2021 MIT CCSE Symposium
March 15, 2021, 1:00 PM EST
Registration is free but required for planning and communication.
1:00 PM – KEYNOTE
FROM THE FARADAY CAGE TO LIGHTNING LAPLACE AND HELMHOLTZ SOLVERS
Professor Nick Trefethen, University of Oxford
We begin with the story of the Faraday cage used for shielding electrostatic fields and electromagnetic waves. Feynman in his Lectures claims the shielding is exponential with respect to the gap between wires and that it works with wires of infinitesimal radius.
In fact, the shielding is much weaker than this and requires wires of finite radius (which is why it’s hard to see into your microwave oven). How can we compute the field inside a 2D cage?
This brings us to the numerical heart of the talk. When the boundaries are smooth, series expansions (going back to Runge in 1885) converge exponentially. When there are corners and associated singularities, the new technique of lightning Laplace and Helmholtz solvers, depending on rational or Hankel functions with poles exponentially clustered near the corners, converges root-exponentially. The name “lightning” comes from the fact that this method exploits the same mathematics that makes lightning strike at sharp points. Lightning solvers and the related AAA approximation algorithm are bringing in a new era of application of rational functions and their relatives to PDEs, conformal mapping, and other numerical problems. A variant known as “log-lightning approximation” offers the prospect of even faster exponential convergence
2:30 PM – MIT FACULTY TALKS
Cecil and Ida Green Professor of Oceanography
Wim van Rees
Assistant Professor of Mechanical Engineering
Professor of Nuclear Science and Engineering
Professor of Materials Science and Engineering
4:00 PM – ANNOUNCEMENT OF CSE MATHWORKS RESEARCH PRIZES
4:15 PM – STUDENT POSTER SESSION
MIT CCSE Virtual Symposium
Monday March 15, 2021 │ 1 PM EST