},
TITLE = {G\'en\'eration de Maillages Anisotropes Adapt\'es --
Application \`a la Capture de Couches Limites},
INSTITUTION = {INRIA--Rocquencourt},
NUMBER = {RR 1360},
MONTH = {December},
YEAR = 1990,
NOTE={Info at http://www.inria.fr/RRRT/RR-1360.html},
}
@INPROCEEDINGS{Vallet91,
AUTHOR={Marie-Gabrielle Vallet and Frederic Hecht and B. Mantel},
TITLE={Anisotropic Control of Mesh Generation Based Upon a {Voronoi}
Type Method},
BOOKTITLE={Numerical Grid Generation in Computational Fluid Dynamics
and Related Fields},
YEAR={1991},
KEYWORDS={Delaunay triangulation, Hessian},
}
@PHDTHESIS{Vallet92,
AUTHOR = {Marie-Gabrielle Vallet},
TITLE={G\'en\'eration de Maillages \'El\'ements Finis Anisotropes
et Adaptatifs},
SCHOOL={L'Universit\'e de Paris {VI}},
MONTH={Sept.},
YEAR=1992,
KEYWORDS={anisotropic, mesh generation, Hessian, fluid flow},
NOTE={Abstract at http://www.inria.fr/RRRT/TU-0197.html},
ANNOTE={159 pages, in French},
}
@INPROCEEDINGS{Castro95round,
AUTHOR = {M.J. Castro-D\'{\i}az and F. Hecht and B. Mohammadi},
TITLE = {New Progress in Anisotropic Grid Adaptation for Inviscid and
Viscous Flows Simulations},
BOOKTITLE = {4th Annual Intl. Meshing Roundtable},
MONTH={Oct.},
YEAR = 1995,
NOTE={http://www.ce.cmu.edu/~sowen/Roundtable.agenda.html},
}
@TECHREPORT{Castro95flow,
AUTHOR = {M.J. Castro-D\'{\i}az and F. Hecht and B. Mohammadi},
TITLE = {New Progress in Anisotropic Grid Adaptation for Inviscid and
Viscous Flows Simulations},
INSTITUTION = {INRIA, Rocquencourt, France},
NUMBER = {RR 2671},
MONTH = {October},
YEAR = 1995,
NOTE={http://www.inria.fr/RRRT/RR-2671.html},
}
@TECHREPORT{Castro95surface,
AUTHOR = {M.J. Castro-D\'{\i}az and F. Hecht},
TITLE = {Anisotropic Surface Mesh Generation},
INSTITUTION = {INRIA, Rocquencourt, France},
NUMBER = {RR 2672},
MONTH = {October},
YEAR = 1995,
NOTE={http://www.inria.fr/RRRT/RR-2672.html},
}
@TECHREPORT{Borouchaki95alg,
AUTHOR={Borouchaki, Houman and George, Paul Louis and Hecht, Frederic
and Laug, Patrick and Mohammadi, Bijan and Saltel, Eric},
TITLE={Mailleur bidimensionnel de Delaunay gouvern\'e
par une carte de m\'etriques. Partie {I}: Algorithmes},
INSTITUTION={INRIA, Rocquencourt, France},
NUMBER={RR 2741},
MONTH={Dec.},
YEAR=1995,
NOTE={http://www.inria.fr/RRRT/RR-2741.html},
ANNOTE={47 pages, in French},
}
@TECHREPORT{Borouchaki95app,
AUTHOR={Borouchaki, Houman and George, Paul Louis and Hecht, Frederic
and Laug, Patrick and Mohammadi, Bijan and Saltel, Eric},
TITLE={Mailleur bidimensionnel de Delaunay gouvern\'e
par une carte de m\'etriques. Partie {II}: Applications},
INSTITUTION={INRIA, Rocquencourt, France},
NUMBER={RR 2760},
MONTH={Dec.},
YEAR=1995,
NOTE={http://www.inria.fr/RRRT/RR-2760.html},
ANNOTE={41 pages, in French},
}
@TECHREPORT{Borouchaki96theory,
AUTHOR={Borouchaki, Houman and George, Paul Louis},
TITLE={Maillage de surfaces param\'etriques.
