An accreting black hole binary system (ABHB) consists of a star<br/>orbiting a small black hole. One particularly interesting example<br/>is a neutron star-black hole (NS-BH) binary, which may be interesting<br/>sources of gravitational waves for gravitational wave observatories such<br/>as Advanced LIGO. The gravitational and electromagnetic wave signals<br/>from NS-BH binaries contains information about the particular evolution of<br/>the binary, including magnetic effects and the disruption of the neutron<br/>star by the tidal forces of the black hole.<br/><br/>This award supports the development of computational infrastructure and<br/>techniques to study ABHBs and related systems. This includes the further<br/>development of HAD, a freely available, modular computational toolkit for<br/>solving differential equations in a distributed parallel environment. HAD<br/>provides sophisticated adaptive mesh refinement capabilities, which allow<br/>the user to combine different types of differential equations and/or<br/>numerical methods. Techniques for solving the Einstein equations and<br/>magnetohydrodynamics (MHD) equations will be further developed and<br/>implemented in the code to meet the demands of simulating ABHB systems and<br/>extracting valuable physical information. <br/><br/>This work serves to advance numerical techniques for an important scientific<br/>problem, as well as the creation and dissemination of advanced tools for<br/>distributed computing. The modular design of the infrastructure allows<br/>other researchers to share and extend these tools. Finally, this study<br/>involves the training of postdoctoral researchers, graduate students, and<br/>undergraduates.