Network contention has a significantly adverse effect on the performance of parallel applications with increasing size of parallel machines. Machines of the petascale era are forcing application developers to map tasks intelligently to job partitions to achieve the best performance possible. This paper presents a framework for automated mapping of parallel applications with regular communication graphs to two and three dimensional mesh and torus networks. This framework will save much effort on the part of application developers to generate mappings for their individual applications. One component of the framework is a process topology analyzer to find regular patterns and if found, to determine the dimensions of the communication graphs of applications. The other component is a suite of heuristic techniques for mapping 2D object grids to 2D and 3D processor meshes. The framework chooses the best heuristic from the suite for a given object grid and processor mesh pair based on the hop-bytes metric. We show performance improvements using the framework, for a 2D Stencil benchmark in MPI and the Weather Research and Forecasting model running on the IBM Blue Gene/P. We also compare our algorithms with others discussed in literature. ©2010 IEEE.