Constraint propagation in the family of ADM systems
Constraint propagation in the family of ADM systems
复制标题
ADM 系统系列中的约束传播
DOI：
10.1103/physrevd.63.124019
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发表时间：
2001
影响因子：
5
通讯作者：
H. Shinkai
中科院分区：
文献类型：
--
作者：
G. Yoneda;H. Shinkai
目前数值相对论中的重要问题是确定爱因斯坦方程的哪一种形式为我们提供了稳定和准确的模拟。在我们以前关于渐近约束系统的工作的基础上，我们给出了ArnowittDeser-Misner~ADM！带附加约束项的发展方程~调整项！在右手边。我们猜想，如果约束传播方程的傅立叶分量的放大因子~本征值，系统对违反约束是鲁棒的！都是消极的或纯粹是虚构的。我们证明了这样的系统可以通过选择调整项的乘子来获得。我们的讨论包括了德特韦勒的建议和弗里泰利的分析，我们还提到了所谓的一致性无迹ADM系统。
The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on ‘‘asymptotically constrained’’ systems, we here present constraint propagation equations and their eigenvalues for the ArnowittDeser-Misner ~ADM! evolution equations with additional constraint terms ~adjusted terms! on the right-hand side. We conjecture that the system is robust against violation of constraints if the amplification factors ~eigenvalues of the Fourier component of the constraint propagation equations! are negative or purely imaginary. We show that such a system can be obtained by choosing multipliers of the adjusted terms. Our discussion covers Detweiler’s proposal and Frittelli’s analysis, and we also mention the so-called conformaltraceless ADM systems.