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.

中文翻译：

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时空搭配法：环量子哈密顿约束

提出了一种使用渐近常数基函数的时空配置方法（STCM），并将其应用于量子哈密顿约束，用于对史瓦西内部进行循环量化处理。典型地，这些描述采用偏差分方程 (PDE) 的形式。时空搭配方法为求解此类方程提供了一种计算效率高、收敛性强且易于并行化的方法，这是本研究的主要新颖之处。数值模拟的结果将证明并行计算方法的好处；并展示框架处理任意大小域的一般灵活性。计算的解决方案将在适用时与传统方法中计算的解决方案进行比较，方法是迭代地通过预定义的离散值网格，