المؤلفون: Kosulnikov, S., Cuesta, F. S., Wang, X., Tretyakov, S. A.

المصدر: IEEE Transactions on Antennas and Propagation ; ISSN: 0018-926X, 1558-2221

مصطلحات موضوعية: Metasurfaces, Electromagnetic diffraction, Harmonic analysis, Millimeter wave propagation, Surface impedance, ddc:600, Technology, info:eu-repo/classification/ddc/600

الوصف: Active development is taking place in reconfigurable and static metasurfaces that control and optimize reflections. However, existing designs typically only optimize reflections from the metasurface panels, neglecting interference with reflections originating from supporting walls and nearby objects. In this study, we investigate how engineering the metasurface properties can modify the total scattering pattern, enabling the modification and optimization of reflections from significantly larger illuminated areas than the metasurface panel. To accomplish this, a general design approach is developed to create periodical metasurfaces with controlled reflection phase and amplitude for all propagating Floquet harmonics. By combining metasurface reflections with those from the surrounding walls, the total scattering can be manipulated. The study demonstrates how appropriately designed metasurfaces can modify reflections from surrounding walls, enhancing the functionalities of metasurfaces. These findings are intended to facilitate advancements in engineering and optimizing wave propagation channels, particularly for millimeter-wave communications.

وصف الملف: application/pdf

العلاقة: info:eu-repo/semantics/altIdentifier/issn/0018-926X; info:eu-repo/semantics/altIdentifier/issn/1558-2221; https://publikationen.bibliothek.kit.edu/1000168340Test; https://publikationen.bibliothek.kit.edu/1000168340/152263225Test; https://doi.org/10.5445/IR/1000168340Test

الإتاحة: https://doi.org/10.5445/IR/1000168340Test
https://doi.org/10.1109/TAP.2024.3355208Test
https://publikationen.bibliothek.kit.edu/1000168340Test
https://publikationen.bibliothek.kit.edu/1000168340/152263225Test

المؤلفون: Baumstark, Julian, Jahnke, Tobias

المصدر: ISSN: 2365-662X.

مصطلحات موضوعية: high-frequency wave propagation, nonlinear wave equation, Maxwell–Lorentz system, diffractive geometric optics, slowly varying envelope approximation, error bounds, ddc:510, Mathematics, info:eu-repo/classification/ddc/510

الوصف: High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter ε, which causes oscillations with wavelengths proportional to $\varepsilon$ in time and space. A prominent example is the Maxwell–Lorentz system, which is a well-established model for the propagation of light in nonlinear media. In diffractive optics, such problems have to be solved on long time intervals with length proportional to $1/\varepsilon$. Approximating the solution of such a problem numerically with a standard method is hopeless, because traditional methods require an extremely fine resolution in time and space, which entails unacceptable computational costs. A possible alternative is to replace the original problem by a new system of PDEs which is more suitable for numerical computations but still yields a sufficiently accurate approximation. Such models are often based on the slowly varying envelope approximation or generalizations thereof. Results in the literature state that the error of the slowly varying envelope approximation is of $\cal{O}(\varepsilon)$. In this work, however, we prove that the error is even proportional to $\varepsilon^2$, which is a substantial improvement, and which explains the error behavior observed in numerical experiments. For a higher-order generalization of the slowly varying envelope approximation we improve the error bound from $\cal{O}(\varepsilon^2)$ to $\cal{O}(\varepsilon^3)$. Both proofs are based on a careful analysis of the nonlinear interaction between oscillatory and non-oscillatory error terms, and on a priori bounds for certain “parts” of the approximations which are defined by suitable projections. As an important technical tool we use an advantageous transformation of the coefficient functions which appear in the approximations.

وصف الملف: application/pdf

العلاقة: CRC 1173 Preprint; info:eu-repo/semantics/altIdentifier/issn/2365-662X; https://publikationen.bibliothek.kit.edu/1000168785Test; https://publikationen.bibliothek.kit.edu/1000168785/152332476Test; https://doi.org/10.5445/IR/1000168785Test

الإتاحة: https://doi.org/10.5445/IR/1000168785Test
https://publikationen.bibliothek.kit.edu/1000168785Test
https://publikationen.bibliothek.kit.edu/1000168785/152332476Test

المؤلفون: Baumgarten, Niklas, Krumscheid, Sebastian, Wieners, Christian

المصدر: ISSN: 2365-662X.

