Finite element modelling of printed circuits boards (PCB) is, in particular, concerned with evaluation of parasitic inductances and capacitances. The Finite Element Analysis is a powerful tool for doing that; however, from the geometrical point of view, finite element meshing of the relevant domains represent a very serious challenge.

It is a well-known fact that mesh generators quite often experience significant difficulties in processing "long-and-narrow" domains. In PCB analysis, the problem is further complicated :

• the domain (usually a rectangle) contains up to several hundreds of long-and-narrow internal boundaries representing traces;
• those traces can be separated from each other by narrow gaps, which by themselves represent difficulties for the meshing algorithm;
• resulting meshes, in practical cases, can contain hundreds of thousands of finite elements, in which case the meshing algorithm's performance becomes a very important issue.

Our company invested significant efforts in the development of QUAD-GEN 3.5 : a fast and reliable mesh generator, specifically intended for the processing of extremely irregular geometries with complexly shaped internal boundaries. Below is the mesh obtained from processing of a printed circuit board.

QUAD-GEN 3.5, having been able to generate a quadrilateral mesh, delivers other significant benefits:

• a variety of sophisticated algorithms implemented in QUAD-GEN 3.5 have virtually eliminated a possibility of generating highly distorted elements. Elements with internal angles exceeding 170 degrees (or below 10 degrees) appear quite often in other commercial packages, but not in QUAD-GEN 3.5. Our own statistics show that, on average, QUAD-GEN generates only one "bad" element per 10,000 , and in the majority of cases this is a consequence of selecting too large element size in geometrically highly complex part of the domain. Automatic post-Laplacian refinement algorithms alway correct all distorted elements. Alternatively, the user can simply set a smaller step size along the relevant parts of the boundary.

QUAD-GEN 3.5 is unmatched in its exceptional ability to generate 100% quadrilateral meshes.

• QUAD-GEN 3.5 contains a special algorithm for fully automatic element size calculation. The user can simply set a single parameter in the input data structure, and QUAD-GEN 2.5 will automatically generate a mesh with least possible number of elements. No other information, apart from the geometrical description of the domain's boundary, is required.

• And finally, QUAD-GEN 2.5 is very fast: depending on the complexity of the domain, from one to several thousands of elements are generated within 1 sec. on a Pentium II processor.

To learn more about our mesh generation products, please follow this link. A page devoted to general description of QUAD-GEN 3.5, also contains licensing information.

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How to contact us:

E-mail: comecau@bigpond.com

Postal address:

Computational Mechanics Australia Pty.Ltd.

PO Box 736

Camberwell South VIC 3124

AUSTRALIA

Ph.: + 61-3-9809-0814

Fax: + 61-3-9809-0843