Computational Relativistic Astrophysics via Space-Time Discontinuous Galerkin Finite Element Methods

计算相对论天体物理学领域已经进入了一个新时代，它对引力波信号的预测与LIGO的观测结果进行了比较，并用于解释观测到的事件的特征。第一个观测到的引力波只有一年多一点的历史，并且已经增加了世界范围内对模拟可能的引力波源的兴趣。在所谓的“多信使”天体物理学中，这种模型包括了其他类型的辐射，比如电磁辐射或中微子辐射。在不久的将来，我们将会有突破性的发现，只有x射线或无线电频谱的发现所带来的科学革命才能与之相比。引力波天文学这个新领域的基础正在奠定。

The field of Computational Relativistic Astrophysics has entered a new era where its predictions of gravitational wave signals are compared to LIGO observations, and are used to interpret signatures of observed events. The first observed gravitational wave is only a little more than one year old, and has already multiplied the world-wide interest in modelling possible gravitational wave sources. This modelling includes other kinds of radiation, such as electromagnetic or neutrino counterparts, in so-called "multi-messenger" astrophysics. The very near future will bring us breakthrough discoveries, to be compared only to the scientific revolution brought about by the discovery of X-rays or the radio spectrum. The groundwork in the new field of gravitational wave astronomy is being laid now. Gravitational waves are emitted by very compact (dense) astrophysical objects which are governed by the Einstein equations, such as systems involving black holes, neutron stars, binary systems of these, or collapse scenarios where black holes or neutron stars are formed. Faithfully modelling such systems requires not only solving the Einstein equations, but also modelling matter and radiation. These systems are highly dynamic, and detailed, accurate (faithful) large-scale numerical calculations are the only road towards understanding them. The governing equations are far too complex to be solved analytically, or in simple models that can be calculated on a desktop computer. Progress is severely hindered by the complexity and difficulties in using computational methods on today's high-performance computing (HPC) systems. Accelerators (e.g. GPUs) are commonplace, and future systems are expected to require even more parallelism while providing less memory bandwidth, increasing the burden of scientific programmers. As hardware architectures evolve, many formerly highly efficient algorithms are not efficient any more, as they only make use of a small fraction of the computing power of newer hardware. In the work proposed here, we will develop novel numerical algorithms to address these issues. While general relativity treats spacetime as a single construct in a very elegant formulation, current mainstream numerical methods do not: They explicitly split spacetime into space and time to gain access to large body of numerical methods designed for non-relativistic scenarios, but also foregoing much of the elegance of relativity in the process. The numerical methods developed here will discretize spacetime, not space and time separately, and by doing so, will curiously have the potential to be an order of magnitude more scalable and efficient. This will in turn allow models that are significantly more physically accurate and realistic, as more physics can be incorporated into their description.