مصطلحات موضوعية: Uncertainty quantification, high performance computing, multi-level Monte Carlo method, Knapsack problem, dynamic programming, parallelization, wave propagation, ddc:510, Mathematics, info:eu-repo/classification/ddc/510

الوصف: We present a novel variant of the multi-level Monte Carlo method that effectively utilizes a reserved computational budget on a high-performance computing system to minimize the mean squared error. Our approach combines concepts of the continuation multi-level Monte Carlo method with dynamic programming techniques following Bellman’s optimality principle, and a new parallelization strategy based on a single distributed data structure. Additionally, we establish a theoretical bound on the error reduction on a parallel computing cluster and provide empirical evidence that the proposed method adheres to this bound. We implement, test, and benchmark the approach on computationally demanding problems, focusing on its application to acoustic wave propagation in high-dimensional random media.

وصف الملف: application/pdf

العلاقة: CRC 1173 Preprint; info:eu-repo/semantics/altIdentifier/issn/2365-662X; https://publikationen.bibliothek.kit.edu/1000161083Test; https://publikationen.bibliothek.kit.edu/1000161083/151086936Test; https://doi.org/10.5445/IR/1000161083Test

الإتاحة: https://doi.org/10.5445/IR/1000161083Test
https://publikationen.bibliothek.kit.edu/1000161083Test
https://publikationen.bibliothek.kit.edu/1000161083/151086936Test

المؤلفون: Baumstark, Julian, Jahnke, Tobias, Lubich, Christian

المصدر: ISSN: 2365-662X.

مصطلحات موضوعية: semilinear high-frequency wave propagation, modulated Fourier expansions, nonlinear polarization, error analysis, ddc:510, Mathematics, info:eu-repo/classification/ddc/510

الوصف: This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein–Gordon equations and the Maxwell–Lorentz system. The interest here is in solutions that are polarized in the sense that up to a small error, the oscillations in the solution depend on only one of the frequencies that satisfy the dispersion relation with a given wave vector appearing in the initial wave packet. The construction and analysis of such polarized solutions is done using modulated Fourier expansions. This approach includes higher harmonics and yields approximations to polarized solutions that are of arbitrary order in the small parameter, going well beyond the known first-order approximation via a nonlinear Schrödinger equation. The given construction of polarized solutions is explicit, uses in addition a linear Schrödinger equation for each further order of approximation, and is accessible to direct numerical approximation.

وصف الملف: application/pdf

العلاقة: CRC 1173 Preprint; info:eu-repo/semantics/altIdentifier/issn/2365-662X; https://publikationen.bibliothek.kit.edu/1000148063Test; https://publikationen.bibliothek.kit.edu/1000148063/148943754Test; https://doi.org/10.5445/IR/1000148063Test

الإتاحة: https://doi.org/10.5445/IR/1000148063Test
https://publikationen.bibliothek.kit.edu/1000148063Test
https://publikationen.bibliothek.kit.edu/1000148063/148943754Test

المؤلفون: Baumstark, Julian, Jahnke, Tobias

المصدر: ISSN: 2365-662X.

مصطلحات موضوعية: high-frequency wave propagation, semilinear wave equation, Maxwell–Lorentz system, diffractive geometric optics, slowly varying envelope approximation, error bounds, ddc:510, Mathematics, info:eu-repo/classification/ddc/510

الوصف: We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, and typical solutions oscillate with frequency proportional to $1/\varepsilon$ in time and space. Moreover, solutions have to be computed on time intervals of length $1/\varepsilon$ in order to study nonlinear and diffractive effects. As a consequence, direct numerical simulations are extremely costly or even impossible. We propose an analytical approximation and prove that it approximates the exact solution up to an error of $\mathcal{O}(\varepsilon^2)$ on time intervals of length $1/\varepsilon$. This is a significant improvement over the classical nonlinear Schrödinger approximation, which only yields an accuracy of $\mathcal{O}(\varepsilon)$.

