标题： 爱因斯坦-麦克斯韦系统的伪谱实现 显示英文标题

标题： Pseudospectral implementation of the Einstein-Maxwell system

摘要： 电磁学在我们希望研究的重力各种应用中起着重要作用。为此，在这项工作中，我们在自适应网格伪谱数值相对论代码bamps中实现了麦克斯韦方程。我们对作为一阶对称双曲型PDE系统的演化方程进行了详尽分析，包括为我们的惩罚边界通信方案构建特征变量，以及辐射控制、约束保持的外部边界条件，根据Kreiss-Agranovich-Métivier的语言，这些边界条件被证明是边界稳定的。在介绍了我们可以用于初始数据求解的麦克斯韦约束形式后，我们接着展示了一系列数值测试。我们的模拟，无论是基于Cowling近似还是全非线性演化，都显示出误差随分辨率快速收敛，以及与Kerr背景上已知的准正常衰减率一致。最后，我们展示了强数据下的电真空运动方程的演化，这是典型临界塌缩运行的良好表示。 显示英文摘要

摘要： Electromagnetism plays an important role in a variety of applications in gravity that we wish to investigate. To that end, in this work, we present an implementation of the Maxwell equations within the adaptive-mesh pseudospectral numerical relativity code bamps. We present a thorough analysis of the evolution equations as a first order symmetric hyperbolic system of PDEs, including the construction of the characteristic variables for use in our penalty boundary communication scheme, and radiation controlling, constraint preserving outer boundary conditions which, in the language of Kreiss-Agranovich-M\'etivier, are shown to be boundary-stable. After presenting a formulation of the Maxwell constraints that we may solve for initial data, we move on to present a suite of numerical tests. Our simulations, both within the Cowling approximation, and in full non-linear evolution, demonstrate rapid convergence of error with resolution, as well as consistency with known quasinormal decay rates on the Kerr background. Finally we present evolutions of the electrovacuum equations of motion with strong data, a good representation of typical critical collapse runs.