The PIC (Particle-in Cell) codes represent powerful tools for plasma transport study [1,2]. They are frequently used in fusion plasma applications and contribute to design of next generation fusion devices. As it was demonstrated in , PIC simulations with Cartesian grid do conserve momentum and energy simultaneously only for uniform grids. This requirement represents very heavy condition for plasma edge modelling, when nonuniform space resolution is favorable. Some time ago a solution for 1D codes has been found , but so far up to now no multidimensional generalization of this approach has been done.
The aim of this PhD work is to develop a multidimensional energy and momentum conserving PIC code with nonuniform Cartesian grid. We expected significant speedup, by order of magnitude, of such code against the conventional codes, which will save tens of millions of CPU hours per year for average PIC user on high performance computer facilities.
 D. Tskhakaya, Plasma Phys. Cont. Fus., 59 (2017) 114001
 T. Takizuka, et al., Contrib. Plasma Phys., 59 (2017) 034008
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 J. Duras, et al., Contrib. Plasma Phys., 54 (2014) 697