Distance field from a surface geometry is used in several scientific algorithms and applications from computer graphics, visualization, computational fluid dynamics and more. Distance field can be calculated efficiently by solving the eikonal equation at each grid point using the fast-sweeping method. There has been an increased interest to develop parallel algorithms for the fast-sweeping method to accelerate its computational turnaround time. Most parallel strategies have focused on shared-memory parallelism and do not readily extend to distributed-memory parallelism to handle large-scale problems. To address this issue, we propose a domain-decomposition strategy to enable distributed-memory parallelism for the fast-sweeping method on heterogeneous computing clusters with accelerators. In our strategy, we make use of the Cuthill-McKee ordering for both fine and coarse-grain parallelism such that parallel computations proceed in direction of solution characteristics. We consider both CUDA and OpenACC implementations to compute the distance field from arbitrarily complex geometries and demonstrate parallel computations of large-scale problems that necessitate distributed-memory parallelism. We also discuss the implications of the proposed strategy for scalability of the fastsweeping method.