Computing the solutions of a nonlinear equation as a parameter is varied is a central task in applied mathematics and engineering. In this talk I will present a new algorithm, deflated continuation, for this task.
Deflated continuation has two main advantages over previous approaches. 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 extremely simple: it only requires a minor modification to any existing Newton-based solver, and does not require solving any new auxiliary problems. As a consequence, it can scale to very large discretisations if a good preconditioner is available.
We will demonstrate the utility of the new algorithm by using it to discover previously unknown solutions to several problems of physical interest.
Computing disconnected solution branches of nonlinear partial differential equations
Date
2018/03/13 Tue 10:30 - 12:00
Room
6号館809号室
Speaker
Dr. Patrick Farrell
Affiliation
Mathematical Institute and Oriel College, University of Oxford
Abstract