Wave equations help us to understand phenomena ranging from earthquakes to
tsunamis. These phenomena materialise over very large scales. It would be
computationally infeasible to track them over a regular mesh. Yet, since the
phenomena are localised, adaptive mesh refinement (AMR) can be used to
construct meshes with a higher resolution close to the regions of interest.
ExaHyPE is a software engine created to solve wave problems using AMR, and we
use it as baseline to construct our numerical relativity application called
ExaGRyPE. To advance the mesh in time, we have to interpolate and restrict
along resolution transitions in each and every time step. ExaHyPE’s vanilla
code version uses a d-linear tensor-product approach. In benchmarks of a
stationary black hole this performs slowly and leads to errors in conserved
quantities near AMR boundaries. We therefore introduce a set of higher-order
interpolation schemes where the derivatives are calculated at each coarse grid
cell to approximate the enclosed fine cells. The resulting methods run faster
than the tensor-product approach. Most importantly, when running the stationary
black hole simulation using the higher order methods the errors near the AMR
boundaries are removed.

Dieser Artikel untersucht Zeitreisen und deren Auswirkungen.

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