Speaker: Franco Dassi (Weierstrass Institute for Applied Analysis and Stochastics, Berlin)

Room: SISSA - Santorio A - room 135

Abstract: 
One of the most common representation of surfaces with complicated topology and geometry is through composite parametric surfaces, this is the case of Computer Aided Design models (CAD Models).

These models provide a very accurate representation of the geometry itself, but there are some issue when we use them to build a suitable discrete surface, for instance a piece-wise triangular mesh. First of all a CAD model can be composed by surfaces that are not topologically connected but they are joint up to a specified tolerance. In such cases, finding a new point on this input surfaces can be really expensive from the computational point of view.

Moving from the projectors developed in DEALII, [4, 5] and other new features, [2], we present an optimization-based surface re-meshing scheme that is able to overcome all the previous points. This new re-meshing technique is inspired by the work of Lévy and Bonneel [1], which embeds a smooth surface into a high-dimensional space and re-mesh it uniformly in this space, [3]. The final result is a curvature-adapted anisotropic surface mesh, where the triangles are properly oriented according to the curvature of the surface.

References:

[1] B. Lévy and N. Bonneel, Variational anisotropic surface meshing with Voronoi parallel linear enumeration, Proceedings 21st International Meshing Roundtable, 2012, pp. 349–366.

[2] F. Dassi and A. Mola and H. Si, Curvature-Adapted Surface Remeshing of CAD Surfaces, Proceedings 23rd International Meshing Roundtable, 2014, pp. 253–265.

[3] F. Dassi and H. Si, A curvature-adapted anisotropic surface re-meshing method, Tetrahedron IV Proceedings, 2013, to appear.

[4] A. Mola and L. Heltai and A. De Simone, A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures, International Society of Offshore and Polar Engineers (ISOPE), 2014, Busan Conference Proceedings.

[5] A. Mola and L. Heltai, Reference documentation for deal.II version 8.2.1, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, https://www.dealii.org/8.2.1/doxygen/deal.II/step_54.html