Transfinite Interpolations in Free and Moving Boundary Problems
Speaker: Prof. Dr. Michel Delfour
Affiliation: Université de Montréal
Abstract: The object of this talk is the mesh adaptation via the transfinite mean value interpolation of Dyken and Floater [Computer Aided Geometric Design 26 (2009), 117–134] in 2009 and the new k-Transfinite Barycentric Interpolation of Delfour and Garon [J. Pure Applied Functional Analysis 4, no. 4 (2019), 765–801 and 5, no. 3 (2020), J. Comp. Phys. 407 (2020)] in 2019 which is an extension of the Inverse Distance Weighted Interpolation of Shepard in 1968 from unstructured finite sets of data points to structured infinite sets such as the boundary of an open set and rectifiable curves or surfaces. This work is motivated by numerical and theoretical issues in free/moving boundary problems, Arbitrary Lagrangian-Eulerian methods, and iterative schemes in shape optimization.