Judith Angel

Parallel-in-time algorithms for shallow water equations

For the numerical simulation of tsunamis, a model of the bathymetry, the topography of the ocean bottom, is indispensable as it greatly impacts the behaviour of the wave. It is possible to approximately reconstruct the bathymetry from measurements of the water height by solving an optimisation problem with the shallow water equations (SWE) as constraints. A simple approach to such PDE-constrained optimisation problems is the application of the gradient descent method to minimize the reduced objective functional. This is computationally expensive, because at each step of the iterative optimisation algorithm the governing state equations as well as backward-in-time adjoint equations have to be solved numerically to compute the gradient. To speed up the computations we use parallel-in-time methods.

Advisor: Prof. Dr. Daniel Ruprecht

Co-Advisor: Prof. Dr. Jörn Behrens

05.02.2024

PinT 2024: 13th Workshop on Parallel-in-Time Integration, Bruges (Belgium): "Bathymetry Reconstruction with Parallel-in-Time Methods"

17.07.2023

PinT 2023: 12th Workshop on Parallel-in-Time Integration, Hamburg: "PDE-constrained Optimisation with Asymptotic Parareal"

26.02.-03.03.2023

SIAM Conference on Computational Science and Engineering (CSE23), Amsterdam (NED) : "Parallel-in-time Solution of PDE-Constrained Optimization Problems with Hyperbolic PDEs" (Talk)

12.07.2022

PinT 2022: 11th Conference on Parallel-in-Time Integration: "Bathymetry Reconstruction with Shallow Water Equations" (Poster)

1. Judith Angel, Jörn Behrens, Sebastian Götschel, Marten Hollm, Daniel Ruprecht, Robert Seifried: Bathymetry reconstruction from experimental data using PDE-constrained optimisation. arXiv (https://arxiv.org/abs/2404.05556), 2024