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TrueGrid®Automatic Hex & Quad

This page serves both as a description of the automatic capabilities being developed at XYZ Scientific Applications, Inc. as well as a progress report on that development. There are two related projects, automatic quadralateral (quad) mesh generation and automatic hexahedral (hex) mesh generation. Automatic hex mesh generation depends on the automatic quad mesh generation because the quad mesh serves as the boundary for the hex.

The methods employed in TrueGrid produce quad meshes that are ideal as boundaries for hex meshes. This is because the quad meshes have few irregular nodes. An irregular node is one that has more or less than 4 quads meeting it. Irregular nodes reduce the quality of the mesh because it causes the angles in the mesh to deviate from 90 degrees. A block structured mesh, like those produced in standard TrueGrid, usually have the best angles. Notice, in the example below, produced by a prototype of TrueGrid AutoQuad, the appearance of blocks with angles close to 90 degrees. The method used in TrueGrid AutoQuad is revolutionary because of these block structures.

Below is an example of a quad mesh automatically generated by TrueGrid AutoQuad. This is only a prototype. It is not the final version of the method. There will be significant improvements made to this method before it is released. You can zoom in with your browser to see more details.

The block structures that form the quad boundary mesh are then propagated through the interior of the automatically generated hex mesh produced by TrueGrid AutoHex. The work on the AutoHex feature is in a much earlier stage of development, and no pictures of automatic hex meshes are available at this time.

Automatic hex mesh generation is probably the most difficult problem in mesh generation. For many years, the industry has been handicaped because there were certain types of boundary quad meshes which no automatic hex mesh generator could mesh. XYZ Scientific Applications, Inc. has solved this problem and, as a result, TrueGrid AutoHex has the unique ability to automatically fill any valid quad boundary mesh with an all hex mesh. It works the first time and every time.

It is designed to be as simple or as sophisticated as you want. In the simplest case, you choose a 3D solid. You then select a 3D curve on the surface, and choose a nodal spacing or the number of nodes to be placed along the curve. Then click on the "mesh" button. The TrueGrid AutoQuad kicks in first by meshing both sides of the 3D curve so that the entire boundary of the solid is meshed with quads. Then the TrueGrid AutoHex kicks in to fill the interior with hex elements.

The unique method employed by AutoHex is efficient on massively parallel systems, making it possible to build meshes with trillions of elements. The are significant problems is biomechanics, weather prediction, particle physics, chemstry, and astro physics that demand meshes of this size.

Not much is known, outside of XYZ Scientific Applications, about automatic hex mesh generation. One exception is the CUBIT project at Sandia National Laboratory. Below are some additional links to the subject.


A strategy of automatic hexahedral mesh generation by using an improved whisker-weaving method with a surface mesh modification procedure.

Automated hexahedral mesh generation of complex biological objects - using voxel hexahedral meshing (VHM)

Unconstrained plastering Hexahedral mesh generation via advancing-front geometry decomposition

From MIT as a part of "Application Challenges to Computational Geometry" a list of open questions in mesh generation. Some are outstanding theoretical problems; others represent serious computational bottlenecks in practice.

Mesh generation: Art or science? (2005) by Timothy J. Baker

An Automatic Hexahedral Mesh Generation System with Feature Line Extraction Technique - Journal of Solid Mechanics and Materials Engineering

The Physics of Climate Modeling (NASA)

NOAA Research - Weather Modeling and Prediction

Modelling the climate (GCM -General Circulation Modeling) - explains the horizontal and vertical resolutions and time steps.

Modeling for more accurate weather forcast (LLNL)