CgMx User Guide: an Overture Solver for Maxwell’s Equations on Composite Grids. Cgmx: Electromagnetics Solver. solves the time-domain Maxwell’s equations in two and three space dimensions. fourth-order accurate in space and time, very fast and memory efficient. accurate representation of material interfaces. Efficient time-stepping with the modified-equation approach , allowing a large (cfl=1) time step. High-order accurate symmetric difference approximations. High-order-accurate boundary and interface conditions.