The efficient execution of scientific simulations on HPC systems requires a partitioning of the underlying mesh among the processors such that the load is balanced and the inter-processor communication is minimized. Graph partitioning algorithms have been applied with much success for this purpose. However, the parallelization of multi-phase and multi-physics computations poses new challenges that require fundamental advances in graph partitioning technology. In addition, most existing graph partitioning algorithms are not suited for the newer heterogeneous high-performance computing platforms. This talk will describe research efforts in our group that are focused on developing novel multi-constraint and multi-objective graph partitioning algorithms that can support the advancing state-of-the-art in numerical simulation technologies. In addition, we will present our preliminary work on new partitioning algorithms that are well suited for heterogeneous architectures.