Upcoming Events
"Computing multiple solutions of PDEs with deflation" with Dr. Patrick Farrell
Oct 22, 2021, 10:00 - 11:00 AM
Dear All,
The next CMAI Colloquium will be on
Date: | Friday October 22, 2021 at 10:00 am (Eastern Time) |
Speaker: | Mathematical Institute University of Oxford |
Title: | Computing multiple solutions of PDEs with deflation |
Zoom Link: | |
Abstract: | Computing the distinct solutions $u$ of an equation $f(u, \lambda) = 0$ as a parameter $\lambda \in \mathbb{R}$ is varied is a central task in applied mathematics and engineering. The solutions are captured in a bifurcation diagram, plotting (some functional of) $u$ as a function of $\lambda$. In this talk I will present a useful idea, deflation, for this task. Deflation has three advantages. First, it is capable of computing disconnected bifurcation diagrams; previous algorithms only aimed to compute that part of the bifurcation diagram continuously connected to the initial data. Second, its implementation is very simple: it only requires a minor modification to an existing Newton-based solver. Third, it can scale to very large discretisations if a good preconditioner is available; no auxiliary problems must be solved. We will present applications to hyperelastic structures, liquid crystals, and Bose-Einstein condensates, and discuss how PDE-constrained optimisation problems may be solved to design systems with certain bifurcation properties.
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Best,
CMAI Team