Keller Colloquium in Computing and Mathematical Sciences

There is much truth to the conventional wisdom that computational wave propagation is harder when the frequency is higher. Ten years ago, it was unclear that scalable sequential algorithms could even exist for the Helmholtz equation. Today, linear complexity is not only available in many scenarios of interest, but it is becoming clear that parallelism can take us much further. I will show recent results that indicate that genuinely sublinear parallel runtimes are possible in the 3D case, both with respect to the total number of unknowns, and the number of right-hand sides. The ideas that enable such scalings do not seem to be available in the low-frequency regime, hence the title of the talk. Joint work with Matthias Taus (MIT), Leonardo Zepeda-Nunez (Berkeley), Russell Hewett (Total), Adrien Scheuer (UCL).