Visualizing mesh construction

A comprehensive upgrade of our 2D TriComp series of programs (Version 7.0) is nearing completion. Beta versions of the major packages will be announced in our June NewsNote, and the complete set of programs will be available for update in October. We’ve made some serious technical improvements:

  • The number of solution-volume regions has been increased to 250.
  • The programs employ consistent double-precision arithmetic and the numerical accuracy in data files and analysis operations has been increased.
  • For top speed, the 64-bit programs are created with the latest Intel compiler with multi-processor support.
  • As in the AMaze programs, the user has the option to customize plotting and analysis quantities through configuration files.

We’ve also added some features that make the programs more fun and interesting to use. For example, in Mesh the user can activate a graphical display to show the operations the program performs to generate the conformal mesh. The figure below illustrates the display. Starting from the foundation mesh,  the program highlights the nodes and facets of the current region that are shifted for a precise match to specified geometric boundaries. When a region is completed, the fill status and final boundary are updated. The user can include or remove the feature and optimize the display speed in the dialog shown. Mesh remembers the last settings, so it is not necessary to restore them each time the program runs. The speed setting automatically compensates for the size and complexity of the mesh. We are also adding display features to the TriComp technical programs (EStat, PerMag, TDiff,…) to show the convergence or the time evolution of the solutions.

The utility of the mesh-generation display extends beyond its entertainment value:

  • Users can see how regions overlay one another following the order in the Mesh script.
  • It is easy to spot the location of invalid vectors if there is an error in the processing.

We have also made a technical improvement to Mesh with regard to orphan elements. With hundreds of boundary vectors and millions of elements, there is a possibility that the region identity of an element may be misidentified because of floating point degeneracy. Over the years, we have improved the reliability of the Mesh element-identification routines. With double-precision arithmetic and rigorous limits on search domains, the reliability of Mesh 7.0 is close to perfection.

Mesh 7.0, optional display of mesh generation

Mesh 7.0, optional display of mesh generation

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