# Parallel-in-time algorithms for bathymetry reconstruction with SWE

### Working Groups: Chair Computational Mathematics

### Collaborators (MAT): Prof.Â Dr.Â Daniel Ruprecht, Judith Angel, M. Sc., Dr.Â Sebastian GÃ¶tschel

### Collaborators (External): JÃ¶rn Behrens

## Description

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.