Hyperbolic formulations and numerical relativity: II. asymptotically constrained systems of Einstein equations
Hyperbolic formulations and numerical relativity: II. asymptotically constrained systems of Einstein equations
复制标题
双曲公式和数值相对论：II。
DOI：
10.1088/0264-9381/18/3/307
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发表时间：
2000
影响因子：
3.5
通讯作者：
H. Shinkai
中科院分区：
文献类型：
--
作者：
G. Yoneda;H. Shinkai
我们研究了爱因斯坦方程数值积分的渐近约束系统，该系统旨在对初始数据的自由演化的微扰误差具有鲁棒性。首先，我们研究了先前提出的“λ系统”，该系统基于对称双曲公式将人工流引入约束表面。我们使用Ashtekar的连接公式证明了该系统在麦克斯韦系统和广义相对论中的波传播问题中如预期的那样工作。其次，我们提出了一种控制稳定性的新机制，我们称之为“调整系统”。这可以通过在动力学方程中加入约束项和调整乘数来实现。我们解释了为什么乘数的特定选择减少了调整约束传播方程的非正或纯虚特征值的数值误差。这种“调整系统”也在Maxwell系统和Ashtekar系统中进行了测试。这种机制影响的不仅仅是系统的对称双曲度。
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously proposed `λ system', which introduces artificial flows to constraint surfaces based on the symmetric hyperbolic formulation. We show that this system works as expected for the wave propagation problem in the Maxwell system and in general relativity using Ashtekar's connection formulation. Second, we propose a new mechanism to control the stability, which we call the `adjusted system'. This is simply obtained by adding constraint terms in the dynamical equations and adjusting their multipliers. We explain why a particular choice of multiplier reduces the numerical errors from non-positive or pure-imaginary eigenvalues of the adjusted constraint propagation equations. This `adjusted system' is also tested in the Maxwell system and in the Ashtekar system. This mechanism affects more than the system's symmetric hyperbolicity.