A quasi-interactive graded-mesh generation algorithm for finite element/moment method analysis on NURBS-based geometries

It is accepted that the numerical implementation of a finite element or moment method problem should be devised to operate on a user supplied discrete geometrical representation. A mesh of triangles, quadrilaterals, tetrahedrons or hexahedrons are the most common geometrical configurations. The mathematics behind mesh generation is completely different from the mathematics of the problem formulation. However, knowledge of both is essential. There are very difficult questions to answer which can only be answered if the numerical solution process and the mesh generation process are integrated. An algorithm is presented which can be used to triangulate geometries represented by parametric coordinates. The parametrization used defines all curves as non-uniform rational B-splines (NURBS), although any valid parametric representation will work. The algorithm can be used interactively to evaluate the effects of decreasing the sample spacing. This interactive capability is very useful as a teaching tool. The ability to produce a graded-mesh is a practical alternative to using higher order basis functions. The algorithm can also run in default mode to automatically triangulate a region with an appropriately-graded mesh. The output mesh is exported in suitable form for numerical computation or for post-processing graphical representations.