Haicheng:
I want to implement a Semi-Lagrangian DG method (a type of characteristic
method) for solving advection-dominated problems. The method is primarily
based on tracing characteristics, as the upstream cells used in the
computation are obtained by solving along the characteristic curves, while the
current computational grid remains fixed. Besides, the upstream cell will be
divided into a few subdomains by the background grid (the same as the current
grid). Each subdomain has its basic functions.
Given that this method requires a robust characteristic tracing capability, I
would like to ask whether the deal.II supports any built-in tools or
frameworks for characteristic-based methods, or if there are recommended
approaches or existing examples in deal.II that could facilitate this.
I don't think that deal.II has any algorithms specifically for characteristic
tracing already built in. The closest I can think is Rene Gassmoeller's
methods for particle tracing, which you can find here:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018GC007508
https://arxiv.org/pdf/1612.03369
I imagine that algorithms for determining characteristics will use many
similar tools.
In general, if you want to know what people have been doing with deal.II, this
is always a good resource:
https://dealii.org/community/publications/
There is a search box (well hidden to the left of the "clear" button) where
you can filter for publications that have specific keywords in their title.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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