16:00
Dynamic Programming for Finite Ensembles of Nanomagnetic Particles
Dr. Max Jensen | University of Sussex | United Kingdom
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Authors:
Dr. Max Jensen | University of Sussex | United Kingdom
Prof. Dr. Ananta Majee | IIT Delhi
Prof. Dr. Andreas Prohl | Universität Tübingen
Dr. Christian Schellnegger | Universität Tübingen
The stochastic Landau-Lifshitz-Gilbert equation describes magnetization dynamics in ferromagnetic materials in a thermal bath. In this presentation I discuss the optimal control of a finite spin system governed by the stochastic Landau-Lifshitz-Gilbert equation in order to guide the configuration optimally into a target state. At the heart of our analysis is the problem statement with a Bellman PDE on the state manifold. We show the wellposedness of the Bellman formulation and establish the regularity of the value function and the optimal controls to prove the existence of a strong solution of the optimal control problem. Numerical experiments in a high-dimensional setting are presented. The talk is based on joint work with Ananta Majee, Andreas Prohl and Christian Schellnegger (Universitaet Tuebingen).
16:20
Shape optimization for a viscous Eikonal equation with applications in electrophysiology
Dr. Philip Trautmann | Uni Graz | Austria
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Authors:
Dr. Philip Trautmann | Uni Graz | Austria
Prof. Dr. Karl Kunisch
Prof. Dr. Gernot Plank
Dr. Aurel Neic
This talk is concerned with a shape optimization problem involving a viscous Eikonal equation as the
state equation. This problem is motivated by an inverse problem from cardiac electrophysiology. The
viscous Eikonal equation under consideration is a semilinear elliptic equation. Its solution models
the arrival time of a electromagnetic wave in the heart which is initiated at several activation sites.
The heart is modeled by a domain and the activation sites are given by small domains inside the
heart. The state equation is posed on the heart without the activation sites and thus has Dirichlet
boundary conditions on the surface of the activation sites. Given measurements on the surface of
the heart the locations of the activations sites are sought-after. This constitutes a shape optimization
problem. First the wellposeness of the state and adjoint state equation is discussed. Then shape
derivative of the involved cost functional is derived. Based on this derivative a perturbation field is
calculated which is used to translate the activation sites. The talk is concluded with two numerical
experiments in 2D and on a realistic geometry of a heart in 3D.
16:40
Fireshape: a shape optimization toolbox for Firedrake
Dr. Alberto Paganini | University of Oxford | United Kingdom
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Authors:
Dr. Alberto Paganini | University of Oxford | United Kingdom
M. Sc. Florian Wechsung | University of Oxford | United Kingdom
Fireshape is a shape optimization toolbox for the finite element library Firedrake. Fireshape can tackle optimization problems constrained by boundary value problems and offers the following features: decoupled discretization of control and state variables, automatic derivation of shape derivatives and adjoint equations, different metrics to define shape gradients, and numerous optimization algorithms. The shape optimization knowledge required to use this library is minimal.
Fireshape is available at https://github.com/fireshape/fireshape