论文标题
多域盖素 - 同路方法：标量场的球形崩溃II
Multidomain Galerkin-Collocation method: spherical collapse of scalar fields II
论文作者
论文摘要
我们遵循参考文献中启动的策略。 [1]并继续实现Galerkin-Colocation域分解（GCDD），该域应用于凯奇公式中的字段方程，应用于球形自我散布标量场的动力学。我们采用了面积切片量表。我们已经为任意数量的子域提出了详细的实施，并采用了传输条件的最简单形式。此外，通过对内部子域中基本函数的选择，我们完全消除了磁场方程中存在的原点附近的1/r项。使用两个错误措施验证了该代码：在时空动态过程中必须满足的ADM质量和哈密顿量约束。通常，这两个误差测量在所有子域中都呈指数收敛。作为将更多子域放置在强场区域附近的有用说明，这意味着在原点附近有效地集中了搭配点，即使数值积分有所不同，我们也表现出明显的地平线的形成。
We follow the strategy initiated in Ref. [1] and proceed with the implementation of the Galerkin-Collocation domain decomposition (GCDD) applied to the dynamics of a spherical self-gravitating scalar field with the field equation in the Cauchy formulation. We have adopted the areal slicing gauge. We have presented a detailed implementation for an arbitrary number of subdomains and adopted the simplest form of the transmission conditions. Further, by an appropriated choice of the basis functions in the inner subdomain, we eliminated exactly the 1/r terms near the origin present in the field equations. The code is validated using two error measures: the conservation of the ADM mass and the Hamiltonian constraint that must be satisfied during the spacetime dynamics. In general, both error measures converge exponentially in all subdomains. As a useful illustration of placing more subdomains near the strong-field region, meaning an efficient concentrating of collocation points near the origin, we exhibited the formation of an apparent horizon even though the numerical integration diverges.
