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What and Who

Partial Optimal Transport for a Constant-Volume Lagrangian Mesh with Free Boundaries

Bruno Levy
INRIA Nancy, France
Talk

Bruno Levy was hired by INRIA in 2000, and created the ALICE computer graphics team in 2004. He directed ALICE until 2018. Since 2018, he is directing the INRIA research center in Nancy and Strasbourg. Bruno's research focuses on geometry and applied math.: from 2004 to 2014, he worked on several geometry processing topics (mainly mesh parameterization and optimal sampling), with the support of two ERC grants (in 2007 and 2013), and tinkered some code that works reasonably well (GEOGRAM and GRAPHITE) and transferred part of it to the industry (the TESSAEL startup). In 2015, he started slowly moving from computer graphics to computational physics. His recent research focuses on finding efficient ways to solve some PDEs (e.g. Monge-Ampère that plays a central role in optimal transport), and to develop their applications in astrophysics. During his free time, Bruno is tinkering with electronics and FPGAs: he developed FemtoRV, an easy-to-understand and compact RISC-V soft core for teaching VERILOG and CPU design.
AG 1, AG 2, AG 3, INET, AG 4, AG 5, SWS, RG1, MMCI  
Public Audience
English

Date, Time and Location

Thursday, 10 June 2021
11:30
45 Minutes
Virtual talk
Virtual talk
Saarbrücken

Abstract

I'll explain how to create a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation and some astrophysical simulations at cosmological scale. The algorithm decomposes the simulated object into a set of convex cells called a Laguerre diagram, parameterized by the position of N points in 3D and N additional parameters that control the volumes of the cells. These parameters are found as the (unique) solution of a convex optimization problem-- semi-discrete Monge-Amp\`ere equation -- stemming from optimal transport theory. I'll explain how to extend this setting to objects with free boundaries and arbitrary topology, evolving in a domain of arbitrary shape, by solving a partial optimal transport problem. The resulting Lagrangian scheme makes it possible to accurately control the volume of the object, while precisely tracking interfaces, interactions, collisions, and topology changes.

Contact

Ellen Fries
+49 681 9325 4003

Virtual Meeting Details

Zoom
953 4609 5716
752121
public

Ellen Fries, 06/04/2021 11:47
Ellen Fries, 06/04/2021 10:20 -- Created document.