Browsing by Author "Monk, Peter B."
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Item Accurate Discretisation of a Nonlinear Micromagnetic Problem(Department of Mathematical Sciences, 2000) Monk, Peter B.; Vacus, O.In this paper we propose a finite element discretization of the Maxwell-Landau-Lifchitz-Gilbert equations governing the electromagnetic field in a ferromagnetic material. Our point of view is that it is desirable for the discrete problem to possess conservation properties similar to the continuous system. We first prove the existence of a new class of Liapunov functions for the continuous problem, and then for a variational formulation of the continuous problem. We also show a special continuous dependence result. Then we propose a family of mass-lumped finite element schemes for the problem. For the resulting semi-discrete problem we show that magnetization is conserved and that semi-discrete Liapunov functions exist. Finally we show the results of some computations that show the behavior of the fully discrete Liapunov functions.Item Bifacial flexible CIGS thin-film solar cells with nonlinearly graded-bandgap photon-absorbing layers(JPhys Energy, 2024-03-06) Ahmad, Faiz; Monk, Peter B.; Lakhtakia, AkhleshThe building sector accounts for 36% of energy consumption and 39% of energy-related greenhouse-gas emissions. Integrating bifacial photovoltaic solar cells in buildings could significantly reduce energy consumption and related greenhouse gas emissions. Bifacial solar cells should be flexible, bifacially balanced for electricity production, and perform reasonably well under weak-light conditions. Using rigorous optoelectronic simulation software and the differential evolution algorithm, we optimized symmetric/asymmetric bifacial CIGS solar cells with either (i) homogeneous or (ii) graded-bandgap photon-absorbing layers and a flexible central contact layer of aluminum-doped zinc oxide to harvest light outdoors as well as indoors. Indoor light was modeled as a fraction of the standard sunlight. Also, we computed the weak-light responses of the CIGS solar cells using LED illumination of different light intensities. The optimal bifacial CIGS solar cell with graded-bandgap photon-absorbing layers is predicted to perform with 18%–29% efficiency under 0.01–1.0-Sun illumination; furthermore, efficiencies of 26.08% and 28.30% under weak LED light illumination of 0.0964 mW cm−2 and 0.22 mW cm−2 intensities, respectively, are predicted.Item Buffer layer between a planar optical concentrator and a solar cell(American Institute of Physics, 2015-09-15) Solano, Manuel E.; Barber, Greg D.; Lakhtakia, Akhlesh; Faryad, Muhammad; Monk, Peter B.; Mallouk, Thomas E.; Manuel E. Solano, Greg D. Barber, Akhlesh Lakhtakia, Muhammad Faryad, Peter B. Monk and Thomas E. Mallouk; Monk, Peter B.The effect of inserting a buffer layer between a periodically multilayered isotropic dielectric (PMLID) material acting as a planar optical concentrator and a photovoltaic solar cell was theoretically investigated. The substitution of the photovoltaic material by a cheaper dielectric material in a large area of the structure could reduce the fabrication costs without significantly reducing the efficiency of the solar cell. Both crystalline silicon (c-Si) and gallium arsenide (GaAs) were considered as the photovoltaic material. We found that the buffer layer can act as an antireflection coating at the interface of the PMLID and the photovoltaic materials, and the structure increases the spectrally averaged electron-hole pair density by 36% for c-Si and 38% for GaAs compared to the structure without buffer layer. Numerical evidence indicates that the optimal structure is robust with respect to small changes in the grating profile.Item The Direct and Inverse Scattering Problems for Partially Coated Obstacles(Department of Mathematical Sciences, 2002) Cakoni, Fioralba; Colton, David; Monk, Peter B.We consider the direct and inverse scattering problems for partially coated obstacles. To this end, we first use the method of integral equations of the first kind to solve a scattering problem for the Helmholtz equation where the scattered field satisfies mixed Dirichlet-impedance boundary conditions on the Lipschitz boundary of the scatterer D. We then use the linear sampling method to solve the inverse scattering problem of determining D from a knowledge of the far field pattern of the scattered field. Numerical examples are given showing the performance of the linear sampling method in this case.Item The Direct and Inverse Scattering Problems for Partially Coated Obstacles(Department of Mathematical Sciences, 2002) Monk, Peter B.The time harmonic Maxwell's equations for a lossless medium are neither elliptic or definite. Hence the analysis of numerical schemes for these equations presents some unusual difficulties. In this paper we give a simple proof, based on the use of duality, for the convergence of edge finite element methods applied to the cavity problem for Maxwell's equations. The cavity is assumed to be a general Lipschitz polyhedron, and the mesh is assumed to be regular but not quasi-uniform.Item Effects of defect density, minority carrier lifetime, doping density, and absorber-layer