Tomasz Jurczyk, Barbara Glut


Many physical phenomena can bc modelcd by partial diffcrcntial cąuations. The dcvclopmcnt of numcrical methods bascd on the spatial subdivision of a domain into fmitc clcmcnts immcdiatcly cxtcnded interests to the tasks of generating a mesh. With the availability of vcrsatilc field solv- crs and powerful computcrs, the simulations of cver inereasing gcometrical and physical com- plcxity arc attempted. At somc point the main bottleneck becomcs the mesh generation itsclf.

The papcr prcsents a dctailcd description of the triangular mcsh gcneration schcmc on the piane bascd upon the Dclaunay triangulation. A mcsh generator should be fully automatic and simplify input data as much as possible. It should offer rapid gradation from smali to large sizes of elcmcnts. The generated mcsh must be always valid and of good quality. Ali thesc rcquiremcnts were taken into account during the selection and elaboration of utilized algorithms.

Successive chapters describe procedures connected with the specification of a modeled domain, gcneration and triangulation of boundary vertices, introducing inner nodes, improving the quality of the crcated mcsh, and renumbering of vertices.

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Baker T.J.: Automatic mesh generation for complex three-dimensional regions using a constrainedDelaunay triangulation. Engineering with Computers, 5, 1989, 161-175

Banachowski L., Diks K., Rytter W.: Algorytmy i struktury danych. Warszawa, WNT

Bowyer A.: Computing Dirichlet tesselllations. The Computer Journal, 24,1981,162-166 Cannan S.A., Muthukrishnan S.N.,

Phillips R.K.: Topological refinementprocedures

for triangularfinite element meshes. Engineering with Computers, 12 (3&4), 1996, 243-255

Chew L.P.: Constrained Delaunay triangulations. Proceedings of the 3rd Symposium on Computational Geometry, ACM Press, 1987, 215-222

Coulomb J.L.: Experimentation de la triangulation de Delaunay. Conf. Proc. Automated mesh generation and adaptation, Grenoble, IMAG 1987

Field D.A.: Laplacian smoothing and Delaunay triangulations. Communications in Applied Numerical Methods, 4, 1988, 709-712

Filipiak M.: Mesh generation. The University of Edinburgh, 1996 (technical report) Frey W.H.: Selective refinement: A new strategy for automatic node placement in graded triangular meshes. International Journal for Numerical Methods in Engi neering, 24(11), November 1987, 2183-2200

Frey W.H., Field D.A.: Mesh relaxation: A new techniąuefor improving triangula tions. International Journal for Numerical Methods in Engineering, 31, 1991,


George P.L.: Automatic mesh generation: application to finite element methods. Chichester, Wiley 1991

George P.L., Hecht F., Saltel E.: Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering, 92(3), November 1991, 269-288

Glut B.: Generowanie i adaptacja siatek w modelowaniu procesów metodą elementów skończonych. Kraków, Akademia Górniczo-Hutnicza, 1996( Ph.D. thesis)

Glut B., Boryczko K., Jurczyk T., Aida W.: Comparison o f algorithm efficiency and mesh ąuality in Delaunay triangulation fo r complex 2D domains. Accepted for 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, BC, Canada, 25-28 September 2000

Lo S.H., Lee C.K.: Generation of gradation meshes by the background grid techniąue. Computers & Structures, 50(1), 1994, 21-32

Lóhner R.: Automatic unstructured grid generators. Finite Elements in Analysis and Design, 25, 1997, 111-134

Muller J.D.: On Triangles and Flow. The University of Michigan, 1996 (Ph.D. thesis)

Watson D.F.: Computing the n-Dimensional Delaunay tesselation with application to

Foronoi polytopes. The Computer Journal, 24, 1981, 167-172

Weatherill N.P.: Delaunay triangulation in computationalfluid dynamics. Computers and Mathematics Applications, 24(5/6), September 1992,129-150



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