Department of Mathematics
"Recent Advances in High-Level PDE Software"
Automated PDE software such as FEniCS and Firedrake present users with high-level and composable abstractions behind which tedious and error-prone tasks are dealt with systematically by code internals. This greatly shortens development cycles and increases code reliability and frequently performance. Additionally, these abstractions increasingly provide the potential to integrate work in computational science. As one example of this theme, a portion this talk will illustrate scalable solvers via a model nonlinear thermal convection problem, rapidly deployed. As another example, we will also describe recent work on FInAT, a new basis function layer that allows the expression and exploitation of fine-grained structure to enable generation of optimal-complexity algorithms and nonstandard element transformations. In these cases, software provides a natural medium of collaboration between aspects of discretizations, algorithms, analysis, and/or high-performance computing.