thickness in CIGS and CZTSSe thin-film solar cells(Journal of Photonics for Energy, 2023-06-02) Ahmad, Faiz; Civiletti, Benjamin J.; Monk, Peter B.; Lakhtakia, AkhleshDetailed optoelectronic simulations of thin-film photovoltaic solar cells (PVSCs) with a homogeneous photon-absorber layer made of with CIGS or CZTSSe were carried out to determine the effects of defect density, minority carrier lifetime, doping density, composition (i.e., bandgap energy), and absorber-layer thickness on solar-cell performance. The transfer-matrix method was used to calculate the electron-hole-pair (EHP) generation rate, and a one-dimensional drift-diffusion model was used to determine the EHP recombination rate, open-circuit voltage, short-circuit current density, power-conversion efficiency, and fill factor. Through a comparison of limited experimental data and simulation results, we formulated expressions for the defect density in terms of the composition parameter of either CIGS or CZTSSe. All performance parameters of the thin-films PVSCs were thereby shown to be obtainable from the bulk material-response parameters of the semiconductor, with the influence of surface defects being small enough to be ignored. Furthermore, unrealistic values of the defect density (equivalently, minority carrier lifetime) will deliver unreliable predictions of the solar-cell performance. The derived expressions should guide fellow researchers in simulating the graded-bandgap and quantum-well-based PVSCs.Item Error Analysis of a Finite Element-Integral Equation Scheme for Approximating the Time-Harmonic Maxwell System(Department of Mathematical Sciences, 2002) Hsiao, George C.; Monk, Peter B.; Nigam, N.In 1996 Hazard and Lenoir suggested a variational formulation of Maxwell's equations using an overlapping integral equation and volume representation of the solution. They suggested a numerical scheme based on this approach, but no error analysis was provided. In this paper, we provide a convergence analysis of an edge finite element scheme for the method. The analysis uses the theory of collectively compact operators. It's novelty is that a perturbation argument is needed to obtain error estimates for the solution of the discrete problem that is best suited for implementation.Item Finite Element Method for Approximating Electro-Magnetic Scattering from a Conducting Object(Department of Mathematical Sciences, 2000) Kirsch, A.; Monk, Peter B.We provide an error analysis of a fully discrete finite element – Fourier series method for approximating Maxwell’s equations. The problem is to approximate the electromagnetic field scattered by a bounded, inhomogeneous and anisotropic body. The method is to truncate the domain of the calculation using a series solution of the field away from this domain. We first prove a decomposition for the Poincare-Steklov operator on this boundary into an isomorphism and a compact perturbation. This is proved using a novel argument in which the scattering problem is viewed as a perturbation of the free space problem. Using this decomposition, and edge elements to discretize the interior problem, we prove an optimal error estimate for the overall problem.Item Inverse Electromagnetic Scattering Problem for a Partially Coated Dielectric(Department of Mathematical Sciences, 2004) Cakoni, Fioralba; Colton, David; Monk, Peter B.We use the linear sampling method to determine the shape and surface conductivity of a partially coated dielectric from a knowledge of the far field pattern of the scattered electromagnetic wave at fixed frequency. A mathematical justification of the method is provided for both the scalar and vector case based on the use of a complete family of solutions. Numerical examples are given for the scalar case.Item Recent Developments in Inverse Acoustic Scattering Theory(Department of Mathematical Sciences, 2000) Colton, David; Coyle, J.; Monk, Peter B.We survey some of the highlights of inverse scattering theory as it has developed over the past fifteen years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves. Included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects.Item Scattering of Time-Harmonic Electromagnetic Waves by Anisotropic Inhomongeneous Scatters or Impenetrable Obstacles(Department of Mathematical Sciences, 2000) Monk, Peter B.; Coyle, J.We investigate an overlapping solution technique to compute the scattering of time-harmonic electromagnetic waves in two dimensions. The technique can be used to compute waves scattered by penetrable anisotropic inhomogeneous scatterers or impenetrable obstacles. The major focus is on implementing the method using finite elements. We prove existence of a unique solution to the disctretized problem and derive an optimal convergence rate for the scheme, which is verified numerical by examples.Item Stabilized interior penalty methods for the time-harmonic Maxwell equations(Department of Mathematical Sciences, 2002) Perugia, I.; Schötzau, D.; Monk, Peter B.We propose stabilized interior penalty discontinuous Galerkin methods for the indefinite time–harmonic Maxwell system. The methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field. We prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach.