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Dear all,
given the portability of PICONGPU on CPU with the "omp2b" I will try to integrate some advanced PIC algorithms developed in the NMPP division at IPP and TUM in Garching based on the current development branch. The charge conserving scheme of Esirkepov can actually be reformulated as a strong Ampere/weak Faraday GEMPIC (geometric PIChttps://doi.org/10.1017/S002237781700040X <https://doi.org/10.1017/S002237781700040X>) algorithm with linear finite elements for Vlasov-Maxwell. The only thing way off is the time discretization which one can change to a Hamiltionan splitting providing very good energy conservation and additionally a momentum conservation depending on the spline degree. As a start I would use the particle mesh interface as it is and just change the time integrator. If this works out improvements/features should be:
* Hamiltonian Vlasov-Maxwell splitting of high order (using composition)
* Standard Vlasov-Maxwell (Poisson) single species test cases for
comparison against a given dispersion relation such as Landau
damping, Bump-on-Tail instability, Weibel and Weibel streaming
instability.
* High order finite element field solver using B-Splines of arbitrary
degree (this is not the same as changing the particle shape)
* Splitting methods for strong magnetic field
(https://doi.org/10.1103/PhysRevE.92.063310)
* Extension to fully energy and momentum conserving Particle in Fourier
* Variance reduction by control variates (an enhanced delta-f scheme)
* Quasi random numbers in order to improve the devastating 1/sqrt(N)
convergence to 1/N. Given the large particle numbers typically used
this would massively reduce the noise. (Eventually use boost
https://github.com/boostorg/random/pull/36 or GSL)
Is someone else working on similar objectives? What is the current status of Esirkepovs scheme in devel?
Concerning the standard test-cases for PIC, are they already implemented somewhere else?
As I am completely new to the code itself, I would very much appreciate any help pointing me in the right direction, which files to look at or what may be possible to be reused or a good starting point. Actually I am very thankful for any comments. If it is possible I could also come to Dresden for a coding session.
Best regards,
Jakob Ameres
--
Jakob Ameres, M.Sc.
Numerical Methods in Plasma Physics
Max-Planck-Institut für Plasmaphysik
Boltzmannstr. 2
85747 Garching, Germany
Phone: +49 (89)-3299-1588, Room: D2.430
http://www-m16.ma.tum.de/Allgemeines/JakobAmeres
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