  Modeling of laser-plasma wakefield accelerators in an optimal frame of
reference \cite{VayPRL07} is shown to produce orders of magnitude speed-up of
calculations from first principles. Obtaining these speedups requires
mitigation of a high-frequency instability that otherwise limits effectiveness
in addition to solutions for handling data input and output in a
relativistically boosted frame of reference. The observed high-frequency
instability is mitigated using methods including an electromagnetic solver with
tunable coefficients, its extension to accomodate Perfectly Matched Layers and
Friedman's damping algorithms, as well as an efficient large bandwidth digital
filter. It is shown that choosing the frame of the wake as the frame of
reference allows for higher levels of filtering and damping than is possible in
other frames for the same accuracy. Detailed testing also revealed
serendipitously the existence of a singular time step at which the instability
level is minimized, independently of numerical dispersion, thus indicating that
the observed instability may not be due primarily to Numerical Cerenkov as has
been conjectured. The techniques developed for Cerenkov mitigation prove
nonetheless to be very efficient at controlling the instability. Using these
techniques, agreement at the percentage level is demonstrated between
simulations using different frames of reference, with speedups reaching two
orders of magnitude for a 0.1 GeV class stages. The method then allows direct
and efficient full-scale modeling of deeply depleted laser-plasma stages of 10
GeV-1 TeV for the first time, verifying the scaling of plasma accelerators to
very high energies. Over 4, 5 and 6 orders of magnitude speedup is achieved for
the modeling of 10 GeV, 100 GeV and 1 TeV class stages, respectively.
