Exascale systems, expected to emerge by the end of the next decade, will require the exploitation of billion-way parallelism at multiple hierarchical levels in order to achieve the desired sustained performance. The task of assessing future machine performance is approached by identifying the factors which currently challenge the scalability of parallel applications. It is suggested that the root cause of these challenges is the incoherent coupling between the current enabling technologies, such as Non-Uniform Memory Access of present multicore nodes equipped with optional hardware accelerators and the decades older execution model, i.e., the Communicating Sequential Processes (CSP) model best exemplified by the message passing interface (MPI) application programming interface. A new execution model, ParalleX, is introduced as an alternative to the CSP model. In this paper, an overview of the ParalleX execution model is presented along with details about a ParalleX-compliant runtime system implementation called High Performance ParalleX (HPX). Scaling and performance results for an adaptive mesh refinement numerical relativity application developed using HPX are discussed. The performance results of this HPX-based application are compared with a counterpart MPI-based mesh refinement code. The overheads associated with HPX are explored and hardware solutions are introduced for accelerating the runtime system.