The concept of trimmed tree structures for multilevel fast multipole algorithm (MLFMA), referred to as trimmed-MLFMA (T-MLFMA), is proposed for the solution of volume integral equations for the fast analysis of scattering from large, inhomogeneous objects, where the conventional MLFMA suffers from high number of iterations and matrix vector multiplication (MVM) of large matrices at each iteration. In T-MLFMA, thresholding and machine learning techniques are used to eliminate the redundant interactions as the iterations proceed. In particular, the converged basis function coefficients are estimated with a fully connected neural network and, together with the thresholding, the MLFMA tree structure is systematically pruned, and the resulting far-interaction matrix becomes sparser. As a result, both the number of iterations and the MVM time per iteration are dramatically reduced. Using only a group of small homogeneous dielectric spheres with different permittivity values at the training stage, we are able to show that scattering from large, highly inhomogeneous and fairly complex objects are solved accurately and significantly faster than the conventional MLFMA solution (up to 10 times).

We consider accurate and iteratively efficient solutions of electromagnetic problems involving homogenized near-zero-index (NZI) bodies using surface-integral-equation formulations in the frequency domain. NZI structures can be practically useful in a plethora of optical applications, as they possess near-zero permittivity and/or permeability values that cannot be found in nature. Hence, numerical simulations are of the utmost importance for rigorous design and analysis of NZI structures. Unfortunately, small values of electromagnetic parameters bring computational challenges in numerical solutions of homogeneous models. Conventional formulations available in the literature encounter stability issues that make them inaccurate and/or inefficient as permittivity and/or permeability approach zero. We propose a novel formulation that involves a well-balanced combination of operators and that can provide both accurate and efficient solutions for all NZI cases. Numerical results are presented to demonstrate the superior properties of the developed formulation in comparison to the conventional ones.

In this work, we present a trimming scheme for the multilevel tree structure of multilevel fast multipole algorithm (MLFMA), which is applied on D-type volume integral equations. With this approach, the number of iterations and the durations of matrix-vector multiplications are significantly reduced for the solution of multi-scale volumetric problems. The trimming operation is performed on rows and columns of the impedance matrix. In order to eliminate the matrix columns, the current coefficients are estimated via machine learning techniques. The implementation particularly provides significant acceleration for the iterative solutions of electrically large volumetric problems.

We present preconditioning strategies based on the $\mathcal{H}^{2}$ -matrix arithmetic for solving dense, complex, symmetric, non-Hermitian linear systems which arise from boundary element discretizations of the Electric Field Integral Equation in electromagnetic scattering analysis. The proposed preconditioner incorporates a multilevel mechanism that offers a good balance between memory used and reduction of the number of iterations.

We present a novel approach to accelerate the electromagnetic simulations by the multilevel fast multipole algorithm (MLFMA). The strategy is based on a progressive elimination of the electromagnetic interactions, resulting in trimmed tree structures, during iterative solutions. To perform such eliminations systematically, artificial neural network (ANN) models are constructed and trained to estimate the errors in the updated surface current coefficients. These column eliminations are supported by straightforward row eliminations, leading to increasingly sparse tree structures and matrix equations as iterations continue. We show that the proposed implementation, namely, trimmed MLFMA (T-MLFMA), leads to significantly accelerated electromagnetic simulations of the large-scale objects, while the accuracy is still much better than the high-frequency techniques. T-MLFMA can be seen as an exemplar of the implementations, where machine learning is successfully integrated into an electromagnetic solver for enhanced simulations.

We present a novel strategy to accelerate large-scale electromagnetic simulations with the multilevel fast multipole algorithm (MLFMA). The approach is based on a systematic reduction of electromagnetic interactions during an iterative solution such that both the number of iterations and time per iteration can be reduced. In order to eliminate matrix columns, errors in current coefficients are estimated via machine learning. The resulting implementation, namely trimmed MLFMA, provides significantly accelerated solutions without sacrificing the accuracy of results in comparison to high-frequency techniques.

We consider numerical solutions of electromagnetic problems involving near-zero-index materials with permittivity and/or permeability values close to zero. These types of problems are inherently multiscale due to the large variety of the wavelength from very large values to ordinary values in the same problem. In addition to developing a stable formulation for extreme values of the intrinsic impedance, we employ a broad-band multilevel fast multipole algorithm based on approximate diagonalization for efficient solutions. Examples involving near-zero-index materials inside ordinary waveguides are presented to demonstrate interesting electromagnetic responses of these exotic materials, as well as the effectiveness of the developed solver.

We present surface-integral-equation formulations for accurate and stable solutions of electromagnetic problems involving near-zero-index materials with arbitrarily small permittivity and/or permeability values. The formulations are developed for conventional discretizations, while they can be implemented by using interaction routines of existing solvers. Initial results on canonical objects clearly demonstrate the superiority of the developed formulations in comparison to the conventional ones.

We present horn-shaped cavities in order to improve the efficiency of energy harvesting in solar cells with traditional materials. Nano-cavities, which are already used for this purpose in the literature, are generally based on the principles of ray optics, while their sizes are in fact comparable to wavelength. Inspired by their effectiveness at radio and microwave frequencies, we design horn-shaped cavities that can effectively trap light and reduce reflections. Based on electromagnetic responses of initial structures, horn geometries are further optimized to minimize reflections and improve absorption efficiency. Numerical results demonstrate excellent performances of the designed cavities, which may even eliminate need for matching layers.

