The answers to some scientific questions are to be found in phenomena so complex that the only effective way to uncover them is through simulation and subsequent comparison to experiment or observation.

Near-future HPC platforms promise complexity themselves: deep memory hierarchies, massive parallelism, and sophisticated data analysis workflow infrastructures. Stellar astrophysics simulation is a quintessential example where these twin complexities collide: The origin of the elements that make up the world around us (including ourselves), the production of gravitational waves, and the fundamental nature of neutrinos are all issues that require leadership-class stellar astrophysics simulations for progress to be made in their understanding. I will describe how current and future HPC architectures shape choices and decisions for multiphysics software design and what new things about supernovae, neutron stars, and black holes might be uncovered at the exascale if efficient use of computational power can be realized.