Title : Multiscale methods : From subatomic particles to pixels and galaxies
From the depths of the known universe to the tiniest subatomic particles, our understanding of the world around us spans roughly 40 orders of magnitude in space and time. As such it is not surprising that multiscale models play a key role in many parts of science. Even at just a small subset of those scales multiscale methods provide computational benefits leading to some of the fastest algorithms for solving problems in many areas of science and engineering. And yet the development of these methods can be deceptively difficult.
In this talk, I will first present existing work towards efficient multigrid methods for simulation of deformable objects with a focus on thin shells (for cloth simulation). This includes subtleties regarding enforcing boundary conditions correctly which has uncovered a mistake in one of the seminal thin shell papers from 50 years ago.
Next, I will discuss work related to the associated frictional contact problems including both collision detection and response. Friction is inherently a multiscale phenomenon with macroscopic friction typically being due to shearing among microscopic asperities. However, here I will focus on a single length scale and present computationally tractable methods for frictional contact while ensuring some notion of provable correctness.
To finish off, I will branch out and briefly touch on analogies between multigrid and MERA (multiscale entanglement renormalization ansatz) tensor networks, potential applications of hierarchical techniques in neuromorphic computing, and future directions of research.