وصف الملف: application/pdf

العلاقة: CRC 1173 Preprint; info:eu-repo/semantics/altIdentifier/issn/2365-662X; https://publikationen.bibliothek.kit.edu/1000142639Test; https://publikationen.bibliothek.kit.edu/1000142639/143847655Test; https://doi.org/10.5445/IR/1000142639Test

الإتاحة: https://doi.org/10.5445/IR/1000142639Test
https://publikationen.bibliothek.kit.edu/1000142639Test
https://publikationen.bibliothek.kit.edu/1000142639/143847655Test

المؤلفون: Müller, Marvin M., Maier, Bernhard, Rockstuhl, Carsten, Hochbruck, Marlis

المصدر: ISSN: 2365-662X.

مصطلحات موضوعية: SQUIDs, photonic structures, metamaterials, electromagnetic wave propagation, transparent boundary conditions, time integration, ddc:530, Physics, info:eu-repo/classification/ddc/530

الوصف: We derive a model to describe the interaction of an rf-SQUID (radio frequency Superconducting QUantum Interference Device) based metasurface with free space electromagnetic waves. The electromagnetic fields are described on the base of Maxwell’s equations. For the rf-SQUID metasurface we rely on an equivalent circuit model. After a detailed derivation, we show that the problem that is described by a system of coupled differential equations is wellposed and, therefore, has a unique solution. In the small amplitude limit, we provide analytical expressions for reflection, transmission, and absorption depending on the frequency. To investigate the nonlinear regime, we numerically solve the system of coupled differential equations using a finite element scheme with transparent boundary conditions and the Crank-Nicolson method. We also provide a rigorous error analysis that shows convergence of the scheme at the expected rates. The simulation results for the adiabatic increase of either the field’s amplitude or its frequency show that the metasurface’s response in the nonlinear interaction regime exhibits bistable behavior both in transmission and reflection.

وصف الملف: application/pdf

العلاقة: CRC1173; info:eu-repo/semantics/altIdentifier/issn/2365-662X; https://publikationen.bibliothek.kit.edu/1000088565Test; https://publikationen.bibliothek.kit.edu/1000088565/20721232Test; https://doi.org/10.5445/IR/1000088565Test; http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-885654Test

الإتاحة: https://doi.org/10.5445/IR/1000088565Test
https://publikationen.bibliothek.kit.edu/1000088565Test
https://publikationen.bibliothek.kit.edu/1000088565/20721232Test
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-885654Test

المؤلفون: Baumstark, Julian

المساهمون: Jahnke, Tobias, Hochbruck, Marlis

مصطلحات موضوعية: High-frequency wave propagation, semilinear wave equation, Maxwell–Lorentz, system, Klein--Gordon system, diffractive geometric optics, slowly varying envelope approximation, error analysis, time integration, modulated Fourier expansion, ddc:510, Mathematics, info:eu-repo/classification/ddc/510

الوصف: In this thesis we investigate a specific type of semilinear hyperbolic systems with highly oscillatory initial data. This type of systems is numerically very challenging to treat since the solutions are highly oscillatory in space and time. The goal is to derive suitable analytical and numerical approximations. Based on the classical slowly varying envelope approximation (SVEA), an improved error estimate is proven for this analytical approximation. The envelope equation avoids oscillations in space, making this approximation attractive for numerical computations. Furthermore, more accurate analytical approximations are obtained by extending the ansatz of the SVEA. In addition to the analytical study of the SVEA two numerical time integrators are constructed and analyzed without any step-size restrictions. Numerical examples are provided to illustrate the theoretical results. Finally, a complementary approach is presented which address both problems, the oscillations in space and time, simultaneously.

وصف الملف: application/pdf

العلاقة: https://publikationen.bibliothek.kit.edu/1000149719Test; https://publikationen.bibliothek.kit.edu/1000149719/149204683Test; https://doi.org/10.5445/IR/1000149719Test

الإتاحة: https://doi.org/10.5445/IR/1000149719Test
https://publikationen.bibliothek.kit.edu/1000149719Test
https://publikationen.bibliothek.kit.edu/1000149719/149204683Test

المؤلفون: Kirsch, Andreas, Lechleiter, Armin

المصدر: ISSN: 2365-662X.

