三维非均匀介质体的精确电场积分方程

Accurate formulations of EFIE for three-dimension inhomogeneous dielectric objects

三维非均匀介质体的电磁散射问题可由电场体积分描述。矩量法、共轭梯度傅里叶变换法、快速多极子方法等均可用来求解此问题。提出三维非均匀介质体之精确电场积分方程的三种形式,分别基于电流、内部电场和内部电位移。当介质体与背景空间的介电常数存在突变时,证明除原体积分外,电场积分方程还应该包含面积分,对应于介质体表面电荷。对介质球的数值实验证实了该方法的有效性。

For the electromagnetic scattering of three-dimensional （3D） inhomogeneous didectric objects, the volume electric-field integral equation （EFIE） is usually used, which can be solved by the method of moments （MOM）, the conjugate-gradient fast Fourier transform （CG-FFT） algorithms, and the fast multipole method （FMM）. In the traditional MOM, CG-FFT, and FMM implementations, however only volume integrals are involved. Three versions of EFIE are presented for 3D inhomogeneous dielectric objects when the unknown function is chosen as the electric current, the internal electric field, and the internal deetric displacement, respectively. We have shown that a surface integral （or several surface integrals） will be involved besides the volume integrals if the permittivity has a jump from the Background to the dielectric object, which corresponds to the surface electric charges on the didectric object. Hence, the accurate implementation of an inhomogeneous dielectric object should include both volume and surface integrals. Numerical experiments for a dideetric sphere are given to verify above conclusions.