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A Comparison of Mesh Morphing Methods for Shape Optimization

Steven J. Owen and Matthew L. Staten

Research Notes, 19th International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 3-6 2010

IMR
PROCEEDINGS

19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

Sandia National Laboratoriesy, Albuquerque, NM, U.S.A.
Email: sjowen@sandia.gov
Sandia National Laboratories, Albuquerque, NM, U.S.A.
Email: mlstate@sandia.gov

Summary
The modeling and simulation process for design often involves many small iterations through multiple changes to geometry. In an automated setting, geometric characteristics are represented as parameters that are driven via an optimization procedure. The ability to automatically adjust and update an existing mesh to conform to modifications in the geometry is a necessary capability that can enable rapid prototyping of many alternate geometric de- signs. It is clear however, that a mesh morph or update capability will have its limitations based upon the magnitude of the geometric changes required, however extending the range in which the connectivity of a mesh may be reused through many iterations of the design process is the desired outcome of this research. In this research note we propose three di erent methods for morphing a mesh onto an updated geometry: 1. Smoothing, 2. Weighted Residuals, and 3. Simplex-based transformations. In each case we assume the geometric topol- ogy description of the model through all iterations of the optimization, remains constant. This assumption allows for the geometric ownership of nodes and elements in the mesh to also remain unchanged through design iterations.

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