MultiAIM: Fast Electromagnetic Analysis of Multiscale Structures Using Boundary Element Methods

Integral equation methods are extensively used for computational electromagnetism, and can be applied to large problems when accelerated with fast multipole or fast Fourier transform (FFT) techniques. Unfortunately, the efficiency of FFT-based acceleration schemes can be dramatically reduced by the presence of multiscale features. Large triangles will impose a relatively coarse mesh, and large regions where FFT must be replaced by integration. Since many small triangles can fall in this region, integration costs will become prohibitive, diminishing the benefits provided by FFT. We propose an efficient and robust algorithm to overcome this barrier, based on multigrid concept. A hierarchy of grids of different resolution is used to simultaneously resolve subwavelength details and propagate fields efficiently across large distances with the FFT. Integration and precorrection costs are minimized by adapting projection stencils to the size of each triangle and enabling the use of the quasi-static Green’s function for short distances. Finally, a clever implementation based on sparse matrices exploits empty areas to reduce computational cost and memory consumption. The method is fully automated, and was tested on several structures including layouts of commercial products. Compared to existing adaptive integral method (AIM) algorithms, we demonstrate a speed-up between 7.1 and
$24.7\times $
and a reduction in memory consumption by up to 2.9 times.