arXiv subjects

Constantine Sideris

Publications and source records attributed to Constantine Sideris.

15 recordsLinked to original sources

arXiv2026

High-Order-Accurate Continuity Enforcing Nystr\"om Discretization of 3D Maxwell Combined Field Integral Equations

In Nystr\"om-collocation discretizations of the electric field integral equation (EFIE), the surface divergence acts on surface densities that may be discontinuous across patch boundaries, which degrades accuracy and convergence. We show that this not only affects the EFIE but every formulation in which the operator occurs, either in the equation itself or in the scattered field computation, and propose a high-order-accurate continuity-enforcing scheme for smooth surfaces as a remedy for the direct and indirect EFIEs, magnetic field integral equations (MFIEs), and regularized combined field integral equations (CFIEs) alike. The scheme comprises two ingredients: i) We show how to discretize the equations via a Chebyshev-based Nystr\"om scheme, which admits closed quadrature rules. ii) Since unknowns and test vectors are in terms of patch-local curvilinear bases, continuity is enforced by a change of basis: we construct sparse mapping matrices assembled solely from the curvilinear geometry description. In doing so, we restore the accuracy of the EFIE such that it can be combined with the MFIEs with equal weights to form CFIEs. Numerical studies for the scattering from canonical and realistic geometries show that all considered formulations individually and combined benefit from the continuity enforcement in terms of better conditioning, reduced iterations of an iterative solver, and several more digits of accuracy in the scattered fields, despite reducing the total number of unknowns.

math.NA↗

arXiv2026

Fast 3D Nanophotonic Inverse Design using Volume Integral Equations

Designing nanophotonic devices with minimal human intervention has gained substantial attention due to the complexity and precision required in modern optical technologies. While inverse design techniques typically rely on conventional electromagnetic solvers as forward models within optimization routines, the substantial electrical size and subwavelength characteristics of nanophotonic structures necessitate significantly accelerated simulation methods. In this work, we introduce a forward modeling approach based on the volume integral equation (VIE) formulation as an efficient alternative to traditional finite-difference (FD)-based methods. We derive the adjoint method tailored specifically for the VIE framework to efficiently compute optimization gradients and present a novel unidirectional mode excitation strategy compatible with VIE solvers. Comparative benchmarks demonstrate that our VIE-based approach provides multiple orders of magnitude improvement in computational efficiency over conventional FD methods in both time and frequency domains. To validate the practical utility of our approach, we successfully designed three representative nanophotonic components: a 3 dB power splitter, a dual-wavelength Bragg grating, and a selective mode reflector. Our results underscore the significant runtime advantages offered by the VIE-based framework, highlighting its promising role in accelerating inverse design workflows for next-generation nanophotonic devices.

physics.optics↗

arXiv2026

A Low-Dispersion Depressed Core Waveguide for Dielectric Waveguide Interconnects

Dielectric waveguide (DWG) interconnects frequently utilize multimode waveguides due to their low dispersion in the fundamental mode. However, these links are more vulnerable to cross-modal coupling that significantly impacts their overall performance. This study presents a technique aimed at minimizing the coupling of energy into higher-order modes within weakly coupled rectangular dielectric waveguides that are excited by a linear taper. The approach involves wrapping the waveguide with a material of a higher dielectric constant than both the core and the cladding of the waveguide. The added material significantly improves the modal confinement factor of the fundamental mode to the core, leading to a much smaller coupling to the parasitic higher-order cladding modes. The new waveguide with the additional material cladding is analyzed, and semi-analytical approximate expressions are derived to predict the mode profiles and cutoffs. Design equations are given to choose the thickness of the wrapping material. The waveguide is fabricated and compared against a similar cross-section waveguide without the additional wrapping material. Unlike the unwrapped waveguide, the group delay (GD) results of the proposed (wrapped) waveguide closely match the EM-simulated GD of the fundamental mode, confirming the significant isolation of higher-order modes. The measured GD of the proposed DWG is 50 ps/m, while the expected fundamental mode GD from EM simulations is 35 ps/m. On the contrary, the unwrapped DWG shows a measured GD of 200 ps/m with significant oscillations, while the expected fundamental mode GD from EM simulations is 25 ps/m, demonstrating that wrapping the waveguide significantly improves the GD by reducing the higher-order mode propagation.

