Speaker
Description
Conventional space-time domain simulations suffer from the explicit breaking of continuum symmetries, once a mesh is introduced. In turn, central quantities, such as e.g. energy or angular momentum do not remain preserved after discretization. In this talk we present a novel geometric variational discretization for second order initial value problems (IVPs) [1], which builds upon insight from the theory of general relativity, where space and time are treated on the same footing. By discretizing the dynamics along a world-line parameter, instead of physical time directly, we retain manifest translation symmetry and conservation of the associated continuum Noether charge. A non-equidistant time discretization emerges dynamically, realizing a form of automatic adaptive mesh refinement (AMR), guided by the system symmetries. We show that the Noether charge, associated with the continuum symmetry of the system, is exactly preserved if summation-by-parts finite difference operators are deployed.
[1] A. Rothkopf and J. Nordström arXiv:2307.04490
| Conference Topic Areas | Track2: Advanced Computational Methods and Applications in Marine, Subsea and Offshore Technology |
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