Surface integral equation (SIE) methods are of great interest for the efficient electromagnetic modeling of various devices, from integrated circuits to antenna arrays. Existing acceleration algorithms for SIEs, such as the adaptive integral method (AIM), enable the fast approximation of interactions between well-separated mesh elements. Nearby interactions involve the singularity of the kernel, and must instead be computed accurately with direct integration at each frequency of interest, which can be computationally expensive. In this work, a novel algorithm is proposed for reducing the cost-per-frequency associated with near-region computations for both homogeneous and layered background media. In the proposed extended AIM (AIMx), the SIE operators are decomposed into a frequency-independent term, which contains the singularity of the kernel, and a frequency-dependent term, which is a smooth function. The expensive near-region computations are only required for the frequency-independent term, and can be reused at each frequency point, leading to significantly faster frequency sweeps. The frequency-dependent term is accurately captured via the AIM even in the near region, as confirmed through error analysis. The accuracy and efficiency of the proposed method are demonstrated through numerical examples drawn from several applications, and CPU times are significantly reduced by factors ranging from three to 16.

中文翻译：

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AIMx：复杂结构快速电磁建模的扩展自适应积分方法

表面积分方程 (SIE) 方法对于从集成电路到天线阵列的各种设备的高效电磁建模具有重要意义。现有的 SIE 加速算法，例如自适应积分法 (AIM)，可以快速逼近分离良好的网格元素之间的相互作用。附近的相互作用涉及内核的奇异性，必须在每个感兴趣的频率上通过直接积分进行准确计算，这可能会导致计算成本高昂。在这项工作中，提出了一种新算法，用于降低与同质和分层背景媒体的近区域计算相关的每频率成本。在提议的扩展 AIM (AIMx) 中，SIE 算子被分解为与频率无关的项，其中包含内核的奇异性，和频率相关项，它是一个平滑函数。仅频率无关项需要昂贵的近区域计算，并且可以在每个频率点重复使用，从而显着加快频率扫描。通过误差分析确认，即使在附近区域，频率相关项也可以通过 AIM 准确捕获。通过从多个应用程序中提取的数值示例证明了所提出方法的准确性和效率，并且 CPU 时间显着减少了 3 到 16 个因素。通过误差分析确认，即使在附近区域，频率相关项也可以通过 AIM 准确捕获。通过从多个应用程序中提取的数值示例证明了所提出方法的准确性和效率，并且 CPU 时间显着减少了 3 到 16 个因素。通过误差分析确认，即使在附近区域，频率相关项也可以通过 AIM 准确捕获。通过从多个应用程序中提取的数值示例证明了所提出方法的准确性和效率，并且 CPU 时间显着减少了 3 到 16 个因素。