From: "Jakob Ameres Jakob.Ameres@ipp.mpg.de" <picongpu-users@hzdr.de>
Subject: Geometric PIC for PICONGPU
To: picongpu-users@hzdr.de
Message-ID: <c6d7e4be-388e-39b7-113d-c92fc5410d2a@ipp.mpg.de>
Date: Tue, 27 Feb 2018 15:14:35 +0100
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101
 Thunderbird/52.6.0
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Content-Language: en-US

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