  A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver
is developed for full electromagnetic Particle-in-Cell (PIC) codes for the
simulations of plasma-based acceleration. The solver projects the volumetric
Yee lattice into planes transverse to a selected axis (the particle
acceleration direction) that makes the scheme quasi-one-dimensional. The scheme
removes the numerical dispersion of electromagnetic waves running parallel the
selected axis. The fields locations in the transverse plane are selected so
that the scheme is Lorentz-invariant for relativistic transformations along the
selected axis. The solver results in "Galilean shift" of transverse fields by
exactly one cell per time step. This removes the problem of numerical Cerenkov
instability (NCI). The fields positions build rhombi in plane (RIP) patterns.
The RIP scheme uses a compact local stencil that makes it perfectly suitable
for massively parallel processing via domain decomposition along all three
dimensions. No global/local spectral methods are involved.