Partie {I}: Aspects th\'eoriques},
INSTITUTION={INRIA, Rocquencourt, France},
NUMBER={RR 2928},
MONTH={July},
YEAR=1996,
NOTE={http://www.inria.fr/RRRT/RR-2928.html},
KEYWORDS={surface mesh},
ANNOTE={25 pages, in French},
}
@ARTICLE{Chew89,
AUTHOR = {L. Paul Chew},
TITLE = {Constrained {Delaunay} Triangulations},
JOURNAL = {Algorithmica},
VOLUME = 4,
PAGES = {97--108},
YEAR = 1989,
}
@ARTICLE{Weatherill92,
AUTHOR = {N.P. Weatherill},
TITLE = {{Delaunay} Triangulation in Computational Fluid Dynamics},
JOURNAL = {Computers Math. Applic.},
VOLUME = 24,
NUMBER = {5/6},
PAGES = {129--150},
YEAR = 1992,
}
@INPROCEEDINGS{Turk91,
AUTHOR = {Greg Turk},
TITLE = {Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion},
BOOKTITLE = {SIGGRAPH '91 Proceedings},
YEAR = 1991,
PAGES = {289--298}
}
@INPROCEEDINGS{Witkin94,
AUTHOR={Andrew P. Witkin and Paul S. Heckbert},
TITLE={Using Particles to Sample and Control Implicit Surfaces},
BOOKTITLE={SIGGRAPH 94 Proceedings},
YEAR={1994},
MONTH={July},
PAGES={269-277},
keywords={physically based modeling, constrained optimization,
adaptive sampling, interaction},
NOTE={http://www.cs.cmu.edu/~ph},
}
@TECHREPORT{Bossen96tr,
AUTHOR = {Frank J. Bossen},
TITLE = {Anisotropic Mesh Generation with Particles},
INSTITUTION = {CS Dept., Carnegie Mellon University},
NUMBER = {CMU-CS-96-134},
MONTH = {May},
YEAR = 1996,
NOTE={http://ltswww.epfl.ch/~bossen/}
}
@INPROCEEDINGS{Bossen96round,
AUTHOR={Frank J. Bossen and Paul S. Heckbert},
TITLE={A Pliant Method for Anisotropic Mesh Generation},
BOOKTITLE={5th Intl. Meshing Roundtable},
MONTH={Oct.},
YEAR=1996,
PAGES={63-74},
NOTE={http://www.cs.cmu.edu/~ph},
KEYWORDS={unstructured mesh, Delaunay triangulation,
element size function, Riemannian metric tensor, smoothing},
}
@TECHREPORT{Bern92,
AUTHOR = {Marshall Bern and David Eppstein},
TITLE = {Mesh Generation and Optimal Triangulation},
INSTITUTION = {Xerox PARC},
YEAR = 1992,
NUMBER = {P92-00047}
}
@ARTICLE{Mavriplis90jcp,
AUTHOR = {Dimitri J. Mavriplis},
TITLE = {Adaptive Mesh Generation for Viscous Flows using {Delaunay}
Triangulation},
JOURNAL = {J. of Computational Physics},
VOLUME = 90,
NUMBER = 2,
MONTH = {Oct.},
YEAR = 1990,
PAGES = {271--291}
}
@TECHREPORT{Mavriplis92aero,
AUTHOR={Dimitri J. Mavriplis},
TITLE={Unstructured Mesh Algorithms for Aerodynamic Calculations},
INSTITUTION={NASA Langley},
ADDRESS={Hampton VA},
NUMBER={ICASE 92-35},
YEAR={1992},
KEYWORDS={mesh generation, computational fluid dynamics},
}
@TECHREPORT{Mavriplis95survey,
AUTHOR={Dimitri J. Mavriplis},
TITLE={Unstructured Mesh Generation and Adaptivity},
INSTITUTION={NASA Langley},
ADDRESS={Hampton VA},
NUMBER={ICASE 95-26},
MONTH={Apr.},
YEAR={1995},
KEYWORDS={survey, anisotropic, advancing front, Delaunay triangulation,
computational fluid dynamics},
NOTE={Abstract at http://techreports.larc.nasa.gov/cgi-bin/NTRS},
}
@INCOLLECTION{Mavriplis96survey,
AUTHOR={Dimitri J. Mavriplis},
TITLE={Mesh Generation and Adaptivity for Complex Geometries and Flows},
BOOKTITLE={Handbook of Computational Fluid Mechanics},
EDITOR={Roger Peyret},
PUBLISHER={Academic},
ADDRESS={London},
YEAR={1996},
KEYWORDS={survey, computational fluid dynamics,
structured mesh, unstructured mesh, multigrid},
}
@UNPUBLISHED{Devroye95,
AUTHOR = {L. Devroye and E.P. M\"ucke and B. Zhu},
TITLE = {A note on point location in {Delaunay} triangulations of
random points},
NOTE = {Submited for publication},
YEAR = 1995,
}
@INCOLLECTION{Lischinski94,
AUTHOR = {Dani Lischinski},
TITLE = {Incremental {Delaunay} Triangulations},
EDITOR = {Paul S. Heckbert},
BOOKTITLE = {Graphics Gems IV},
PUBLISHER = {Academic Press},
YEAR = 1994,
PAGES = {47--59}
}
@TECHREPORT{Kao91,
AUTHOR = {Thomas Kao and David M. Mount},
TITLE = {Dynamic Maintenance of {Delaunay} Triangulations},
INSTITUTION = {University of Maryland},
YEAR = 1991,
NUMBER = {CS-TR-2585}
}
@INPROCEEDINGS{Shimada92,
AUTHOR = {Kenji Shimada and David C. Gossard},
TITLE = {Computational Methods for Physically-based {FE} Mesh Generation},
BOOKTITLE = {Proc. of the IFIP TC5/WG5.3 8th Intl. Conf. on PROLAMAT},
YEAR = 1992,
KEYWORDS = {bubble, smoothing},
}
@PHDTHESIS{Shimada93phd,
AUTHOR = {Kenji Shimada},
TITLE = {Physically-Based Mesh Generation: Automated Triangulation of
Surfaces and Volumes via Bubble Packing},
SCHOOL = {ME Dept., MIT},
YEAR = 1993,
KEYWORDS = {bubble, smoothing},
}
@ARTICLE{Shimada93japan,
AUTHOR={Kenji Shimada},
TITLE={Physically-Based Automatic Mesh Generation},
JOURNAL={J. of the Japan Soc. for Simulation Technology},
VOLUME=12,
NUMBER=1,
PAGES={11-20},
YEAR=1993,
KEYWORDS={bubble, smoothing},
ANNOTE={in Japanese?},
