发表机构
Google Quantum AI（谷歌量子AI）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对三维麦克斯韦积分方程离散化的不连续问题，提出含切比雪夫奈斯特龙方案与稀疏映射矩阵的连续性增强方法，提升了EFIE等公式的精度与求解效率。
AI 中文摘要
在电场积分方程（EFIE）的奈斯特龙配点离散化中，面散度作用于面片边界处可能不连续的面密度，这会降低精度和收敛性。我们证明该问题不仅影响EFIE，还会影响所有包含该算子的公式，无论是方程本身还是散射场计算中；为此我们提出一种适用于光滑曲面的高阶精度连续性增强方案，可同时用于直接和间接EFIE、磁场积分方程（MFIE）以及正则化组合场积分方程（CFIE）。该方案包含两个核心部分：i）我们展示如何通过基于切比雪夫多项式的奈斯特龙方案离散方程，该方案支持闭式求积规则；ii）由于未知量和测试向量采用面片局部曲线基表示，连续性通过基变换实现：我们构建仅由曲线几何描述组装的稀疏映射矩阵。通过该方案，我们恢复了EFIE的精度，使其能与MFIE以相等权重结合形成CFIE。对典型和实际几何结构散射的数值研究表明，尽管未知量总数减少，但所有考虑的公式（单独或组合）均从连续性增强中获益，表现为条件数更优、迭代求解器迭代次数减少，且散射场精度提升了数个数量级。
英文摘要
In Nyström-collocation discretizations of the electric field integral equation (EFIE), the surface divergence acts on surface densities that may be discontinuous across patch boundaries, which degrades accuracy and convergence. We show that this not only affects the EFIE but every formulation in which the operator occurs, either in the equation itself or in the scattered field computation, and propose a high-order-accurate continuity-enforcing scheme for smooth surfaces as a remedy for the direct and indirect EFIEs, magnetic field integral equations (MFIEs), and regularized combined field integral equations (CFIEs) alike. The scheme comprises two ingredients: i) We show how to discretize the equations via a Chebyshev-based Nyström scheme, which admits closed quadrature rules. ii) Since unknowns and test vectors are in terms of patch-local curvilinear bases, continuity is enforced by a change of basis: we construct sparse mapping matrices assembled solely from the curvilinear geometry description. In doing so, we restore the accuracy of the EFIE such that it can be combined with the MFIEs with equal weights to form CFIEs. Numerical studies for the scattering from canonical and realistic geometries show that all considered formulations individually and combined benefit from the continuity enforcement in terms of better conditioning, reduced iterations of an iterative solver, and several more digits of accuracy in the scattered fields, despite reducing the total number of unknowns.
