Space-time evolutionary models that require long simulation and resolving fine structures occur in many physical processes that depend on both space and time variables. Fine meshes with large degrees of freedom (DoF) are needed in order to obtain relatively accurate solutions with fine spatial scale structures. Consequently, we need to solve for tens of million of unknowns at each discrete time-step. For long time simulation, implicit time-stepping discretization methods (such as the Crank-Nicolson and Implicit Euler) require large number of discrete time-steps. One approach to overcome this difficulty is through high performance computing (HPC). For time-stepping scheme, we can achieve parallelization only in the fine mesh spatial variables. However, for long time simulation this cannot be achieved within reasonable simulation time and computational cost. In addition to spatial parallelization, we avoid the time-stepping computational bottleneck by developing an offline/online parallel-in-time procedure. We demonstrate the HPC algorithm for a class of three dimensional evolutionary models.