}
@INPROCEEDINGS{Shimada95solid,
AUTHOR={Kenji Shimada and David C. Gossard},
TITLE={Bubble mesh: Automated triangular meshing
of non-manifold geometry by sphere packing},
BOOKTITLE={Third Symp. on Solid Modeling and Appls.},
PAGES={409-419},
MONTH={May},
YEAR=1995,
KEYWORDS={mesh generation, smoothing},
NOTE={http://www.trl.ibm.co.jp/projects/s7340/meshing/meshingE.htm},
ANNOTE={Solid Modeling '95},
}
@INPROCEEDINGS{shimada95ipsj,
AUTHOR={Kenji Shimada},
TITLE={Automatic Anisotropic Mesh Generation},
BOOKTITLE={Proc. 51st Ann. Conf., Inf. Proc. Soc. of Japan},
VOLUME={1},
PAGES={59-60},
MONTH={Nov.},
YEAR=1995,
NOTE={4C-7. In Japanese},
KEYWORDS={bubble, smoothing},
}
@INPROCEEDINGS{Baum91,
AUTHOR = {Daniel R. Baum and Stephen Mann and Kevin P. Smith and James
M. Winget},
TITLE = {Making radiosity usable: automatic Preprocessing and meshing
techniques for the generation of accurate radiosity
solutions},
BOOKTITLE = {SIGGRAPH '91 Proceedings},
MONTH = {July},
YEAR = 1991,
PAGES = {51--59}
}
@PHDTHESIS{Welch95,
AUTHOR={William Welch},
TITLE={Serious Putty: Topological Design for Variational Curves and Surfaces},
SCHOOL={CS Dept, Carnegie Mellon University},
MONTH={Dec.},
YEAR={1995},
KEYWORDS={curvature, triangulation, fair surface design, adaptive mesh,
Delaunay triangulation, Laplacian smoothing},
NOTE={CMU-CS-95-217,
ftp://reports.adm.cs.cmu.edu/usr/anon/1995/CMU-CS-95-217A.ps,
217B.ps, 217C.ps},
ANNOTE={
also http://www.cs.cmu.edu/afs/cs.cmu.edu/user/claude/www/welch-home.html},
}
@ARTICLE{Guibas85,
AUTHOR = {Leonidas Guibas and Jorge Stolfi},
TITLE = {Primitives for the Manipulation of General Subdivisions and
the Computation of {Voronoi} Diagrams},
JOURNAL = {ACM Trans. on Graphics},
VOLUME = 4,
NUMBER = 2,
MONTH = {April},
YEAR = 1985,
PAGES = {74--123}
}
@TECHREPORT{Guibas90,
AUTHOR = {L.J. Guibas and D.E. Knuth and M. Sharir},
TITLE = {Randomized Incremental Construction of {Delaunay} and
{Voronoi} Diagrams},
INSTITUTION = {Stanford University},
YEAR = 1990,
NUMBER = {STAN-CS-90-1300}
}
@TECHREPORT{Garland95,
AUTHOR = {Michael Garland and Paul Heckbert},
TITLE = {Fast Polygonal Approximation of Terrains and Height Fields},
INSTITUTION = {Carnegie Mellon University},
YEAR = 1995,
NUMBER = {CMU-CS-95-181}
}
@INPROCEEDINGS{Ruppert93,
AUTHOR = {Jim Ruppert},
TITLE = {A new and simple algorithm for quality 2-dimensional mesh
generation},
BOOKTITLE = {4th ACM-SIAM Symp. on Discrete Algorithms},
YEAR = {1993},
PAGES = {83--92},
}
@ARTICLE{Greengard90,
AUTHOR = {L. Greengard},
TITLE = {The numerical solution of the N-body problem},
JOURNAL = {Computers in Physics},
VOLUME = 4,
NUMBER = 2,
MONTH = {March--April},
YEAR = 1990,
PAGES = {142--152},
}
@ARTICLE{Lewis79,
AUTHOR = {B.A. Lewis and J.S. Robinson},
TITLE = {Triangulation of planar regions with applications},
JOURNAL = {Comput J},
YEAR = 1979,
VOLUME = 21,
NUMBER = 4,
PAGES = {324--332}
}
@MANUAL{Java,
AUTHOR = {James Gosling and Henry McGilton},
TITLE = {The Java Language Environment: a white paper},
ORGANIZATION = {Sun Microsystems},
MONTH = {October},
YEAR = 1995
}
@ARTICLE{Green78,
AUTHOR = {P.J. Green and R. Sibson},
TITLE = {Computing {Dirichelet} tesselations in the plane},
JOURNAL = {Computer Journal},
VOLUME = 21,
NUMBER = 2,
YEAR = 1978,
PAGES = {168--173}
}
@ARTICLE{Edelsbrunner86,
AUTHOR = {H. Edelsbrunner and R. Seidel},
TITLE = {{Voronoi} diagrams and arrangements},
JOURNAL = {Disc. and Comp. Geom.},
VOLUME = 8,
NUMBER = 1,
YEAR = 1986,
PAGES = {25--44}
}
@INPROCEEDINGS{Leach92,
AUTHOR = {Geoff Leach},
TITLE = {Improving Worst-Case Optimal {Delaunay} Triangulation Algorithms},
BOOKTITLE = {4th Canadian Conference on Computational Geometry},
YEAR = 1992
}
@BOOK{Shamos85,
AUTHOR = {Franco P. Preparata and Michael Ian Shamos},
TITLE = {Computational Geometry: an Introduction},
PUBLISHER = {Springer-Verlag},
YEAR = 1985
}
@ARTICLE{Fortune87,
AUTHOR = {S. Fortune},
TITLE = {A Sweepline algorithm for {Voronoi} Diagrams},
JOURNAL = {Algorithmica},
VOLUME = 2,
PAGES = {153--174},
YEAR = 1987
}
@INPROCEEDINGS{Szeliski92,
AUTHOR = {Richard Szeliski and David Tonnesen},
TITLE = {Surface Modeling with Oriented Particle Systems},
BOOKTITLE = {SIGGRAPH '92 Proceedings},
YEAR = 1992,
PAGES = {185--194}
}
@INCOLLECTION{Lawson77,
AUTHOR = {Charles L. Lawson},
TITLE = {Software for {$C^1$} Surface Interpolation},
BOOKTITLE = {Mathematical Software III},
EDITOR = {John R. Rice},
PUBLISHER = {Academic Press},
YEAR = 1977,
PAGES = {161--194}
}
@BOOK{Becker81,
AUTHOR={Eric B. Becker and Graham F. Cary and J. Tinsley Oden},
TITLE={Finite Elements: An Introduction},
VOLUME={1},
YEAR={1981},
