Transfinite Mappings and their Application to Grid Generation
DREXEL UNIV PHILADELPHIA PA DEPT OF MATHEMATICAL SCIENCES
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The two essential ingredients of any boundary value problem are the field equations which describe the physics of the problem and a set of relations which specify the geometry of the problem domain. Mesh generations or grid generators are preprocessors which decompose the problem domain into a large number of interconnected finite elements or curvilinear finite difference stencils. A number of such techniques have been developed over the pat decade to alleviate the frustration and reduce the time involved in the tedious manual subdividing of a complex-shaped region or 3-D structure into finite elements. Our purpose here is to describe how the techniques of bivariate and trivariate blending function interpolation, which were originally developed for and applied to geometric problems of computer-aided design of sculptured surfaces and 3-D solids, can be adapted and applied to the geometric problems of grid generation. In contrast to other techniques which require the numerical solution of complex partial differential equations and, hence, a great deal of computing, the transfinite methods proposed herein are computationally inexpensive.
- Numerical Mathematics