physics.app-ph↗

arXiv2026

Quantization-aware Photonic Homodyne computing for Accelerated Artificial Intelligence and Scientific Simulation

Modern problems in high-performance computing, ranging from training and inferencing deep learning models in computer vision and language models to simulating complex physical systems with nonlinearly-coupled equations, require exponential growth of computational resources. Photonic analog systems are emerging with solutions of intrinsic parallelism, high bandwidth, and low propagation loss. However, their application has been hindered by the low analog accuracy due to the electro-optic distortion, material nonlinearities, and signal-to-noise ratios. Here we overcome this barrier with a quantization-aware digital-photonic mixed-precision framework across chiplets for accelerated AI processing and physical simulation. Using Lithium Niobate photonics with channel equalization techniques, we demonstrate linear multiplication (9-bit amplitude-phase decoupling) in homodyne optical logics with 6-bit precision at the clock rate of 128 giga-symbol-per-second (128 GS/s), enabling AI processing with 6 ns latency. Codesign hardware-algorithms, including iterative solvers, sparse-dense quantization, and bit-sliced matrix multiplication, explore photonic amplitude and phase coherence for complex-valued, physics-inspired computation. In electromagnetic problems, our approach yields 12-bit solutions for partial differential equations (PDEs) in scattering problems that would conventionally require up to 32-bit and often even 64-bit precision. These results preserve digital-level fidelity while leveraging the high-speed low-energy photonic hardware, establishing a pathway toward general-purpose optical acceleration for generative artificial intelligence, real-time robotics, and accurate simulation for climate challenges and biological discoveries.

cs.ET↗

arXiv2026

Fully Automated Adaptive Parameter Selection for 3-D High-order Nyström Boundary Integral Equation Methods

We present an adaptive Chebyshev-based Boundary Integral Equation (CBIE) solver for electromagnetic scattering from smooth perfect electric conductor (PEC) objects. The proposed approach eliminates manual parameter tuning by introducing (i) a unified adaptive quadrature strategy for automatic selection of the near-singular interaction distance and (ii) an adaptive computation of all self- and near-singular precomputation integrals to a prescribed accuracy using Gauss-Kronrod (h-adaptive) or Clenshaw-Curtis (p-adaptive) rules and singularity-resolving changes of variables. Both h-adaptive and p-adaptive schemes are explored within this framework, ensuring high-order accuracy and robustness across a broad range of geometries without loss of efficiency. Numerical results for canonical and complex CAD geometries demonstrate that the adaptive solver achieves accuracy and convergence rates comparable to optimally tuned fixed-grid CBIE implementations, while offering automation and scalability to electrically large, geometrically complex problems.

math.NA↗

arXiv2026

Near Real-time Full-wave Inverse Design of Electromagnetic Devices

Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic devices require computationally expensive and time-consuming full-wave electromagnetic simulation at each iteration or generation of large datasets for training neural-network surrogate models. This work introduces the Precomputed Numerical Green Function method, an approach for ultrafast electromagnetic inverse design. The static components of the design are incorporated into a numerical Green function obtained from a single fully-parallelized precomputation step, reducing the cost of evaluating candidate designs during optimization to only being proportional to the size of the region under modification. A low-rank matrix update technique is introduced that further decreases the cost of the method to milliseconds per iteration without any approximations or compromises in accuracy. This method is shown to have linear time complexity, reducing the total runtime for an inverse design by several orders of magnitude compared to using conventional electromagnetics solvers. The design examples considered demonstrate speedups of up to 16,000x, shortening the design process from multiple days to weeks down to minutes. The approach enables practical and ultrafast design of complex structures that are prohibitively time-consuming for prior inverse design methods.

physics.comp-ph↗

arXiv2025

High order-accurate solution of scattering integral equations with unbounded solutions at corners

Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth geometries--owing to field enhancement and singularities that arise at sharp edges and corners which, if left untreated, give rise to significant accuracy losses. The problem is particularly challenging in cases in which the "density" (i.e., the solution of the integral equation) tends to infinity at corners and edges--a difficulty that can be bypassed for 2D configurations, but which is unavoidable in 3D Maxwell integral formulations, wherein the component tangential to an edge of the electrical-current integral density vector tends to infinity at the edge. In order to tackle the problem this paper restricts attention to the simplest context in which the unbounded-density difficulty arises, namely, integral formulations in 2D space whose integral density blows up at corners; the strategies proposed, however, generalize directly to the 3D context. The novel methodologies presented in this paper yield high-order convergence for such challenging equations and achieve highly accurate solutions (even near edges and corners) without requiring a priori analysis of the geometry or use of singular bases.

math.NA↗

arXiv2024

H-Matrix Accelerated Direct Matrix Solver for Maxwell's Equations using the Chebyshev-based Nyström Boundary Integral Equation Method

An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performance of the CBIE proves to be fast for small to moderately sized problems compared to its counterparts, e.g. the locally corrected Nyström (LCN) method, due to the way it handles the singularities by means of a global change of variable method. However, in the case of electrically large scattering problems, the matrix fill and factorization still dominate the solution time when using a direct solution approach. To address this issue, an H-Matrix framework is employed, effectively resolving the challenge and establishing the CBIE as a competitive high-order method for solving scattering problems with poorly conditioned matrix equations. The efficacy of this approach is demonstrated through extensive numerical results, showcasing its robustness to problems that are electrically large, near physical resonances, or that have large dielectric permittivities. The capability of the proposed solver for handling arbitrary geometries is also demonstrated by considering various scattering examples from complex CAD models.

math.NA↗

arXiv2024

Accelerated 3D Maxwell Integral Equation Solver using the Interpolated Factored Green Function Method

This article presents an $O(N\log N)$ method for numerical solution of Maxwell's equations for dielectric scatterers using a 3D boundary integral equation (BIE) method. The underlying BIE method used is based on a hybrid Nyström-collocation method using Chebyshev polynomials. It is well known that such an approach produces a dense linear system, which requires $O(N^2)$ operations in each step of an iterative solver. In this work, we propose an approach using the recently introduced Interpolated Factored Green's Function (IFGF) acceleration strategy to reduce the cost of each iteration to $O(N\log N)$. To the best of our knowledge, this paper presents the first ever application of the IFGF method to fully-vectorial 3D Maxwell problems. The Chebyshev-based integral solver and IFGF method are first introduced, followed by the extension of the scalar IFGF to the vectorial Maxwell case. Several examples are presented verifying the $O(N\log N)$ computational complexity of the approach, including scattering from spheres, complex CAD models, and nanophotonic waveguiding devices. In one particular example with more than 6 million unknowns, the accelerated IFGF solver runs 42x faster than the unaccelerated method.

math.NA↗

arXiv2024

A High-order Nyström-based Scheme Explicitly Enforcing Surface Density Continuity for the Electric Field Integral Equation

This paper introduces an efficient approach for solving the Electric Field Integral Equation (EFIE) with high-order accuracy by explicitly enforcing the continuity of the impressed current densities across boundaries of the surface patch discretization. The integral operator involved is discretized via a Nyström-collocation approach based on Chebyshev polynomial expansion within each patch and a closed quadrature rule is utilized such that the discretization points inside one patch coincide with those inside another patch on the shared boundary of those two patches. The continuity enforcement is achieved by constructing a mapping from those coninciding points to a vector containing unique discretization points used in the GMRES iterative solver. The proposed approach is applied to the scattering of several different geometries including a sphere, a cube, a NURBS model imported from CAD software, and a dipole structure and results are compared with the Magnetic Field Integral Equation (MFIE) and the EFIE without enforcing continuity to illustrate the effectiveness of the approach.