PUBLISHER={Prentice-Hall},
ADDRESS={Englewood Cliffs, NJ},
}
@BOOK{Sokolnikoff64,
AUTHOR={I.S. Sokolnikoff},
TITLE={Tensor Analysis, Theory and Applications to Geometry and
Mechanics of Continua},
YEAR={1964},
PUBLISHER={John Wiley},
EDITION={2nd},
ADDRESS={New York},
}
@ARTICLE{Yerry83,
AUTHOR = {M.A. Yerry and M.S. Shepard},
TITLE = {A modified quadtree approach to finite element mesh
generation},
JOURNAL = {IEEE Computer Graphics and Appls.},
VOLUME = {3},
MONTH = {January/February},
YEAR = {1983},
PAGES = {39--46},
}
@Article{Cavendish85,
author = "J. C. Cavendish and D. A. Field and W. H. Frey",
title = "An approach to automatic three-dimensional finite
element mesh generation",
journal = "Intl. J. Numer. Meth. Eng.",
volume = "21",
year = "1985",
pages = "329--347",
}
@TechReport{Field85,
author = "D. Field and W. Frey",
title = "Automation of tetrahedral mesh generation",
institution = "General Motors Research Pub., GMR-4967",
year = "1985",
}
@ARTICLE{Field88,
AUTHOR = {David A. Field},
TITLE = {Laplacian smoothing and {Delaunay} triangulations},
JOURNAL = {Comm. Applied Numer. Meth.},
VOLUME = {4},
YEAR = {1988},
PAGES = {709--712},
}
@ARTICLE{Field95solid,
AUTHOR={David A. Field},
TITLE={The Legacy of Automatic Mesh Generation from Solid Modeling},
JOURNAL={Computer Aided Geometric Design},
VOLUME={12},
YEAR={1995},
PAGES={651-673},
KEYWORDS={finite element method, survey},
}
@ARTICLE{Field95improv,
AUTHOR={David A. Field and William H. Frey},
TITLE={Structural Improvement of Planar Triangulations:
Some Constraints and Practical Issues},
JOURNAL={Comm. Numer. Meth. Eng.},
VOLUME=11,
YEAR=1995,
PAGES={191-198},
KEYWORDS={structured mesh generation},
ANNOTE={attempts to transform an unstructured mesh into a structured mesh;
make each vertex degree 6},
}
@ARTICLE(Frey87,
AUTHOR = "William H. Frey",
TITLE = "Selective refinement: a new strategy for automatic node
placement in graded triangular meshes",
JOURNAL = "Intl. J. Numer. Meth. Eng.",
VOLUME = 24,
YEAR = 1987,
PAGES = "2183--2200"
)
@ARTICLE{Frey91,
AUTHOR={William H. Frey and David A. Field},
TITLE={Mesh Relaxation: A New Technique for Improving Triangulations},
JOURNAL={Intl. J. Numer. Meth. Eng.},
VOLUME=31,
YEAR=1991,
PAGES={1121-1133},
KEYWORDS={unstructured mesh generation},
ANNOTE={iteratively smooth the mesh topology by edge swapping,
makes vertex degrees more uniform},
}
@ARTICLE{Lindholm83,
AUTHOR = {D.A. Lindholm},
TITLE = {Automatic triangular mesh generation on surfaces of
polyhedra},
JOURNAL = {IEEE Trans. Magnetics},
VOLUME = {19},
YEAR = {1983},
PAGES = {2539--2542},
}
@BOOK{Knupp94,
AUTHOR={Patrick Knupp and Stanly Steinberg},
TITLE={Fundamentals of Grid Generation},
PUBLISHER={CRC Press},
ADDRESS={Boca Raton, FL},
YEAR=1994,
KEYWORDS={structured mesh generation},
ANNOTE={info at http://www.webknx.com/dcw/knupp.htm},
}
@TECHREPORT{Posenau93,
AUTHOR={Mary-Anne K. Posenau},
TITLE={Approaches to High Aspect Ratio Triangulations},
INSTITUTION={NASA Technical Memorandum 107684},
MONTH={Aug.},
YEAR={1993},
NOTE={http://geolab.larc.nasa.gov/},
ANNOTE={Longer version of a paper which appeared in
Proceedings of the 5th Canadian Conference on Computational Geometry,
Waterloo, Ontario, Canada, 1993},
}
@INCOLLECTION{Bern97survey,
AUTHOR={Marshall Bern and Paul Plassmann},
TITLE={Mesh Generation},
BOOKTITLE={Handbook of Computational Geometry},
EDITOR={J\"org Sack and Jorge Urrutia},
PUBLISHER={Elsevier Science},
YEAR={to appear},
KEYWORDS={survey, computational geometry, finite element method},
}
@ARTICLE(Ho-Le88,
AUTHOR = "K. {Ho-Le}",
TITLE = "Finite element mesh generation methods: a review and
classification",
JOURNAL = "Computer-Aided Design",
VOLUME = 20,
YEAR = 1988,
PAGES = "27--38")
@ARTICLE{Simpson94,
AUTHOR={R. Bruce Simpson},
TITLE={Anisotropic mesh transformations and optimal error control},
JOURNAL={Applied Numer. Math.},
VOLUME={14},
NUMBER={1-3},
YEAR={1994},
PAGES={183-198},
ABSTRACT={
Recently, research originating in several different applications
has appeared on unstructured triangular meshes in which the
vertex distribution is not locally uniform, i.e., anisotropic
unstructured meshes. The techniques used have the common features
that the distribution of triangle shapes for the mesh is
controlled by specifying a symmetric tensor, and that the
anisotropic mesh is the transform of an isotropic mesh. We
discuss how these mechanisms arise in the theory of optimal error
control, using simple model mesh generation problems, and review
the related research in applications to computational fluid
dynamics, surface triangulation, and semiconductor simulation.
