Sun Qiang, Klaseboer Evert, Yuffa Alex J, Chan Derek Y C
J Opt Soc Am A Opt Image Sci Vis. 2020 Feb 1;37(2):276-283. doi: 10.1364/JOSAA.378665.
A field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation. For scattering by a perfect electrical conductor (PEC), the components of the electric field are obtained directly from surface integral equation solutions of three scalar Helmholtz equations for the field components. The divergence-free condition is enforced via a boundary condition on the normal component of the field and its normal derivative. Field values and their normal derivatives at the surface of the PEC are obtained directly from surface integral equations that do not contain divergent kernels. Consequently, high-order elements with fewer degrees of freedom can be used to represent surface features to a higher precision than the traditional planar elements. This theoretical framework is illustrated with numerical examples that provide further physical insight into the role of the surface curvature in scattering problems.
推导了一种仅基于场的电磁学边界积分公式，无需使用斯特拉顿 - 朱公式中出现的表面电流。对于理想电导体（PEC）的散射问题，电场分量可直接从三个标量亥姆霍兹方程的场分量的表面积分方程解中获得。通过对场的法向分量及其法向导数施加边界条件来强制执行无散条件。PEC表面的场值及其法向导数可直接从不含发散核的表面积分方程中获得。因此，与传统平面单元相比，具有更少自由度的高阶单元可用于以更高精度表示表面特征。通过数值示例说明了该理论框架，这些示例为表面曲率在散射问题中的作用提供了进一步的物理见解。
