PIMS-SFU CSC Seminar: Timm Treskatis

What do toothpaste, paint and glaciers have in common? All three fluids usually behave like a plastic solid, but as soon as the stress exceeds a critical threshold, they suddenly begin to flow like a viscous liquid. Rheologists refer to such materials as viscoplastic fluids.

From an applied mathematical perspective, the problem of simulating viscoplastic fluid flows can be interpreted as a more difficult variant of total-variation image deblurring. Surprisingly, the field of viscoplasticity has received almost no attention from the optimisation community for several decades.

My mission for this talk is to showcase the rich mathematical challenges that viscoplasticity poses in the areas of functional analysis, nonsmooth convex optimisation, numerical analysis of PDEs and VIs as well as high-performance computing. In particular, I will present three main results of my recent work in the field: (1) a new formulation of viscoplastic flow problems, (2) fast algorithms of optimal complexity for their solution and (3) preconditioning techniques for further efficiency gains.