},
ANNOTE={
Third ARO Workshop on Adaptive Methods for Partial Differential
Equations; Part: Troy, NY, USA; Part: 18-20 May 1992;
},
KEYWORDS={
anisotropic mesh transformations; optimal error control;
unstructured triangular meshes; vertex distribution; triangle
shapes; symmetric tensor; mesh generation problems;
computational fluid dynamics; surface triangulation;
semiconductor simulation
},
}
@BOOK{Allen87,
AUTHOR={M. P. Allen and D. J. Tildesley},
TITLE={Computer Simulation of Liquids},
PUBLISHER={Clarendon Press},
ADDRESS={Oxford},
YEAR={1987},
keywords={computational chemistry, molecular dynamics, particle, Monte Carlo},
ANNOTE={nice sections on algorithms for classical dynamics simulations
of molecules in FORTRAN, hard sphere dynamics, Lennard-Jones potential,
Monte Carlo methods, quaternions, statistical mechanics},
FTP={cheme.cornell.edu pub/allen_tildesley},
}
@BOOK{Hockney81,
AUTHOR={R. W. Hockney and J. W. Eastwood},
TITLE={Computer Simulation Using Particles},
PUBLISHER={McGraw-Hill},
ADDRESS={New York},
YEAR={1981},
keywords={molecule, galaxy, particle, liquid},
ANNOTE={grid method for optimizing force calculations between pairs of atoms},
}
@INPROCEEDINGS{Thompson93survey,
AUTHOR={Joe F. Thompson and Nigel P. Weatherill},
TITLE={Aspects of Numerical Grid Generation: Current Science and Art},
BOOKTITLE={11th AIAA Applied Aerodynamics Conf.
(Amer. Inst. of Aeronautics and Astronautics)},
MONTH={Aug.},
YEAR=1993,
PAGES={1029-1070},
NOTE={AIAA paper 93-3539},
KEYWORDS={survey, unstructured mesh, mesh generation, viscous flow},
}
@ARTICLE{Chen94ijnme,
AUTHOR={Ke Chen},
TITLE={Two Dimensional Adaptive Quadrilateral Mesh Generation},
JOURNAL={Comm. Numer. Meth. Eng.},
VOLUME=10,
YEAR=1994,
ABSTRACT={
In this paper we address the problem of 2D adaptive quadrilateral mesh
generation by using the variational principles. We first find the
variational integral which generates the known grid system of
curve-by-curve error equidistributions. We then use the same integral
to generate a new adaptive grid system which is superior to the known
system in that the new system produces smoother meshes. Moreover, the
new integral may be combined linearly with existing smoothness control
integrals to yield more robust adaptive grid systems. Numerical
results and comparisons are reported.
},
KEYWORDS={structured mesh generation, conformal mapping, variational methods},
documentURL ="ftp://ftp.liv.ac.uk/pub/Stats+Comp_Maths/chen/cnme.ps.Z,
http://www.lpac.ac.uk/SEL-HPC/Articles/GeneratedHtml/math.pardiff.html",
ANNOTE={attempting to get both equidistribution of error and smoothness},
}
@ARTICLE{Marcum95aiaajournal,
AUTHOR={David L. Marcum and Nigel P. Weatherill},
TITLE={Unstructured Grid Generation Using Iterative Point Insertion and
Local Reconnection},
JOURNAL={AIAA Journal},
VOLUME=33,
NUMBER=9,
MONTH={Sept.},
YEAR=1995,
PAGES={1619-1625},
ANNOTE={was AIAA paper 94-1926 at 12th Applied Aerodynamics Conf.,
Colorado Springs, CO, June 1994},
KEYWORDS={anisotropic mesh generation, advancing front, advancing normal,
min-max triangulation},
}
@INPROCEEDINGS{Marcum95reno,
AUTHOR={David L. Marcum},
TITLE={Generation of Unstructured Grids for Viscous Flow Applications},
NOTE={AIAA paper 95-0212},
BOOKTITLE={33rd AIAA Aerospace Sciences Mtg.},
ADDRESS={Reno, NV},
MONTH={Jan.},
YEAR=1995,
KEYWORDS={anisotropic mesh generation, advancing front, advancing normal,
min-max triangulation},
}
@BOOK{Borisenko68,
AUTHOR={A. I. Borisenko and I. E. Tarapov},
TITLE={Vector and Tensor Analysis with Applications},
PUBLISHER={Dover},
YEAR={1968},
}
@BOOK{Dubrovin84,
AUTHOR={B. A. Dubrovin and A. T. Fomenko and S. P. Novikov},
TITLE={Modern Geometry -- Methods and Applications.
