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A numerical scheme that uses multi-frequency Newton iterations to reconstruct a rough surface profile between two dielectric media is proposed. At each frequency sample, the scheme employs Newton iterations to solve the nonlinear inverse scattering problem. At every iteration, the Newton step is computed by solving a linear system that involves the Frechet derivative of the integral operator, which represents the scattered fields, and the difference between these fields and the measurements. This linear system is regularized using the Tikhonov method. The multi-frequency data is accounted for in a recursive manner. More specifically, the profile reconstructed at a given frequency is used as an initial guess for the iterations at the next frequency. The effectiveness of the proposed method is validated through numerical examples, which demonstrate its ability to accurately reconstruct surface profiles even in the presence of measurement noise. The results also show the superiority of the multi-frequency approach over single-frequency reconstructions, particularly in terms of handling surfaces with sharp variations., Comment: 33 Pages, 11 figures

A characteristic mode (CM) method that relies on a global multi-trace formulation (MTF) of surface integral equations is proposed to compute the modes and the resonance frequencies of microstrip patch antennas with finite dielectric substrates and ground planes. Compared to the coupled formulation of electric field and Poggio-Miller-Chang-Harrington-Wu-Tsai integral equations, global MTF allows for more direct implementation of a sub-structure CM method. This is achieved by representing the coupling of the electromagnetic fields on the substrate and ground plane in the form of a numerical Green function matrix, which yields a more compact generalized eigenvalue equation. The resulting sub-structure CM method avoids the cumbersome computation of the multilayered medium Green function (unlike the CM methods that rely on mixed-potential integral equations) and the volumetric discretization of the substrate (unlike the CM methods that rely on volume-surface integral equations), and numerical results show that it is a reliable and accurate approach to predicting the modal behavior of electromagnetic fields on practical microstrip antennas.

A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is realized using the numerical flux operating on the equivalent current and the global unknown of the HDG. This approach yields sparse coupling matrices upon discretization. Inclusion of the BI equation ensures that the only error in enforcing the radiation conditions is the discretization. However, the discretization of this equation yields a dense matrix, which prohibits the use of a direct matrix solver on the overall coupled system as often done with traditional HDG schemes. To overcome this bottleneck, a "hybrid" method is developed. This method uses an iterative scheme to solve the overall coupled system but within the matrix-vector multiplication subroutine of the iterations, the inverse of the HDG matrix is efficiently accounted for using a sparse direct matrix solver. The same subroutine also uses the multilevel fast multipole algorithm to accelerate the multiplication of the guess vector with the dense BI matrix. The numerical results demonstrate the accuracy, the efficiency, and the applicability of the proposed HDG-BI solver.

A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and electric field induced in the scatterer is used as an auxiliary equation that complements TD-EFVIE. The ordinary differential equation system that arises from TD-EFVIE's Schaubert-Wilton-Glisson (SWG)-based discretization is integrated in time using a predictor-corrector method for the unknown expansion coefficients of the electric field. Matrix systems that arise from the SWG-based discretization of the nonlinear constitutive relation and its inverse obtained using the Pade approximant are used to carry out explicit updates of the electric field and the electric flux expansion coefficients at the predictor and the corrector stages of the time integration method. The resulting explicit marching-on-in-time (MOT) scheme does not call for any Newton-like nonlinear solver and only requires solution of sparse and well-conditioned Gram matrix systems at every step. Numerical results show that the proposed explicit MOT-based TD-EFVIE solver is more accurate than the finite-difference time-domain method that is traditionally used for analyzing transient electromagnetic scattering from nonlinear objects.

A coupled system of volume integral and hydrodynamic equations is solved to analyze electromagnetic scattering from nanostructures consisting of metallic and dielectric parts. In the metallic part, the hydrodynamic equation relates the free electron polarization current to the electric flux and effectively "updates" the constitutive relation to enable the modeling of nonlocality. In the metallic and the dielectric parts, the volume integral equation relates the electric flux and the free electron polarization current to the scattered electric field. Unknown electric flux and free electron polarization current are expanded using Schaubert-Wilton-Glisson basis functions. Inserting these expansions into the coupled system of the volume integral and hydrodynamic equations and using Galerkin testing yield a matrix system in unknown expansion coefficients. An efficient two-level iterative solver is proposed to solve this matrix system. This approach "inverts" the discretized hydrodynamic equation for the coefficients of the free electron polarization current and substitutes the result in the discretized volume integral equation. Outer iterations solve this reduced matrix system while the inner iterations invert the discretized hydrodynamic equation at every iteration of the outer iterations. Numerical experiments are carried out to demonstrate the accuracy, the efficiency, and the applicability of the proposed method.

The interior resonance problem of time domain integral equations (TDIEs) formulated to analyze acoustic field interactions on penetrable objects is investigated. Two types of TDIEs are considered: The first equation, which is termed the time domain potential integral equation (TDPIE) (in unknowns velocity potential and its normal derivative), suffers from the interior resonance problem, i.e., its solution is replete with spurious modes that are excited at the resonance frequencies of the acoustic cavity in the shape of the scatterer. Numerical experiments demonstrate that, unlike the frequency-domain integral equations, the amplitude of these modes in the time domain could be suppressed to a level that does not significantly affect the solution. The second equation is obtained by linearly combining TDPIE with its normal derivative. Weights of the combination are carefully selected to enable the numerical computation of the singular integrals. The solution of this equation, which is termed the time domain combined potential integral equation (TDCPIE), does not involve any spurious interior resonance modes.

