Courant Institute, New York University
Monday, September 16, 2019, 3:00-4:00 PM
Lecture Room C
Monday, September 16, 2019, 1:00-2:00 PM
Building 1, Room 4072
This talk will be broadcast on-line using BlueJeans. Contact email@example.com for details.
Host: Gunay Dogan
Abstract: The numerical solution of partial differential nist-equations (PDEs) is ubiquitous in computer graphics and engineering applications, ranging from the computation of UV maps and skinning weights, to the simulation of elastic deformations, fluids, and light scattering. The finite element method (FEM) is the most commonly used discretization of PDEs due to its generality and rich selection of off-the-shelf commercial implementations. Ideally, a PDE solver should be a "black box": the user provides as input the domain boundary, boundary conditions, and the governing nist-equations, and the code returns an evaluator that can compute the value of the solution at any point of the input domain. This is surprisingly far from being the case for all existing open-source or commercial software, despite the research efforts in this direction and the large academic and industrial interest. To a large extent, this is due to treating meshing and FEM basis construction as two disjoint problems. The FEM basis construction may make a seemingly innocuous assumption (e.g., on the geometry of elements), that lead to exceedingly difficult requirements for meshing software. This state of matters presents a fundamental problem for applications that require fully automatic, robust processing of large collections of meshes of varying sizes, an increasingly common situation as large collections of geometric data become available. Most importantly, this situation arises in the context of machine learning on geometric and physical data, when one can run large numbers of simulations to learn from, as well as problems of shape optimization, which require solving PDEs in the inner optimization loop on a constantly changing domain. We present recent advancements toward an integrated pipeline, considering meshing and element design as a single challenge, leading to a black-box pipeline that can solve simulations on 10 thousand in the wild meshes, without any parameter tuning.
Bio: Teseo Schneider is an assistant professor/faculty fellow in Computer Science at the Courant Institute of Mathematical Sciences in New York University. Teseo earned his PhD in Computer Science from the Università della Svizzera italiana (2017) with the thesis entitled "Theory and Applications of Bijective Barycentric Mappings". He earned a Postdoc.Mobility fellowship by Swiss National Science Foundation (SNSF) to pursue his research aiming to bridge physical simulations and geometry. His research interests are in finite element simulations, mathematics, discrete differential geometry, and geometry processing. Teseo is the main developer of Polyfem (https://polyfem.github.io/) a flexible and easy to use Finite Element Library.