  We initiate a systematic implementation of the spectral domain decomposition
technique with the Galerkin-Collocation (GC) method in situations of interest
such as the spherical collapse of a scalar field in the characteristic
formulation. We discuss the transmission conditions at the interface of
contiguous subdomains that are crucial for the domain decomposition technique
for hyperbolic problems. We implemented codes with an arbitrary number of
subdomains, and after validating them, we applied to the problem of critical
collapse. With a modest resolution, we obtain the Choptuik's scaling law and
its oscillatory component due to the discrete self-similarity of the critical
solution.
