Title: Towards Moving Picture Simulations in a Discontinuous Galerkin framework
Speaker: Yingjie Wang

Abstract:

Binary black hole simulations play a central role in modern gravitational physics, but accurately evolving systems with large mass ratios remains challenging. We want to simulate these systems with the puncture method to avoid complicated excision, and use our discontinuous Galerkin (DG) code `nmesh` to achieve high efficiency. A nice evolution system is known as Z4c, but it is a second order system, while the DG framework requires a first order evolution system. Thus, we want a first order version of the Z4c system.

This new system has to be strongly hyperbolic to ensure the stability and also dump the constraints to make sure we are getting physical solutions. We are now working on searching for such a system. We have developed a Mathematica-based workflow that takes the equations in a readable tensor form and automatically derives the principal symbol matrix. So far, this search has not yet produced a satisfactory strongly hyperbolic first-order system, and attempts to automate the search with symbolic scripts have been limited by the computational complexity caused by highly degenerate eigenvalues.