math.NA↗

arXiv2022

A High-Order-Accurate 3D Surface Integral Equation Solver for Uniaxial Anisotropic Media

This paper introduces a high-order accurate surface integral equation method for solving 3D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-Müller formulation is leveraged resulting in a second-kind integral formulation, and a finite-difference-based approach is used to deal with the strongly singular terms resulting from the dyadic Green's functions for uniaxially anisotropic media while maintaining the high-order accuracy of the discretization strategy. The integral operators are discretized via a Nyström-collocation approach, which represents the unknown surface densities in terms of Chebyshev polynomials on curvilinear quadrilateral surface patches. The convergence is investigated for various geometries, including a sphere, cube, a complicated NURBS geometry imported from a 3D CAD modeler software, and a nanophotonic silicon waveguide, and results are compared against a commercial finite element solver. To the best of our knowledge, this is the first demonstration of high-order accuracy for objects with uniaxially anisotropic materials using surface integral equations.

physics.comp-ph↗

arXiv2021

A boundary integral method for 3D nonuniform dielectric waveguide problems via the windowed Green function

This paper proposes an efficient boundary-integral based "windowed Green function" methodology (WGF) for the numerical solution of three-dimensional electromagnetic problems containing dielectric waveguides. The approach, which generalizes a two-dimensional version of the method introduced recently, provides a highly effective solver for general electromagnetic problems containing waveguides. In particular, using an auxiliary integral representation, the proposed method is able to accurately model incident mode excitation. On the basis of a smooth window function, the integral operators along the infinite waveguide boundaries are smoothly truncated, resulting in errors that decay faster than any negative power of the window size.

math.NA↗

arXiv2021

A Chebyshev-based High-order-accurate Integral Equation Solver for Maxwell's Equations

This paper introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nyström-collocation method using Chebyshev polynomials to expand the unknown current densities over curvilinear quadrilateral surface patches. As an example, the proposed strategy is applied the to Magnetic Field Integral Equation (MFIE) and the N-Müller formulation for scattering from metallic and dielectric objects, respectively. The convergence is studied for several different geometries, including spheres, cubes, and complex NURBS geometries imported from CAD software, and the results are compared against a commercial Method-of-Moments solver using RWG basis functions.

physics.comp-ph↗

arXiv2020

Nonlinear nanophotonic devices in the Ultraviolet to Visible wavelength range

Although the first lasers invented operated in the visible, the first on-chip devices were optimized for near-infrared (IR) performance driven by demand in telecommunications. However, as the applications of integrated photonics has broadened, the wavelength demand has as well, and we are now returning to the visible (Vis) and pushing into the ultraviolet (UV). This shift has required innovations in device design and in materials as well as leveraging nonlinear behavior to reach these wavelengths. This review discusses the key nonlinear phenomena that can be used as well as presents several emerging material systems and devices that have reached the UV-Vis wavelength range.

physics.optics↗

arXiv2019

Planewave density interpolation methods for the EFIE on simple and composite surfaces

This paper presents an extension of the recently introduced planewave density interpolation (PWDI) method to the electric field integral equation (EFIE) formulation of problems of scattering and radiation by perfect electric conducting (PEC) objects. Relying on Kirchhoff integral formula and local interpolation of surface current densities that regularize the kernel singularities, the PWDI method enables off- and on-surface EFIE operators to be re-expressed in terms of integrands that are globally bounded (or even more regular) over the whole domain of integration, regardless of the magnitude of the distance between target and source points. Surface integrals resulting from the application of the method-of-moments (MoM) using Rao-Wilton-Glisson (RWG) basis functions, can then be directly and easily evaluated by means of elementary quadrature rules irrespective of the singularity location. The proposed technique can be applied to simple and composite surfaces comprising two or more simply-connected overlapping components. The use of composite surfaces can significantly simplify the geometric treatment of complex structures, as the PWDI method enables the use of separate non-conformal meshes for the discretization of each of the surface components that make up the composite surface. A variety of examples, including multi-scale and intricate structures, demonstrate the effectiveness of the proposed methodology.

physics.comp-ph↗