We present new types of nanocavities to improve the absorption of solar cells for energy harvesting in wide frequency ranges of the optical spectrum. Using a full‐wave approach, as opposed to the commonly used ray‐based modeling of the light, antenna‐inspired cavities with horn shapes are proposed and introduced. The effectiveness of the designed cavities is demonstrated in comparison to the conventional textures involving inverted pyramids and nanocones. Highly accurate numerical results show that solar‐cell structures with horn‐type cavities can provide excellent absorbance rates, even without using any matching layer.

We present efficient and accurate frequency-domain analysis of three-dimensional structures involving near-zero-index (NZI) materials with very small permittivity and/or permeability values. Accurate simulations are required to analyze these homogenized models that represent metamaterials with exotic NZI properties, which can be useful in a plethora of applications. When traditional solution methods are directly applied, however, instability and inaccuracy issues arise, making solutions inefficient and inaccurate particularly when electrically large models need to be studied. Identifying that numerical problems are due to unbalanced equations, extremely small/large terms, as well as the traditional low-frequency breakdown, we develop alternative implementations based on novel surface integral equations and broadband multilevel fast multipole algorithm. Numerical examples demonstrate excellent accuracy, stability, and efficiency of the developed solvers for NZI structures.

We present a novel approach of using deep convolutional neural networks (CNN) to predict electromagnetic scattering errors in iterative solutions of electrically large three-dimensional objects. Deep CNN models are constructed and trained by using surface current images to predict far-zone scattering errors. Numerical experiments demonstrate successful predictions with more than 95% accuracy. The constructed models can be useful to quickly assess the accuracy of candidate solutions of current distributions via their images.

In this letter, we present a novel approach based on using convolutional neural networks (CNNs) to visually predict solutions of electromagnetic problems. CNN models are constructed and trained such that images of surface currents obtained at the early stages of an iterative solution can be used to predict images of the final (converged) solution. Numerical experiments demonstrate that the predicted images contain significantly better visual details than the corresponding input images. The developed approach and the constructed CNN models can provide visual information on the solution of a given problem using only a few iterations without performing the whole iterative solution.

We present novel surface-integral-equation formulations for efficient and accurate iterative solutions of electromagnetic problems involving zero-index (ZI) and near-zero-index (NZI) materials. When applied to materials with small permittivity and/or permeability values, conventional implementations employing traditional formulations tend to become inefficient, inaccurate, or both. Such numerical issues arise mainly due to low-frequency breakdowns related to inner problems, as well as due to deteriorating balance of inner and outer terms. By investigating formulations in limit cases, we develop novel formulations by properly balancing integral-equation operators. We show that the resulting formulations can provide efficient, accurate, and stable analysis of three-dimensional structures having ZI and NZI materials with arbitrarily small permittivity/permeability values.

Numerical solutions of electromagnetic problems involving nanostructures at terahertz (THz)frequencies are considered. We particularly focus on nanoparticles that are made of typical metals at the lower THz frequencies. Even though the frequency is relatively low, we show that penetrable models are needed for accurately representing electromagnetic characteristics, especially to predict penetrating magnetic fields inside small particles. Due to large permittivity values with negative real parts, stable formulations are needed to obtain equivalent currents and secondary fields. It is shown that the modified combined tangential formulation, which was proposed for plasmonic simulations in wide frequency ranges, provides accurate solutions that are consistent with analytical results for spherical nanoparticles.

We present optimization and design of nano-optical couplers involving dielectric nanorods. Using tens of elements, optimal array configurations are found to produce alternative responses that can be digitized. For realistic simulations, the couplers are modeled as three-dimensional structures and analyzed via surface integral equations and the multilevel fast multipole algorithm (MLFMA). Initial results are presented demonstrate the feasibility of compact but effective couplers with desired responses.

In computational electromagnetics, nonuniform discretizations with a large variety in the sizes of the discretization elements have always been challenging to handle. Such problems are inherently multi-scale, where different regimes coexist, as small elements are used to model tiny details while large elements are used on suitable parts comparable to the wavelength. When the variety in the element...

In three-dimensional electromagnetic solvers, extreme values for electrical parameters typically lead to instability, inaccuracy, and/or inefficiency issues. Despite using the term “extreme,” such relatively large or small values of conductivity, permittivity, permeability, wavenumber, intrinsic impedance, and other electrical parameters are commonly observed in natural cases. Computational electr...

We present a fully broadband solver for fast and accurate solutions of multiscale electromagnetic problems involving both coarse and fine details. The implementation is based on a multiscale multilevel fast multipole algorithm that employs low-frequency and high-frequency expansions at suitable levels of incomplete tree structures. In addition, hybrid integral equations are used to properly formulate scattering and radiation problems in the frequency domain. Numerical results demonstrate the superior accuracy, efficiency, and stability of the implementation when solving challenging problems that cannot be handled via traditional methods.

We present stable solutions of low-frequency electromagnetic problems involving small objects and their dense discretizations with respect to wavelength. Recently developed potential integral equations (PIEs), which are based on the boundary conditions for the magnetic vector potential and the electric scalar potential, are used to formulate complex problems. A multilevel fast multipole algorithm (MLFMA) based on scaled plane waves for stable computations of short-distance interactions is further employed to achieve fast iterative solutions. The accuracy and stability of the developed PIE-MLFMA implementation are demonstrated on complex subwavelength structures.