Collaborative ITR: Rigorous Techniques in Computational Problems with Distributed Adaptive Mesh Refinement

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This ITR-Medium project will combine expertise in applied mathematics, numerical relativity, computer science, and astrophysics to develop techniques needed to simulate realistic strong-gravitational-field astrophysical systems. To this end, a driver-problem is chosen that involves solving the equations of Einstein's theory of general relativity coupled to electromagnetism and hydrodynamics to describe phenomena such as black hole formation and the accretion of matter around a black hole. Such efforts have historically encountered a number of difficulties, and therefore a number of advanced techniques will be brought to bear upon these problems.Maintaining stability in such evolutions will be studied using properties of hyperbolic equations, and numerical techniques will be developed to take advantage of useful analytical properties. At the same time, development of distributed adaptive mesh refinement will allow for the most efficient use of computational power.A wide range of physical phenomena are modeled by these and similar equations, and thus the techniques and developments studied here should be applicable to a wide range of problems. The physical situations under study attract much interest, and better models of their dynamics willbenefit, in particular, the analysis involved in the LIGO project to detect gravitational waves. This project also will train scientists in these methods as well as publicize them with papers and conferences.