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Mesh Generation

 

Meshers serve as intermediaries between the modelers used to define the geometric regions to be studied, and the tools that actually solve the differential equations governing a system's behavior. Meshers convert the geometric descriptions produced by geometric modelers into collections of small, well shaped polyhedral pieces that cover the geometric region and that are the basis for the numerical equation solving techniques.

Mesh generators are an interesting example of a mathematical software package because they must solve the connectivity problem to be at all useful. In particular, they must accept geometric regions as input, and produce simplicial complexes in a format compatible with a finite element package. This connectivity problem is made difficult by the lack of standard representations for n-dimensional geometric objects and simplicial complexes.

A second peculiarity is that one of the arguments of a mesh generator is a mesh-grading function that indicates the required size of the elements of the mesh for different parts of the geometric region. Sometimes the user wants to specify this real-valued function interactively.

Currently, Vavasis is attempting to connect his n-dimensional mesh generation program [82] to external software packages using interfaces written in Tcl [86]. Tcl is also used to overcome the problem of specifying new functions at run-time. But Vavasis's solution is problematic; for instance, there is no way to specify (automatically) the preconditions on the user's geometric domain as required by the mesher. Similarly, there is no way to specify (let alone verify) that the user's mesh-grading function must be positive. Vavasis has hard-coded his types (for domains, meshes, and mesh-grading functions) into his programs, along with some ad hoc type-checking routines.



nuprl project
Tue Nov 21 08:50:14 EST 1995