مصطلحات موضوعية: wave propagation, closed waveguide, radiation condition, periodic structure, limiting absorption principle, ddc:510, Mathematics, info:eu-repo/classification/ddc/510

الوصف: In this paper we consider the propagation of waves in a closed full- or half-waveguide where the index of refraction is periodic along the axis of the waveguide. Motivated by the limiting absorption principle, proven in the Appendix by a functional analytic perturbation theorem, we formulate a radiation condition which assures uniqueness of a solution and allows the existence of propagating modes. Our approach is quite different to the known one as, e.g., considered in [6] and allows an extension to open wave guides (see [10]). After application of the Floquet-Bloch transform we consider the Floquet-Bloch variable α as a parameter in the resulting quasi-periodic boundary value problem and study the behaviour of the solution when α tends to an exceptional value by a singular perturbation result which we have found in [4].

وصف الملف: application/pdf

العلاقة: CRC 1173; info:eu-repo/semantics/altIdentifier/issn/2365-662X; https://publikationen.bibliothek.kit.edu/1000071358Test; https://publikationen.bibliothek.kit.edu/1000071358/4218313Test; https://doi.org/10.5445/IR/1000071358Test; http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-713587Test

الإتاحة: https://doi.org/10.5445/IR/1000071358Test
https://publikationen.bibliothek.kit.edu/1000071358Test
https://publikationen.bibliothek.kit.edu/1000071358/4218313Test
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-713587Test

المؤلفون: Grote, Marcus J., Mehlin, Michaela, Sauter, Stefan A.

المصدر: ISSN: 2365-662X.

مصطلحات موضوعية: wave propagation, finite element methods, explicit time integration, leap-frog method, error analysis, convergence theory, ddc:510, Mathematics, info:eu-repo/classification/ddc/510

الوصف: Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any explicit time-marching method. In [18] a leap-frog (LF) based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time-steps in the locally refined region and larger steps elsewhere. Here optimal convergence rates are rigorously proved for the fully-discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities.

وصف الملف: application/pdf

العلاقة: CRC 1173; info:eu-repo/semantics/altIdentifier/issn/2365-662X; https://publikationen.bibliothek.kit.edu/1000075943Test; https://publikationen.bibliothek.kit.edu/1000075943/4499417Test; https://doi.org/10.5445/IR/1000075943Test; http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-759433Test

الإتاحة: https://doi.org/10.5445/IR/1000075943Test
https://publikationen.bibliothek.kit.edu/1000075943Test
https://publikationen.bibliothek.kit.edu/1000075943/4499417Test
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-759433Test

المؤلفون: Burgert, Jens

المساهمون: Seemann, W.

المصدر: ISSN: 1614-3914.

مصطلحات موضوعية: Stoßkraft, Charakteristische Impedanz, Wellenausbreitung in elastischen Stäben, Inverser rekursiver Algorithmus, Impact force, Characteristic impedance, Wave propagation in non-uniform elastic rods, Inverse recursive algorithm, ddc:620, Engineering & allied operations, info:eu-repo/classification/ddc/620

الوصف: The impact of two non-uniform elastic rods is considered and a recursive method was developed that solves the inverse problem: Find the location-dependent impedance function of the impacting rod that generates a prescribed impact force. The developed method delivers exact solutions in closed-form. Moreover, a condition is derived which states if a physically meaningful solution exists. Finally, the underlying 1D model has been validated experimentally.

وصف الملف: application/pdf

العلاقة: Schriftenreihe des Instituts für Technische Mechanik, Karlsruher Institut für Technologie; info:eu-repo/semantics/altIdentifier/isbn/978-3-7315-1087-1; info:eu-repo/semantics/altIdentifier/issn/1614-3914; https://publikationen.bibliothek.kit.edu/1000129237Test; https://publikationen.bibliothek.kit.edu/1000129237/111688309Test; https://doi.org/10.5445/KSP/1000129237Test

الإتاحة: https://doi.org/10.5445/KSP/1000129237Test
https://publikationen.bibliothek.kit.edu/1000129237Test
https://publikationen.bibliothek.kit.edu/1000129237/111688309Test