电磁散射体积分算子的谱
Spectrum of the volume integral operator of electromagnetic scattering
摘要：
分析了三维电磁散射体积分算子的谱。该算子既有连续的本质谱，在较低频率处占主导地位，又有离散的本征值，在较高频率处展开。算子符号的显式表达式提供了任何具有Holder连续本构参数的非均匀各向异性散射体的本质谱的精确轮廓。几何边界上的位置离散特征值推导出各种物理方案。数值实验表明，该算子的预测谱与其离散化本征值之间具有良好的一致性。
英文摘要：
Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out at higher ones. The explicit expression of the operator's symbol provides exact outline of the essential spectrum for any inhomogeneous anisotropic scatterer with Holder continuous constitutive parameters. Geometrical bounds on the location of discrete eigenvalues are derived for various physical scenarios. Numerical experiments demonstrate good agreement between the predicted spectrum of the operator and the eigenvalues of its discretized version.
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