Reduced-basis boundary element method for fast electromagnetic field computation

Abstract

In this work, we combine conventional boundary element method (BEM) with the reduced-basis method (RBM) and propose a reduced-basis boundary element method (RB-BEM) to realize efficient modeling for parameterized electromagnetic scattering problems of dielectric scatterers. The RB-BEM allows for splitting the modeling process into a parameter-independent offline part and parameter-dependent online part, and replacing the high-dimensional original model obtained by conventional BEM with a low-dimensional reduced-basis model to improve computational efficiency of the online part. We also propose an improved greedy algorithm based on multi-grid to improve the computational efficiency of the offline part. The numerical experiments indicate that the efficiency of the improved greedy algorithm is several times higher than that of the standard one, and the solving efficiency of the reduced-basis model is several times to dozens of times higher than that of the original model with a prescribed approximation accuracy.

A locally adaptive non-intrusive block reduced basis method for scattering applications using the boundary element method

“…( 4) and ( 6) reveals that the discrete EFIE and MFIE operators are non-affine because the Green kernel couples the spatial variables and the wavenumber. A well-known strategy consists in recovering affine approximations by applying the EIM to the wavenumber-dependent kernel [9,19]. Observe that…”

“…Let us now consider the instantaneous speed-up, defined as the the ratio between the elapsed time for recovering the RCS without the ROM (i.e., with the BEM) and with the ROM. The instantaneous speed-up is the usual measure of speed-up [9,19,31], but let us emphasize that the instantaneous speed-up does not take the offline elapsed time into account. In fact, the instantaneous speed-up must be interpreted as a measure of the speed-up once the ROM is constructed and readily available.…”

“…The drawback of this method is that the series expansion is only valid in the neighborhood of the expansion point. An alternative is to apply the Empirical Interpolation Method (EIM) [18] to the Green kernels, which recovers a similar approximation for the BEM frequency-dependent matrix, with frequency-dependent weighs obtained though imposing some interpolation constraints [9,19].…”

An insight on optical metrology in manufacturing

“…As opposed to polynomial parametric equations, the Bézier-curve-based or B-spline-based models characterize structural profiles by adjusting the coordinates of control points [258]. Many methods have been developed for modeling light-nanostructure interactions: the finite-element method [259,260], the boundary-element method [261,262], the finite-difference time-domain method [263], and the rigorous coupled-wave analysis (RCWA, also known as the Fourier modal method) [264,265], to name just a few. All these computational methods start from the basis of Maxwell's equations, and the main difference between them lies in the specific numerical techniques used to solve the governing equations and boundary conditions.…”