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\title{A 2d/3d r-adaptive Simplificial Mesh Optimization Algorithm}
\tocauthor{S. Basting} \author{} \institute{}
{\large \underline{Steffen Basting}}\\
University Erlangen-Nuremberg\\
\\ \vspace{4mm}{\large Eberhard Baensch}\\
University Erlangen-Nuremberg\\
This talk is concerned with the design of a mesh optimization algorithm based on the minimization of a nonlinear functional. A simplicial mesh is deformed in such a way that an implicitly given geometry is approximated with high accuracy while ensuring optimality of the mesh in a certain sense. The proposed approach is, due to the nature of the underlying functional, very well suited for the use in finite element codes. Minimization of the functionals with respect to a nonlinear constraint deduced from the implicitly given geometry then leads to an optimally deformed mesh aligned with the geometry. We emphasize that in our approach - unlike in many other approaches - no explicit reconstruction of the implicitly given geometry is required. \\
In addition to 2d and 3d examples, implementation details and possible applications are discussed.
{\sc S. Basting and E. Baensch}. {A 2d/3d r-adaptive Simplificial Mesh Optimization Algorithm}. In preparation.