Part {I}: The Geometry of Surfaces, Transformation Groups, and Fields},
PUBLISHER={Springer-Verlag},
ADDRESS={New York},
YEAR={1984},
KEYWORDS={differential geometry, Riemannian space, tensor, curvature},
ANNOTE={translated from Russian},
}
@BOOK{Thomas65,
AUTHOR={Tracy Y. Thomas},
TITLE={Concepts from Tensor Analysis and Differential Geometry},
PUBLISHER={Academic},
ADDRESS={New York},
YEAR={1965},
KEYWORDS={Riemannian space, surface, curvature},
}
@BOOK{Misner73,
AUTHOR={Charles W. Misner and Kip S. Thorne and John Archibald Wheeler},
TITLE={Gravitation},
PUBLISHER={W. H. Freeman},
YEAR={1973},
KEYWORDS={general relativity, differential geometry, tensor,
Riemannian manifold, geodesic, curvature, differential topology},
}
@TECHREPORT{Jones96refine,
AUTHOR={Mark T. Jones and Paul E. Plassmann},
TITLE={Adaptive Refinement of Unstructured Finite-Element Meshes},
INSTITUTION={Math. and CS Div., Argonne Natl. Lab., IL},
NOTE={Preprint MCS-P562-0296,
http://www.mcs.anl.gov/Divisional/techreports.html},
MONTH={Feb.},
YEAR=1996,
KEYWORDS={mesh generation},
}
@ARTICLE{Rebay93,
AUTHOR={S. Rebay},
TITLE={Efficient Unstructured Mesh Generation by Means of Delaunay
Triangulation and Bowyer-Watson Algorithm},
JOURNAL={J. of Computational Physics},
VOLUME=106,
YEAR=1993,
PAGES={125-138},
KEYWORDS={advancing front, incremental Delaunay triangulation},
}
@ARTICLE{Chen95points,
AUTHOR={Chen and Babuska},
TITLE={Approximate Optimal Points for Polynomial Interpolation of Real Functions
in an Interval and in a Triangle},
JOURNAL={Computer Methods in Applied Mechanics and Engineering},
VOLUME=128,
PAGES={405-417},
YEAR=1995,
KEYWORDS={Gauss quadrature, Lobatto quadrature, interpolation},
ANNOTE={best location for internal sample points in triangle},
}
@ARTICLE{Dyn90,
AUTHOR={Nira Dyn and David Levin and Shmuel Rippa},
TITLE={Data Dependent Triangulations for Piecewise Linear Interpolation},
JOURNAL={IMA J. Numer. Anal.},
VOLUME={10},
NUMBER={1},
YEAR={1990},
MONTH={Jan.},
PAGES={137--154},
keywords={long triangles, piecewise linear interpolation,
data dependent triangulations, approximation, long triangles},
ABSTRACT={
Given a set of data points in R2 and corresponding data
values, it is clear that the quality of a piecewise linear
interpolation over triangles depends on the specific
triangulation of the data points. While conventional
triangulation methods depend only on the distribution of the
data points in R2, this paper suggests that the
triangulation should depend on the data values as well.
Several data dependent criteria for defining the triangulation
are discussed and efficient algorithms for computing these
triangulations are presented. It is shown for a variety of
test cases that data dependent triangulations can improve
significantly the quality of approximation and that long and
thin triangles, which are traditionally avoided, are sometimes
very suitable.
},
}
@PHDTHESIS{Rippa90,
AUTHOR={Shmuel Rippa},
TITLE={Piecewise Linear Interpolation and Approximation Schemes Over
Data Dependent Triangulations},
SCHOOL={School of Mathematical Sciences, Tel Aviv U.},
YEAR={1990},
keywords={height field, terrain},
}
@ARTICLE{Rippa92subset,
AUTHOR={Shmuel Rippa},
TITLE={Adaptive Approximation by Piecewise Linear Polynomials on
Triangulations of Subsets of Scattered Data},
JOURNAL={SIAM J. Sci. Stat. Comput.},
VOLUME={13},
NUMBER={5},
MONTH={Sept.},
YEAR={1992},
PAGES={1123--1141},
keywords={surface simplification, least squares fitting},
ABSTRACT={
Given a set V of data points in R2 with corresponding
data values, the problem of adaptive piecewise polynomial
approximation is to choose a subset of points of V, to create
a triangulation of this subset, and to define a piecewise
linear surface over the triangulation such that the deviation
of this surface from the data set is no more than a prescribed
error tolerance. A typical numerical scheme starts with some
initial triangulation and adds more points as necessary until
the resulting piecewise linear surface satisfies the error
bound. In the paper two ingredients of such schemes are
discussed. The first problem is that of constructing a
suitable triangulation of a subset of points. The use of data-
dependent triangulations that depend on the given function
values at the data points is discussed, and some data-
dependent criteria for optimizing a triangulation are
presented and compared to the Delaunay criterion leading to
the well-known Delaunay triangulation. The second problem is
how to select a piecewise linear surface approximating the
given data. The paper uses the least-square approximation to
the data from the space of piecewise linear polynomials
defined over a triangulation of a subset of V. It is proved
that the matrix of the normal equations is always nonsingular
and a bound for its condition number is derived.
