Geodesic
The numerical approximation of discrete Vlasov--Darwin model based on the optimal reformulation of field equations
Matematičeskoe modelirovanie, Tome 18 (2006) no. 11, pp. 117-125

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In this article we discuss the elliptic reformulation of initial-boundary problem for Vlasov–Maxwell equation system in general three-dimensional (3D3V) case. We briefly describe a scheme of its numerical solution with the PIC method, that allows building correct nonradiative algorithms. Achieved redaction of original initial-boundary problem is easily adaptable both to fractional-dimensional (2D3V) formulations and to different sets of boundary conditions. 
@article{MM_2006_18_11_a9,
     author = {L. V. Borodachev and I. V. Mingalev and O. V. Mingalev},
     title = {The numerical approximation of discrete {Vlasov--Darwin} model based on the optimal reformulation of field equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {117--125},
     publisher = {mathdoc},
     volume = {18},
     number = {11},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_11_a9/}
}
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L. V. Borodachev; I. V. Mingalev; O. V. Mingalev. The numerical approximation of discrete Vlasov--Darwin model based on the optimal reformulation of field equations. Matematičeskoe modelirovanie, Tome 18 (2006) no. 11, pp. 117-125. http://geodesic.mathdoc.fr/item/MM_2006_18_11_a9/