时空配置方法：圈量子哈密顿约束
Space-Time Collocation Method: Loop Quantum Hamiltonian Constraints
摘要：
提出了一种基于渐近常数基函数的时空配点法，并将其应用于量子哈密顿约束，对Schwarzschild内部进行了环量子化处理。规范地，这些描述采用偏差分方程（PDE）的形式。时空配点法是一种计算效率高、收敛性好、易于并行化的求解此类方程的方法，这是本研究的主要创新点。数值模拟的结果将证明从并行计算方法的好处，并显示一般的灵活性的框架来处理任意大小的域。当适用时，将计算的解与通过迭代地步进通过离散值的预定义网格、通过递归关系计算解的常规方法中计算的解进行比较。
英文摘要：
A space-time collocation method (STCM) using asymptotically-constant basis functions is proposed and applied to the quantum Hamiltonian constraint for a loop-quantized treatment of the Schwarzschild interior. Canonically, these descriptions take the form of a partial-difference equation (PDE). The space-time collocation approach presents a computationally efficient, convergent, and easily parallelizable method for solving this class of equations, which is the main novelty of this study. Results of the numerical simulations will demonstrate the benefit from a parallel computing approach; and show general flexibility of the framework to handle arbitrarily-sized domains. Computed solutions will be compared, when applicable, to a solution computed in the conventional method via iteratively stepping through a predefined grid of discrete values, computing the solution via a recursive relationship.
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