}
}
@ARTICLE{Rippa92longthin,
AUTHOR={Shmuel Rippa},
TITLE={Long and Thin Triangles Can Be Good for Linear Interpolation},
JOURNAL={SIAM J. Numer. Anal.},
VOLUME={29},
NUMBER={1},
MONTH={Feb.},
YEAR={1992},
PAGES={257--270},
KEYWORDS={approximation error, mesh, finite element method},
ANNOTE={Contrary to some interpretations of Gregory & Babuska-Aziz, large
angles are not always bad. Gives optimal triangle shape to minimize
approximation error of a given function.},
}
@ARTICLE{Dyn93fem,
AUTHOR={Nira Dyn and Shmuel Rippa},
TITLE={Data-Dependent Triangulations for Scattered Data Interpolation
and Finite Element Approximation},
JOURNAL={Applied Numer. Math.},
VOLUME=12,
YEAR=1993,
PAGES={89-105},
KEYWORDS={triangulation, mesh, approximation theory},
ANNOTE={variational triangulation},
}
@ARTICLE{DAzevedo89siam,
AUTHOR={Eduardo F. D'Azevedo and R. Bruce Simpson},
TITLE={On Optimal Interpolation Triangle Incidences},
JOURNAL={SIAM J. Sci. Stat. Comput.},
VOLUME=10,
NUMBER=6,
YEAR=1989,
PAGES={1063-1075},
KEYWORDS={triangulation, curvature, structured mesh, Delaunay triangulation},
}
@PHDTHESIS{DAzevedo89phd,
AUTHOR={Eduardo F. D'Azevedo},
TITLE={On Optimal Triangulation for Piecewise Linear Approximation},
SCHOOL={CS Dept., U. of Waterloo, Waterloo, Ontario, Canada},
YEAR=1989,
KEYWORDS={linear interpolation, triangulation, curvature, structured mesh,
Delaunay triangulation},
}
@ARTICLE{DAzevedo91transform,
AUTHOR={Eduardo F. D'Azevedo},
TITLE={Optimal triangular mesh generation by coordinate transformation},
JOURNAL={SIAM J. Sci. Stat. Comput.},
VOLUME={12},
NUMBER={4},
MONTH={July},
YEAR={1991},
PAGES={755-786},
ABSTRACT={
Presents the motivation for and construction of coordinate
transformations that generate optimally efficient meshes for
linear interpolation. The coordinate transformations are
derived from a result in differential geometry characterizing a
'flat' space. The optimality results are demonstrated for some
numerical examples. Adaptive meshes produced by PLTMG (R.E.
Bank, PLTMG: A Software Package for Solving Elliptic Partial
Differential Equations, Society for Industrial and Applied
Mathematics, Philadelphia, PA, 1990) are included for
comparison. The paper concludes that coordinate transformation
is a promising strategy for investigation into more complex
optimal meshing problems in finite element analysis.
},
KEYWORDS={linear interpolation, Delaunay triangulation, differential geometry,
Riemann-Christoffel tensor, curvature, finite element analysis,
structured mesh},
}
@ARTICLE{DAzevedo91gradient,
AUTHOR={Eduardo F. D'Azevedo and R. Bruce Simpson},
TITLE={On Optimal Triangular Meshes for Minimizing Gradient Error},
VOLUME=59,
JOURNAL={Numerische Mathematik},
YEAR=1991,
PAGES={321-348},
KEYWORDS={linear interpolation, Delaunay triangulation, differential geometry,
Riemann-Christoffel tensor, curvature, finite element analysis,
structured mesh},
}
@PHDTHESIS{Nadler85,
AUTHOR={E. J. Nadler},
TITLE={Piecewise Linear Approximation on Triangulations of a Planar Region},
SCHOOL={Div. Applied Math., Brown U.},
NOTE={Pattern Analysis Report 140},
MONTH={May},
YEAR=1985,
KEYWORDS={data-dependent triangulation, curvature, error analysis},
}
@INPROCEEDINGS{Nadler86,
AUTHOR={Edmond Nadler},
TITLE={Piecewise Linear Best {$L_2$} Approximation on Triangulations},
BOOKTITLE={Approximation Theory V},
EDITOR={C. K. Chui and others},
PUBLISHER={Academic Press},
ADDRESS={Boston},
YEAR={1986},
PAGES={499--502},
KEYWORDS={data-dependent triangulation, curvature, error analysis},
}
@INPROCEEDINGS{Kreiner94,
AUTHOR={R. Kreiner and B. Kr\"oplin},
TITLE={Unstructured Quadrilateral Mesh Generation on Surfaces from {CAD}},
BOOKTITLE={Numerical Grid Generation in Computational Fluid Dynamics
and Related Fields},
YEAR={1994},
PAGES={211-221},
KEYWORDS={surface mesh generation, curvature},
}
@inproceedings{Dompierre95,
author = {Julien Dompierre and Marie-Gabrielle Vallet and Michel Fortin
and Wagdi G. Habashi and Djaffar A\"{\i}t-Ali-Yahia and Sylvain Boivin
and Yves Bourgault and Anna Tam},
title = {Edge-Based Mesh Adaptation for {CFD}},
booktitle = {Conf. on Numerical Methods for the {Euler} and
{Navier-Stokes} Equations},