The terahertz current generated by a photoconductive device (PCD) saturates as the power of the input optical pump is increased. This behavior is induced by various screening effects that stem from the interactions between electromagnetic (EM) fields and semiconductor carriers. In this work, these screening effects are numerically analyzed for the first time using a fully-coupled multiphysics approach. Unlike the previously developed simulation frameworks, this approach rigorously models the nonlinear coupling between the EM fields and the carriers and therefore is capable of accounting for the screening effects. It is demonstrated that the results obtained using this multiphysics approach and actual experiments are in excellent agreement. The optical- and radiation-field screening effects are identified in the simulation results and the optical-field screening is found to play a more dominant role in the saturation of the PCD output under high optical pump power levels.

The generation rate of photocarriers in optoelectronic materials is commonly calculated using the Poynting vector in the frequency domain. In time-domain approaches where the nonlinear coupling between electromagnetic (EM) waves and photocarriers can be accounted for, the Poynting vector model is no longer applicable. One main reason is that the photocurrent radiates low-frequency EM waves out of the spectrum of the source, e.g., terahertz (THz) waves are generated in THz photoconductive antennas. These frequency components do not contribute to the photocarrier generation since the corresponding photon energy is smaller than the optoelectronic material's bandgap energy. However, the instantaneous Poynting vector does not distinguish the power flux of different frequency components. This work proposes a material absorption-based model capable of calculating the carrier generation rate accurately in the time domain. Using the Lorentz dispersion model with poles reside in the optical frequency region, the instantaneous optical absorption, which corresponds to the power dissipation in the polarization, is calculated and used to calculate the generation rate. The Lorentz model is formulated with an auxiliary differential equation method that updates the polarization current density, from which the absorbed optical power corresponding to each Lorentz pole is directly calculated in the time domain. Examples show that the proposed model is more accurate than the Poynting vector-based model and is stable even when the generated low-frequency component is strong.

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a smoothly-increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML. In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory.

In an electrostatic simulation, an equipotential condition with an undefined/floating potential value has to be enforced on the surface of an isolated conductor. If this conductor is charged, a nonzero charge condition is also required. While implementation of these conditions using a traditional finite element method (FEM) is not straightforward, they can be easily discretized and incorporated within a discontinuous Galerkin (DG) method. However, DG discretization results in a larger number of unknowns as compared to FEM. In this work, a hybridizable DG (HDG) method is proposed to alleviate this problem. Floating potential boundary conditions, possibly with different charge values, are introduced on surfaces of each isolated conductor and are weakly enforced in the global problem of HDG. The unknowns of the global HDG problem are those only associated with the nodes on the mesh skeleton and their number is much smaller than the total number of unknowns required by DG. Numerical examples show that the proposed method is as accurate as DG while it improves the computational efficiency significantly.

Incorporation of plasmonic nanostructures in the design of photoconductive devices (PCDs) has significantly improved their optical-to-terahertz conversion efficiency. However, this improvement comes at the cost of increased complexity for the design and simulation of these devices. Indeed, accurate and efficient modeling of multiphysics processes and intricate device geometries of nanostructured PCDs is challenging due to the high computational cost resulting from multiple characteristic scales in time and space. In this work, a discontinuous Galerkin (DG)-based unit-cell scheme for efficient simulation of PCDs with periodic nanostructures is proposed. The scheme considers two physical stages of the device and models them using two coupled systems: a system of Poisson and drift-diffusion equations describing the nonequilibrium steady state, and a system of Maxwell and drift-diffusion equations describing the transient stage. A "potential-drop" boundary condition is enforced on the opposing boundaries of the unit cell to mimic the effect of the bias voltage. Periodic boundary conditions are used for carrier densities and electromagnetic fields. The unit-cell model described by these coupled equations and boundary conditions is discretized using DG methods. Numerical results demonstrate that the proposed DG-based unit-cell scheme has the same accuracy in predicting the THz photocurrent as the DG framework that takes into account the whole device, while it significantly reduces the computational cost.

Plasmonic nanostructures significantly improve the performance of photoconductive devices (PCDs) in generating terahertz radiation. However, they are geometrically intricate and result in complicated electromagnetic (EM) field and carrier interactions under a bias voltage and upon excitation by an optical EM wave. These lead to new challenges in simulations of plasmonic PCDs, which cannot be addressed by existing numerical frameworks. In this work, a multiphysics framework making use of discontinuous Galerkin (DG) methods is developed to address these challenges. The operation of the PCD is analyzed in stationary and transient states, which are described by coupled systems of the Poisson and stationary drift-diffusion (DD) equations and the time-dependent Maxwell and DD equations, respectively. Both systems are discretized using DG schemes. The nonlinearity of the stationary system is accounted for using the Gummel iterative method while the nonlinear coupling between the time-dependent Maxwell and DD equations is tackled during time integration. The DG-based discretization and the explicit time marching help in handling space and time characteristic scales that are associated with different physical processes and differ by several orders of magnitude. The accuracy and applicability of the resulting multiphysics framework are demonstrated via simulations of conventional and plasmonic PCDs.

