Spectral Elements for Numerical Relativity andGravitational Wave Source Modeling

点击翻译按钮获取中文摘要

The first direct detection of gravitational waves in 2015 was a historic breakthrough in gravitational physics. The first observations were associated with the collision of two black holes, while in August 2017 gravitational waves from the merger of two neutron stars were observed for the first time. Neutron star mergers are of great interest in multi-messenger astronomy since they are also accompanied by a wide range of electromagnetic radiation. The interpretation of these observations requires theoretical models, but modeling of binary mergers remains a major challenge.The focus of the proposal is on the development of new numerical methods for numerical general relativity, but with strong ties to the ongoing efforts to provide models for gravitational wave sources. Among the different high-order methods to solve partial differential equations, a particular spectral element method, the discontinuous Galerkin method, has emerged in recent years as a successful general purpose paradigm. To enable the next generation of computer simulations in numerical general relativity, the goal is to develop and implement discontinuous Galerkin methods for general relativity, general relativistic hydrodynamics and magneto hydrodynamics. There are major challenges still ahead, including finding optimal discontinuous Galerkin formulations for the geometry and for general relativistic hydrodynamics, in particular for the treatment of shocks. For high efficiency, the goal is to implement the method with parallel adaptive mesh refinement, involving refinements in space and time.Most of this technology, however, is not available yet for numerical relativity, so the plan is to push the development of a new computational infrastructure. The main challenge in numerical relativity is that we are implementing for a moving target (new equations, new numerical methods, new hardware), so we require professional software engineering, a collaborative infrastructure, and close contact to our science drivers. The goal is to move beyond simple test cases and drive the development of the discontinuous Galerkin method for numerical relativity by full-featured simulations for gravitational wave source modeling. The overarching goal is to provide a theoretical framework for the physics of binary neutron stars and gravitational waves.