This paper presents the simulation and wavefront parallel-programming patterns of the MAP3S pattern-based parallel programming system for distributed-memory environments. Both patterns target iterative computations on static-and-regular meshes. In addition to providing performance-oriented features, such as asynchronous communication and distribution of the computational workload that is tailored to fit the computation, the patterns also provide usability-oriented features, such as direct mesh-access, mesh memory-footprint distribution, and a versatile data-dependency specification scripting-language. Parallel programs developed using MAP3S achieve significant performance gains and capability enhancements on both low-end and high-end interconnect-equipped distributed-memory systems.