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AM Seminar: Optimization-based PDE-constrained discontinuity tracking with high-order curved unstructured meshes

Speaker Name: 
Per-Olof Persson
Speaker Title: 
Speaker Organization: 
University of California, Berkeley
Start Time: 
Monday, January 25, 2021 - 4:00pm
End Time: 
Monday, January 25, 2021 - 5:00pm
via Zoom
Abhishek Halder


We present a framework for generating curved moving meshes which align the element faces with discontinuities in an evolving solution. The solution comes from solving a conservation law discretized using the discontinuous Galerkin (DG) method and an arbitrary Lagrangian-Eulerian formulation. The meshes are evolved by solving an optimization problem, where a carefully chosen indicator penalizes misaligned faces. Our discontinuity indicator monotonically approaches a minimum as element faces approach the discontinuity surface, which allows for efficient gradient-based optimizers. We also include a mesh skewness measure to ensure the meshes are well-shaped. For problems with large deformations, we use local element topology changes such as edge flips on the curved elements to improve the mesh qualities. We demonstrate our methods on a number of problems with moving discontinuities, such as convection problems and flow problems with shocks.


Per-Olof Persson is a Professor of Mathematics at the University of California, Berkeley, since July 2008. Before then, he was an Instructor of Applied Mathematics at the Massachusetts Institute of Technology, from where he also received his PhD in 2005. In his thesis, Persson developed the DistMesh algorithm which is now a widely used unstructured meshing technique for implicit geometries and deforming domains. He has also worked for several years with the development of commercial numerical software, in the finite element package Comsol Multiphysics. His current research interests are in high-order discontinuous Galerkin methods for computational fluid and solid mechanics. He has developed new efficient numerical discretizations, scalable parallel preconditioners and nonlinear solvers, space-time and curved mesh generators, adjoint formulations for optimization, and IMEX schemes for high-order partitioned multiphysics solvers. He has applied his methods to important real-world problems such as the simulation of turbulent flow problems in flapping flight and vertical axis wind-turbines, quality factor predictions for micromechanical resonators, and noise prediction for aeroacoustic phenomena. 

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