  A fully implicit numerical approach based on the space-time finite element
method is implemented for the semilinear wave equation in 1(space) + 1(time)
and 2 + 1 dimensions to explore critical collapse and search for self-similar
solutions. Previous work studied this behavior by exploring the threshold of
singularity formation using time marching finite difference techniques while
this work introduces an adaptive time parallel numerical method to the problem.
The semilinear wave equation with a $p = 7$ term is examined in spherical
symmetry. The impact of mesh refinement and the time additive Schwarz
preconditioner in conjunction with Krylov Subspace Methods are examined.
