Flexible, accurate, efficient, and automatic numerical computations

In this talk I will discuss the latest developments from the Dedalus project.

This will describe an effort to create genuinely flexible and automatic solvers for a wide range of applied partial differential equations. Creating software that operates with minimal human intervention requires mastering some rather interesting mathematics. I will discus some of the latest results in this regard. In particular, the project has made several advancements in coping with coordinate singularities in spherical and polar geometry.

I will also give an overview of several application areas. These include example from Geophysical and Astrophysical Fluid Dynamics, Fluid-Solid interactions, Actively driven Bio-fluids, Quantum Graph Networks, and Pattern formation, and magnetic levitation.