标题： 一种基于因果关系的加速方法，用于有限线源解的快速时间叠加 显示英文标题

标题： A causality inspired acceleration method for the fast temporal superposition of the finite line source solutions

摘要： 我们提出了一种新颖且快速的方法来计算固体中的热相互作用，适用于涉及多个热源以及多个时间和空间尺度的时间相关问题，如闭合环路钻孔换热器场物理中遇到的问题。 新方法基于非历史时间叠加加速算法，但与最初提出的方案相比表现出更好的性能。 其主要思想是利用热波的传播特性。 尽管基本的热传递物理解是非因果的，但可以通过设定可接受的误差容限来建立一个影响区域。 这使得可以以一种有利于数值积分的方式减少必要的积分区域。 由此方法产生的被积函数的更好行为使我们能够用渐近方法代替Bakhalov-Vasil'eva方法来计算高度振荡积分，从计算角度来看，这种方法在当前应用中具有更好的性能。 本文展示了广泛的测试，以评估新方法的鲁棒性，并将其性能与最初提出的非历史方法以及使用FFT算法的卷积进行比较，测试范围包括多种误差容限。 结果表明，预计算的计算成本大幅降低，预计算包括在开始时间步进方案之前进行的所有计算。 这种降低取决于具体情况，可达几个数量级。 这种成本曾是原始非历史实现的瓶颈，通过这种方式降低成本使该方法适用于涉及数百个热源和数十万个时间步长的模拟，这些情况可能出现在钻孔场的模拟中。 显示英文摘要

摘要： We present a novel, fast method to compute thermal interactions in solids, useful for time-dependent problems involving several sources and several time and space scales such as the ones encountered in the physics of fields of closed loop borehole heat exchangers. The new method is based on the non-history temporal superposition acceleration algorithm, but presents better performance compared to the originally proposed scheme. The main idea behind it is to leverage the propagation properties of the heat wave. Despite the basic physical solutions of heat transfer being non-causal, it is possible to establish an influence region by fixing an acceptable error tolerance. This allows to reduce the necessary integration regions in such a way that numerical integration is favored. The better behaviour of the integrand arising from this approach allows us to replace the use of Bakhalov-Vasil'eva method in favor of the asymptotic method for the computation of highly oscillatory integrals that has better properties from a computational perspective in the present application. Extensive testing is presented to evaluate the robustness of the new method and to compare its performance against the originally proposed non-history method and the convolution using the FFT algorithm for a range of error tolerances. The results show that the computational cost is highly reduced for the precomputation, which includes all the computations done before starting the time-stepping scheme. The reduction is of several orders of magnitude, depending on the specific case. This cost was the bottleneck of the original non-history implementation, and reducing it in this way makes the method suitable for simulations involving hundreds of sources and hundreds of thousands of time steps that can arise in simulations of borehole fields.