annote={organization: CRM-CERCA},
year = {1995},
month = {Sept.},
address = {Montr\'eal},
pages = {265--299},
NOTE={Also CERCA Report R95-73,
http://www.cerca.umontreal.ca/~dompiere/postscript/postscript.html},
}
@inproceedings{Vallet96coupling,
author = {Marie-Gabrielle Vallet and Julien Dompierre and Yves Bourgault
and Michel Fortin and Wagdi G. Habashi},
title = {Coupling Flow Solvers and Grids through an Edge-Based
Adaptive Grid Method},
booktitle = {{ASME} Fluids Eng. Conf.},
year = {1996},
month = {July},
address = {San Diego, CA},
note={Also CERCA report R96-1,
http://www.cerca.umontreal.ca/~dompiere/postscript/postscript.html},
}
@inproceedings{Fortin96aniso,
author = {Michel Fortin and Marie-Gabrielle Vallet and Julien Dompierre
and Yves Bourgault and Wagdi G. Habashi},
title = {Anisotropic Mesh Adaptation: Theory, Validation and Applications},
booktitle = {Third {ECCOMAS} Computational Fluid Dynamics Conf.},
year = {1996},
month = {Sept.},
note = {To appear.},
address = {Paris},
annote={organization: GAMNI/SMAI, CNRS, INRIA},
}
@inproceedings{Fortin94error,
author = {Michel Fortin and Marie-Gabrielle Vallet and Diane Poirier
and Wagdi G. Habashi},
title = {Error Estimation and Directionally Adaptative Meshing},
booktitle={AIAA 25th Fluid Dynamics Conf.},
note={AIAA paper 94-2211},
month={June},
year = {1994},
ANNOTE={Colorado Springs. Also CERCA report R94-17},
}
@Techreport{Moore90c,
author = "D.\ Moore and J.\ Warren",
title = "Multidimensional Adaptive Mesh Generation",
institution = "Department of Computer Science, Rice University",
year = "1990",
month = February,
number = "{Rice COMP TR90-106}",
}
@TechReport{Moore91a,
author = "D. Moore and J. Warren",
title = "Mesh Displacement: An Improved Contouring Methods for
Trivariate Data",
year = "1991",
month = September,
institution = "Department of Computer Science, Rice University",
address = "P.\O. Box {1892}, Houston, {TX 77251-1892}",
number = "{COMP TR91-166}",
}
@TechReport{Moore91b,
author = "D.\ Moore and J.\ Warren",
title = "Adaptive Mesh Generation {II}: Packing Solids",
institution = "Department of Computer Science, Rice University",
address = "Houston, Texas",
year = "1991",
month = March,
number = "{Rice COMP TR90-139}",
}
@TechReport{Moore90space,
author = "D. Moore and J. Warren",
title = "Adaptive mesh generation {I}: packing space",
number = "TR 90-106",
institution = "Dept. of Computer Science, Rice University",
year = "1990",
}
@INPROCEEDINGS{Chouraqui96,
AUTHOR={Patrick Chouraqui and Gershon Elber},
TITLE={Physically Based Adaptive Triangulation of Freeform Surfaces},
BOOKTITLE={Computer Graphics Intl. 1996 (CGI 96)},
NOTE={Pohang, Korea},
MONTH={June},
YEAR=1996,
PAGES={144-153},
KEYWORDS={parametric surface},
}
@Article{Filip86,
author = "D. Filip and R. Magedson and R. Markot",
title = "Surface algorithms using bounds on derivatives",
journal = "Computer Aided Geometric Design",
year = "1986",
volume = "3",
number = "4",
pages = "295--311",
keywords={surface mesh},
}
@InProceedings{Rockwood89a,
author = "Alyn Rockwood and Kurt Heaton and Tom Davis",
title = "Real-Time Rendering of Trimmed Surfaces",
pages = "107--116",
journal = "Computer Graphics (SIGGRAPH '89 Proceedings)",
volume = "23",
number = "3",
year = "1989",
month = jul,
keywords = "surface mesh, NURBS, Bezier surface, adaptive polygonization",
}
@BOOK{Carey93,
AUTHOR={G. F. Carey},
TITLE={Grid Generation, Refinement, and Redistribution},
PUBLISHER={Wiley},
ADDRESS={New York},
YEAR=1993,
KEYWORDS={unstructured mesh generation},
}
@ARTICLE{Winslow66,
AUTHOR={A. M. Winslow},
TITLE={Numerical solution of the quasilinear {Poisson} equation in a
nonuniform triangle mesh},
JOURNAL={J. of Computational Physics},
VOLUME=1,
NUMBER=2,
PAGES={149-172},
YEAR=1966,
KEYWORDS={mesh generation, Laplacian smoothing},
ANNOTE={David Field says: earliest Laplacian smoothing reference},
}
@InProceedings{Aguas93,
author = "Miguel P. N. Aguas and Stefan Mueller",
title = "Mesh Redistribution in Radiosity",
booktitle = "Fourth Eurographics Workshop on Rendering",
pages = "327--326",
address = "Paris, France",
month = jun,
year = "1993",
keywords={adaptive methods, mesh generation},
}