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Constructing accurate, high dimensional molecular potential energy surfaces (PESs) for polyatomic molecules is challenging. Reproducing Kernel Hilbert space (RKHS) interpolation is an efficient way to construct such PESs. However, the…
Scattering by an isolated defect embedded in a dielectric medium of two dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely either on the Born approximation and…
A boundary integral formulation of electromagnetics that involves only the components of $\boldsymbol{E}$ and $\boldsymbol{H}$ is derived without the use of surface currents that appear in the classical PMCHWT formulation. The kernels of…
Accurate, global Potential Energy Surfaces (PES) expressed in sum-of-products (SOP) form are a prerequisite for efficient high-dimensional quantum dynamics simulations using the MCTDH method. This work introduces a methodology for…
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)…
We propose new electromagnetic surface waves at the interface formed by connecting a perfect electric conductor (PEC) and a perfect magnetic conductor (PMC) parallel plate waveguides containing materials with positive permittivities and…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
We analyze the well posedness of certain field-only boundary integral equations (BIE) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the…
The electromagnetic (EM) features of reconfigurable intelligent surfaces (RISs) fundamentally determine their operating principles and performance. Motivated by these considerations, we study a single-input single-output (SISO) system in…
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…
In this paper we present a new regularized electric flux volume integral equation (D-VIE) for modeling high-contrast conductive dielectric objects in a broad frequency range. This new formulation is particularly suitable for modeling…
A generalized dispersion equation is derived featuring coupled mode theory, parity-time symmetry, and leaky wave antennas of arbitrary periodic modulation. It can be specialized to each of these cases individually or can describe a…
Harnessing modern parallel computing resources to achieve complex multi-physics simulations is a daunting task. The Multiphysics Object Oriented Simulation Environment (MOOSE) aims to enable such development by providing simplified…
The design and optimization of Reconfigurable Intelligent Surfaces (RISs) are key challenges for future wireless communication systems. RISs are devices that can manipulate electromagnetic (EM) waves in a programmable way, thus enhancing…
Continuum solvation models are becoming increasingly relevant in condensed matter simulations, allowing to characterize materials interfaces in the presence of wet electrified environments at a reduced computational cost with respect to all…
The PMCHWT integral equation enables the modelling of scattering of time-harmonic fields by penetrable, piecewise homogeneous, systems. They have been generalised to include the modelling of composite systems that may contain junctions,…
Reconfigurable Intelligent Surface (RIS) modeling and optimization are a crucial steps in developing the next generation of wireless communications. To this aim, the availability of accurate electromagnetic (EM) models is of paramount…
The boundary element method (BEM) enables the efficient electromagnetic modelling of lossy conductors with a surface-based discretization. Existing BEM techniques for conductor modelling require either expensive dual basis functions or the…
Sparse autoencoders (SAEs) are used to analyze embeddings, but their role and practical value are debated. We propose a new perspective on SAEs by demonstrating that they can be naturally understood as topic models. We propose a continuous…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…