Reformulation of Vlasov–Maxwell system and a new method for its numerical solution

A new method of numerical integration of the non-relativistic Vlasov-Maxwell system with 2nd order accuracy in time is suggested. This method ensures the fulfillment of the law of conservation of charge and is convenient for using parallel computations on GPUs. The method uses the expansion of the electric field in the solenoidal and potential part. The potential part is determined instantaneous action at a distance within the current distribution of the charge density. The magnetic field and solenoidal part of the electric field are determined from the system of hyperbolic equations of the 1st order. For the numerical integration of the system proposed a new explicit monotone high order accuracy scheme. To approximate the distribution function a fixed regular grid in the coordinate space and a movable regular grid in velocity space with a fixed size and pitch, and with a center at the local hydrodynamic velocity are used. A new algorithm for calculating the charge path is also used. This algorithm has shown high efficiency and can be used in the calculation of the actual charge to mass ratio of the electron.