Eulerian Finite-Difference Vlasov-Poisson Solver with Non-Uniform Momentum Grid

An Eulerian finite-difference method solving the Vlasov–Poisson system is developed with a static, non-uniform momentum grid. The computational cost of this transformation differs negligibly from the uniform case with the same number of grid points. Analytic optimization of curvilinear momentum results from balancing the linear theory field structure against equipartition. A general grid parametrization is tested against classic instabilities and driven cases and is found to provide significant efficiencies over the uniform grid case. This technique introduces implicit distribution of computational resources commensurate to kinetic activity while preserving variationally conserved quantities from the formal bracket. The comparative advantages of this scheme are evidenced by its versatile modularity, adaptability, and extension to relativity.