AI 中文总结
该研究针对介质散射的MOT-JVIE求解器，突破CFL条件限制实现16倍大步长操作，采用无矩阵FFT策略解决计算瓶颈，在1560万未知量下使计算成本降低一个数量级以上。
AI 中文摘要
在瞬态电磁分析中，显式时域求解器受Courant-Friedrichs-Lewy（CFL）条件限制，导致精细离散化的介质散射问题计算成本高昂。本研究针对介质散射的时间域电流密度体积分方程（MOT-JVIE）求解器，探究其大步长操作。对于所考虑的带限激励，当时间步长达到与体素离散化相关的参考CFL限制时间步长的16倍时，仍可实现准确的瞬态分析。研究揭示了大步长机制下的基本计算转变：随时间步长增大，当前时间的因果相互作用区域扩大，导致当前时间相互作用矩阵中的非零元素数量增加，使主导计算成本从历史项评估转变为涉及该矩阵的重复矩阵-向量乘积。因此，当前时间相互作用矩阵成为大步长机制下的主要可扩展性瓶颈。为解决该瓶颈，采用一种无矩阵的基于FFT的矩阵-向量乘积策略，该策略利用与格林函数相关的体积积分算子的多级Toeplitz结构处理当前时间相互作用矩阵。通过非均匀介质立方体和代表多尺度超表面结构的8×8非均匀介质纳米柱阵列对所提框架进行评估，结果显示计算成本降低一个数量级以上。在单线程执行中，该方法针对1560万个未知量进行了验证，实现了在单个CPU线程上处理超过1500万个未知量的大规模MOT-JVIE应用。
英文摘要
In transient electromagnetic analysis, explicit time-domain solvers are restricted by the Courant-Friedrichs-Lewy (CFL) condition, making finely discretized dielectric scattering problems computationally expensive. This work investigates large-time-step operation in a marching-on-in-time time-domain current-density volume integral equation (MOT-JVIE) solver for dielectric scattering. For the considered band-limited excitations, accurate transient analysis is demonstrated for time steps up to 16 times larger than the reference CFL-limited time step associated with the voxel discretization. The study reveals a fundamental computational shift in the large-time-step regime. As the time-step size increases, the present-time causal interaction region expands, increasing the number of nonzero entries in the present-time interaction matrix and causing the dominant computational cost to transition from history-term evaluations to repeated matrix--vector products involving this matrix. Consequently, the present-time interaction matrix emerges as the principal scalability bottleneck in the large-time-step regime. To address this bottleneck, a matrix-free FFT-based matrix--vector-product strategy that exploits the multilevel Toeplitz structure of the Green-function-related volume-integral operator is employed for the present-time interaction matrix. The proposed framework is evaluated through an inhomogeneous dielectric cube and an 8 X 8 array of inhomogeneous dielectric nanopillars representative of multiscale metasurface structures, demonstrating more than an order-of-magnitude reduction in computational cost. In single-threaded execution, the method is demonstrated for 15.6 million unknowns, providing a large-scale MOT-JVIE demonstration beyond 15 million unknowns on one CPU thread.
Comments11 pages, 12 figures
