A Massive Parallel Simulations for Relativistic Astrophysical Problems: Current Efforts and Challenges

With the recent groundbreaking discovery of gravitational waves from merging black holes, more direct detection of binary compact object mergers including neutron stars is only a matter of time. Observational signatures include gravitational waves and faint supernova-like transients powered by radioactive decay of freshly synthesized heavy elements. Due to the complexity of the problem, the only way to understand these observations is to confront them with the predictions obtained via simulation. Therefore, highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics including templates for gravitational wave and testing general relativity. In this presentation, we report several different efforts for massive parallel simulation for relativistic astrophysical problems. We report on an ongoing development effort to solve the Einstein equations using iterated interpolating wavelets. These are readily incorporated into a parallel implementation using DENDRO, a highly scalable parallel algorithm for multigrid and AMR methods on 2:1 balanced octrees. Furthermore, we present a numerical approach based on the space-time finite element method and time decomposition method for studying singularity formation from the semilinear wave equation. The impact of mesh refinement and the time additive Schwarz preconditioner in conjunction with Krylov Subspace Methods are examined.