[EDITORIALI

This special issue of Advances in Engineering Software and Workstations has been prepared by our special guest editor Cecil Armstrong on the subject of Au- tomatic Mesh Generation. This topic is of particular interest to readers of AES because most engineering analysis and simulation techniques require some form of subdivision of the problem into simple shapes or elements. Finite difference and finite element meth- ods require the volume to be described whereas the boundary element method requires only the surface or boundary to be described.

In Cecils guest editorial he points out the wide vari-

ety of techniques which are being used by" engineers for automatic mesh generation and proposes that a series of benchmarks be established to evaluate the various technologies.

We would be pleased to publish the proposals for the benchmarks and any results or comments in a fu- ture issue of AES.

Finally I would like to thank Cecil and the contrib- utors for an excellent contribution to the literature.

Dr. Robert A Adey (Editor)

GUEST EDITORIAL]

A u t o m a t i c M e s h G e n e r a t i o n - B e n c h m a r k s N e e d e d ?

by Dr. C.G. Armstrong

This issue of Advances in Engineering Software and Workstations will be entirely devoted to the topic of Automatic Mesh Generation.

In recent years there has been substantial aca- demic and commercial interest in making finite element analysis much more accessible to the non-specialist. Putt ing FEA on the designer's desk so that he may conduct "what if" analyses of design changes requires the integration of a number of techniques such as er- ror analysis and adaptive mesh refinement. However generating meshes of controllable density in arbitary geometries is an essential precursor to the entire pro- cess. Since the integration of a Geometric Modelling and Simulation is one of the major themes of this jour- nal, an issue on automatic mesh generation seemed timely and desirable.

The contributors to this issue are from several coun- tries and are associated with academic, commercial and government research organisations. The methods described cover the spect rum of those algorithms cur- rently employed or under development. Itopefully the collected papers should serve as a useful reference to the current state of the art.

Dr. C.G. Armstrong

The issue opens with "Criteria for Comparison of Automatic Mesh Generation Methods" by Malcolm Sabin. In his paper, Dr Sabin has provided a candidate set of criteria against which meshing algorithms might

218 Adv. Eng. Software, 1991, VoI. 13, No. 5/6 combined

be measured and developed. Doubtless his list will be carefully scrutinised by other contributors!

The remainder of the papers describe meshing al- gorithms and/or their integration in FE modelling sys- tems. Delaunay triangulation techniques are currently very popular. Algorithms for use in 2D and 3D solids are described by Joe and are available from that au- thor. The development from a basic space filling tri- angulation to an isotropic or anisotropic mesh of con- trolled and variable density is described by George, IIecht and Vallet. A mathematical framework for ex- tending the Delaunay triangulation to cover k dimen- sional meshes embedded in n dimensions, e.g. in shell meshing, is described by Field.

Shell meshing is also discussed by Cavendish, Frey and Martin in the context of integrated feature based design and mesh generation for multi-featured func- tional surfaces. Meshing on parametric or planar sur- faces using an alternative technique called the advanc- ing front method is covered by Hinton, Rao and Oza- kca, who additionally consider techniques for error es- timation, adaptive analysis and shape optimisation.

One of the advantages of Delaunay point triangula- tions in 2D is that the triangles are well shaped. To de- compose a complex 2D shape into topolo~cally simple, well shaped subdomains, both Gursoy & Patrikalakis and Tam & Armstrong use the medial axis transform of the 2D shape. Another new 2D algorithm is the Paving technique of Blacker, Stephenson and Canaan, who also describe a limited extension to 3D. Finally, the generation of the coarsest possible meshes in gen- eral 3D solids using a set of tetrahedral element re- moval operators is described by Shephard and Lo, who intend using this mesh as the starting point of an hp-

adaptive analysis. Reviewing these papers one is struck by the diver-

sity of approach and the difficulty in assessing the rel- ative merits of each. Sabin has provided some possi- ble criteria but surely the community need some stan- dard benchmarks against which to test candidate al- gorithms. Presumably benchmarks should be

• simple and easily specified, i.e. not too difficult to replicate

• testing, without being pathological or overly re- strictive

• illustrative of particluar meshing features or prob- lems

The readers are hereby invited to submit their 2D, shell or solid meshing benchmarks, for publication in a fol- low up to this special issue. Please send your contri- bution in the general form of a Technical Note, to the guest editor below before 31 July 1992.

Finally the guest editor gratefully acknowledges the hard work of all the contributors and reviewers. Many thanks also to the Editor for his advice and assistance.

Cecil G Armstrong Department of Mechanical and Manufacturing Engineering Ashby Building Stranmillis Road Belfast BT9 5AH Northern Ireland (Guest Editor).

Biographical Sketch ]

Cecil G Armstrong is a Reader in the Department of Mechanical and Manufacturing Engineering at the Queen's University of Belfast, Northern Ireland. IIe obtained a BSc in Mechanical Engieering from that in- stitution in 1973 followed by a PhD in Biomechanics in 1977. The next six years were spent at Rensselaer Polytechnic Institute in Troy, New York, first as a post doctoral researcher in tile biomechanics area and then

as a member of the faculty. Following a brief spell at Durham University he returned to Belfast in 1984.

tits main research interests are in automatic mesh generation, analysis automation and FE modelling and the way in which these processes can be facilitated us- ing techniques such as the medial axis transform. He also retains an interest in biomechanics.

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