非均匀物体的横向电散射：积分算子谱与预处理
Transverse electric scattering on inhomogeneous objects: spectrum of integral operator and preconditioning
AI总结：
针对横向电（TE）散射中积分方程迭代收敛慢的问题，通过显式乘法正则化算子将系统转化为“恒等加紧”形式，并结合特征值消去预处理，在有限内存下加速GMRES收敛。
摘要：
域积分方程方法及其基于FFT的矩阵-向量乘积是自由空间散射问题中局部方法的一种可行替代。然而，它常常受到迭代方法收敛极慢的影响，特别是在大或负介电常数的横向电（TE）情况下。我们识别出相关积分算子的非平凡本质谱是导致这一行为的部分原因，也是通常有效的消去预处理子失效的主要原因。我们通过应用一个显式乘法正则化算子来解决这个问题，该算子将系统转化为“恒等加紧”形式，同时允许以FFT速度进行矩阵-向量乘积。然后，通过消去一组幅度最大的稳定特征值，对该正则化系统进一步预处理，从而在有限内存条件下稳健地加速重启GMRES。
英文摘要：
The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods, especially in the transverse electric (TE) case with large or negative permittivity. We identify the nontrivial essential spectrum of the pertaining integral operator as partly responsible for this behavior, and the main reason why a normally efficient deflating preconditioner does not work. We solve this problem by applying an explicit multiplicative regularizing operator, which transforms the system to the form `identity plus compact', yet allows the resulting matrix-vector products to be carried out at the FFT speed. Such a regularized system is then further preconditioned by deflating an apparently stable set of eigenvalues with largest magnitudes, which results in a robust acceleration of the restarted GMRES under constraint memory conditions.
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