(untitled) (Communications in Computational Physics, 2018)
A new multi-dimensional scheme for the Maxwell equations is established by the CIP method in combination with the method of characteristics (CIP-MOC). In addition, the CIP-MOC can be extended to arbitrary grid system by the Soroban grid without losing the third-order accuracy. With the accuracy fixed, the grid points required for the CIP are 40 times less than the conventional schemes like the FDTD in three dimensions. Numerical solutions obtained by the CIP-MOC are compared with analytical solution and the FDTD in plane-wave scattering by a perfectly-conducting circular cylinder, and the CIP-MOC agrees very well with analytical solutions. The Soroban grid is also applied to the Vlasov equation that describes the kinematics of plasmas that is frequently combined with the Maxwell equation. The adaptively moving points in velocity space are similar to the particle codes but can provide accurate solutions.