  We present a sub-matrix update algorithm for the continuous-time auxiliary
field method that allows the simulation of large lattice and impurity problems.
The algorithm takes optimal advantage of modern CPU architectures by
consistently using matrix instead of vector operations, resulting in a speedup
of a factor of $\approx 8$ and thereby allowing access to larger systems and
lower temperature. We illustrate the power of our algorithm at the example of a
cluster dynamical mean field simulation of the N\'{e}el transition in the
three-dimensional Hubbard model, where we show momentum dependent self-energies
for clusters with up to 100 sites.
