Dear all,

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.

Thank you for your time and assistance.

Best regards,
Haicheng

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