A finite-volume method for the Maxwell equations in the time domain

A finite-volume scheme for the Maxwell equations is proposed using collocat ed nonorthogonal curvilinear grid arrangements, with the advantage that all components of the electric and magnetic field are stored at the same compu tational location and time. It is based on construction principles of high- resolution schemes for hyperbolic conservation laws and takes into account the local wave propagation. The implementation of boundary conditions based on the characteristic theory is described. A new divergence correction tec hnique is proposed to preserve locally the charge conservation. This is imp ortant if the Maxwell solver is used within an electromagnetic particle-in- cell ( PIC) code. The accuracy and efficiency of this finite-volume framewo rk is demonstrated with problems of electromagnetic wave propagation and of the self-consistent motion of charged particles.