Greedy pursuit algorithms (GPAs) are widely used to reconstruct sparse signals. Even though many electromagnetic (EM) inverse scattering problems are solved on sparse investigation domains, GPAs have rarely been used for this purpose. This is because (i) they require a priori knowledge of the sparsity level in the investigation domain, which is often not available in EM imaging applications, and (ii) the EM scattering matrix does not satisfy the restricted isometric property. In this work, these challenges are respectively addressed by (i) using an artificial neural network (ANN) to estimate the sparsity level, and (ii) adding a Tikhonov regularization term to the diagonal elements of the scattering matrix. These enhancements permit the compressive sampling matching pursuit (CoSaMP) algorithm to be efficiently used to solve the two-dimensional EM inverse scattering problem, which is linearized using the Born approximation, on spatially sparse investigation domains. Numerical results, which demonstrate the efficiency and applicability of the proposed ANN-enhanced CoSaMP algorithm, are provided.

An efficient nonlinear contrast source inversion scheme for electromagnetic imaging of sparse two-dimensional investigation domains is proposed. To avoid generating a sequence of linear sparse optimization problems, the non-linearity is directly tackled using the nonlinear Landweber (NLW) iterations. A self-adaptive projected accelerated steepest descent (A-PASD) algorithm is incorporated to enhance the efficiency of the NLW iterations. The algorithm enforces the sparsity constraint by projecting the result of each steepest descent iteration into the L1-norm ball and selects the largest-possible iteration step without sacrificing from convergence. Numerical results, which demonstrate the proposed schemes accuracy, efficiency, and applicability, are presented.

Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is developed to simulate steady-state response of semiconductor devices. The proposed framework solves a system of Poisson equation (in electric potential) and drift-diffusion equations (in charge densities), which are nonlinearly coupled via the drift current and the charge distribution. This system is decoupled and linearized using the Gummel method and the resulting equations are discretized using a local DG scheme. The proposed framework is used to simulate geometrically intricate semiconductor devices with realistic models of mobility and recombination rate. Its accuracy is demonstrated by comparing the results to those obtained by the finite volume and finite element methods implemented in a commercial software package.

We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential equation with appropriate boundary conditions of the velocity potential. Making use of multipole expansions, we reduce the scattering problem to a linear algebraic system. The response of a floating plate in the quasistatic limit simplifies, considering a distinct behavior for water and flexural waves. Unlike similar studies in electromagnetics and acoustics, scattering of gravity-flexural waves is dominated by the zeroth-order multipole term and this results in non-vanishing scattering cross-section also in the zero-frequency limit. Potential applications lie in floating structures manipulating ocean waves., Comment: 19 pages, 4 figures

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme., Comment: 25 pages, 10 Figures

Algorithmic and architecture-oriented optimizations are essential for achieving performance worthy of anticipated energy-austere exascale systems. In this paper, we present an extreme scale FMM-accelerated boundary integral equation solver for wave scattering, which uses FMM as a matrix-vector multiplication inside the GMRES iterative method. Our FMM Helmholtz kernels treat nontrivial singular and near-field integration points. We implement highly optimized kernels for both shared and distributed memory, targeting emerging Intel extreme performance HPC architectures. We extract the potential thread- and data-level parallelism of the key Helmholtz kernels of FMM. Our application code is well optimized to exploit the AVX-512 SIMD units of Intel Skylake and Knights Landing architectures. We provide different performance models for tuning the task-based tree traversal implementation of FMM, and develop optimal architecture-specific and algorithm aware partitioning, load balancing, and communication reducing mechanisms to scale up to 6,144 compute nodes of a Cray XC40 with 196,608 hardware cores. With shared memory optimizations, we achieve roughly 77% of peak single precision floating point performance of a 56-core Skylake processor, and on average 60% of peak single precision floating point performance of a 72-core KNL. These numbers represent nearly 5.4x and 10x speedup on Skylake and KNL, respectively, compared to the baseline scalar code. With distributed memory optimizations, on the other hand, we report near-optimal efficiency in the weak scalability study with respect to both the logarithmic communication complexity as well as the theoretical scaling complexity of FMM. In addition, we exhibit up to 85% efficiency in strong scaling. We compute in excess of 2 billion DoF on the full-scale of the Cray XC40 supercomputer.

We report on a new concept of cloaking objects in diffusive light regime using the paradigm of the scattering cancellation and mantle cloaking techniques. We show numerically that an object can be made completely invisible to diffusive photon density waves, by tailoring the diffusivity constant of the spherical shell enclosing the object. This means that photons' flow outside the object and the cloak made of these spherical shells behaves as if the object were not present. Diffusive light invisibility may open new vistas in hiding hot spots in infrared thermography or tissue imaging., Comment: 16 pages, 5 figures