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Algebraic grid generation on trimmed parametric surface using non-self-overlapping planar coons patch.
| Content Provider | CiteSeerX |
|---|---|
| Author | Wang, Charlie C. L. Tang, Kai |
| Abstract | Using a Coons patch mapping to generate the structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic PDE methods when only 1C continuous boundary is given; the error of converting generic parametric 1C boundary curves into a specified representation form is also avoided. However, overlap may happen on some portions of the algebraically generated grid when a linear or naïve cubic blending function is used in the mapping; this severely limits its usage in most of engineering and scientific applications where a grid system of non-self-overlapping is strictly required. To solve the problem, non-trivial blending functions in a Coons patch mapping should be determined adaptively by the given boundary so that self-overlapping can be averted. We address the adaptive determination problem by a functional optimization method. The governing equation of the optimization is derived by adding a virtual dimension in the parametric space of the given trimmed surface. Both one-parameter and two-parameter blending functions are studied. To resolve the difficulty of guessing good initial blending functions for the conjugate gradient method used, a progressive optimization algorithm is then proposed which has been shown to be very effective in a variety of practical examples. Also, an extension is on the objective function to control the element shape. Finally, experiment results are shown to illustrate the usefulness and effectiveness of the presented method. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Algebraic Grid Generation Trimmed Parametric Surface Non-self-overlapping Planar Coon Patch Coon Patch Mapping Good Initial Blending Function Parametric Space Element Shape Presented Method Objective Function Experiment Result Structured Grid Grid System Functional Optimization Method Boundary Curve Continuous Boundary Elliptic Pde Method Non-trivial Blending Function Progressive Optimization Algorithm Scientific Application Virtual Dimension Parametric Region Trimmed Surface Adaptive Determination Problem Conjugate Gradient Method Two-parameter Blending Function Practical Example Na Ve Cubic Specified Representation Form |
| Content Type | Text |
