CVC Seminar: Wed Jan 19 1:30-3pm ACES 4.304

Andrew Gillette

Conforming Vector Interpolation Functions for Polyhedral Meshes

Convex polyhedra offer a flexible domain meshing alternative to tetrahedra or hexahedra and can be generated automatically by Voronoi-based methods. For scientific computation, polyhedra meshes are infrequently used due in part to the lack of basis functions suited to their irregular shapes. In this talk, I will first review some methods for constructing generalized barycentric scalar-valued functions over polyhedra which can be used to interpolate scalar data over the domain. I will then discuss how these functions can be leveraged to create vector-valued basis functions akin to the edge elements used in electromagnetics. The vector functions can be used to create H() conforming vector fields which interpolate degrees of freedom associated to edges of the polyhedral mesh.