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Explore a technical seminar presentation where Pablo Brubeck from the University of Oxford discusses recent developments in the FInite element Automatic Tabulator (FIAT) Python library for tabulating basis functions. Dive into two major advancements: the extension of FIAT abstraction to support macroelements, providing conforming discretizations with properties like divergence-free vector fields and divergence-conforming symmetric tensors, and the improved performance of tabulation and quadrature for simplicial high-order elements. Learn about implementations including the Hsieh-Clough-Tocher macroelement for biharmonic problems, the Guzmán-Neilan macroelement for Stokes, and the Johnson-Mercier macroelement for solid mechanics. Discover how new degrees of freedom on simplices are defined using numerically-computed orthogonal polynomial basis to enable fast solvers for high-order discretizations of Riesz maps, with practical demonstrations using Firedrake for spaces of the de Rham complex.
