高阶无色散“快速混合”Wave Equation求解器。第一部分：通过事件字段窗口和重定中心计算$\mathcal{O}(1)$采样成本
High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: $\mathcal{O}(1)$ Sampling Cost via Incident-Field Windowing and Recentering
摘要：
本文对二维和三维空间域中的不定常波动方程提出了一种频率/时间混合积分方程方法。该方法依赖于时间上的傅立叶变换，利用固定（与时间无关）数量的频域积分方程解来评估任意长时间的时域解，具有超代数小误差。该方法依赖于两个主要元素，即，1）一个平滑的时间窗口的方法，使精确的带限表示任意长的时间信号，和2）一种新的傅里叶变换的方法，在时间并行的方式，而不会导致虚假的周期性效应，提供数字色散频谱精确的解决方案。基于拉普拉斯变换而不是傅里叶变换，可以得到类似的混合技术，但是在本贡献中我们不考虑基于拉普拉斯的方法。该算法可以处理色散介质，它可以处理复杂的物理结构，它使并行化的时间在一个简单的方式，它允许时间跳跃-也就是说，解决方案采样在任何给定的时间$T$在$\mathcal{O}(1)$有界的采样成本，为任意大的值$T$，而不需要评估的解决方案在中间时间。所提出的频时混合策略推广到时域中的任何线性偏微分方程，可以得到频域解（包括例如时域Maxwell方程），并且其可应用于广泛的科学和工程背景中，提供了优于其他可用替代方案的显著优点，所述其他可用替代方案例如体积离散化、时域积分方程、和卷积-正交方法。
英文摘要：
This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times. The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables accurate band-limited representations for arbitrarily-long time signals, and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally-accurate solutions. A similar hybrid technique can be obtained on the basis of Laplace transforms instead of Fourier transforms, but we do not consider the Laplace-based method in the present contribution. The algorithm can handle dispersive media, it can tackle complex physical structures, it enables parallelization in time in a straightforward manner, and it allows for time leaping---that is, solution sampling at any given time $T$ at $\mathcal{O}(1)$-bounded sampling cost, for arbitrarily large values of $T$, and without requirement of evaluation of the solution at intermediate times. The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization, time-domain integral equations, and convolution-quadrature approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
