Christian Lessig, Professor at the Otto-von-Guericke-Universität Magdeburg, Germany, will give a talk entitled Exterior Calculus, its Fourier transform based discretization, and Applications on July 27th 2021 (Tuesday) at 11 am in the Poincaré room of the Alan Turing Building. The conference will also be held on Zoom.
Abstract: Exterior calculus has become an important tool in computational science and engineering (including related fields such as computer graphics). Existing discretizations are typically finite element based, i.e. they presume a mesh as a fundamental structure. We will discuss the Fourier transform of exterior calculus in Rn and on S2. We will then employ it to obtain a local spectral exterior calculus that combines structure preservation, adaptivity and higher order convergence rates. As applications we discuss fluid simulations on S2, post-capture refocus of light fields, and structure preserving neural networks.