发表机构
University of Manitoba（曼尼托巴大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将量化张量列车压缩融入三维FDTD，通过界面平滑降低系数秩，在512^3网格上实现点误差10^-4，减少存储但增加计算成本，验证了可行性。
AI 中文摘要
将量化张量列车（QTT）压缩纳入均匀Yee网格上的全矢量三维散射场时域有限差分（FDTD）公式中。所有六个电磁场分量、材料相关的更新系数、等效电流源和交错有限差分算子均以兼容的QTT形式表示。采用体素化材料界面的高斯正则化来降低由突变介电常数和电导率跃迁产生的系数秩。该公式在包含多达$512^3$个空间单元的网格上，针对解剖学异质人脑模型和均匀介质球进行了评估。报告的结果表明，界面平滑显著降低了材料系数秩，且TT-FDTD解再现了全网格瞬态场，在所检查切片中的逐点绝对误差约为$10^{-4}$。与传统FDTD相比，张量表示在精细离散化下大大减少了存储，尽管张量收缩和重新压缩引入了额外的每步计算成本。这些结果证明了QTT加速的三维FDTD在大型结构化网格模拟中的可行性和内存-时间权衡。
英文摘要
Quantized tensor-train (QTT) compression is incorporated into a full-vector three-dimensional scattered-field finite-difference time-domain (FDTD) formulation on uniform Yee grids. All six electromagnetic-field components, material-dependent update coefficients, equivalent-current sources, and staggered finite-difference operators are represented in compatible QTT form. Gaussian regularization of voxelized material interfaces is used to reduce the coefficient ranks generated by abrupt dielectric and conductivity transitions. The formulation is evaluated for an anatomically heterogeneous human-head model and a homogeneous dielectric sphere on grids containing up to $512^3$ spatial cells. The reported results show that interface smoothing substantially reduces material-coefficient ranks and that the TT--FDTD solution reproduces the full-grid transient fields with pointwise absolute errors on the order of $10^{-4}$ in the examined slices. Compared with conventional FDTD, the tensor representation greatly reduces storage at fine discretizations, although tensor contractions and recompression introduce additional per-step computational cost. These results demonstrate the feasibility and memory--time tradeoff of QTT-accelerated three-dimensional FDTD for large structured-grid simulations.
CommentsSubmitted to IEEE Transaction on Microwave Theory and Techniques on July 27, 2026
