Adaptive mesh refinement computations are complicated by their dynamic nature. In the serial environment they require substantial infrastructures to support the regridding processes, intergrid operations, and local bookkeeping of positions of grids relative to one another. In the parallel environment the dynamic behavior is more problematic because it requires dynamic distribution support and load balancing. Parallel AMR is further complicated by the substantial task parallelism, in addition to the obvious data parallelism, this task parallelism requires additional infrastructure to support efficiently. The degree of parallelism is typically dependent upon the algorithms in use and the equations being solved.
Different algorithms have significant compromises between computation and communication.
Substantial research work is often required to define efficient methods and suitable infrastructure. Different AMR algorithms place different requirements upon the distribution of the adaptive grid in the parallel environment.