The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations

We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.

Schrodinger-Poisson equations without Ambrosetti-Rabinowitz condition

We prove the existence of ground state solutions for a stationary Schrodinger-Poisson equation in R(3). The proof is based on the mountain pass theorem and it does not require the Ambrosetti-Rabinowitz condition. (C) 2010 Elsevier Inc. All rights reserved.

A FEM approach to the equations of magneto-aerodynamics

In this work, a Finite Element Method treatment is outlined for the equations of Magnetoaerodynamics. In order to provide a good basis for numerical treatment of Magneto-aerodynamics, a full version of the complete equations is presented and FEM contribution matrices are deduced, as well as further terms of stabilization for the compressible flow case.

A Simple maxwell Based Model in Order to Represent the frequency-dependent viscosity measured by ultrasound

A previous work showed that viscosity values measured high frequency by ultrasound agreed with the values at low frequency by the rotational viscometer when conditions are met, such as relatively low frequency viscosity. However, these conditions strongly reduce the range of the measurement cell. In order to obtain a measurement range and sensitivity high frequency must used, but it causes a frequency-dependent decrease on the viscosity values. This work introduces a new simple in order to represent this frequency-dependent behavior.model is based on the Maxwell model for viscoelastic , but using a variable parameter. This parameter has physical meaning because it represents the linear behavior the apparent elasticity measured along with the viscosity by .Automotive oils SAE 90 and SAE 250 at 22.5±0.5oC viscosities at low frequency of 0.6 and 6.7 Pa.s, respectively,tested in the range of 1-5 MHz. The model was used in to fit the obtained data using an algorithm of non-linear in Matlab. By including the viscosity at low frequency an unknown fitting parameter, it is possible to extrapolate its . Relative deviations between the values measured by the and extrapolated using the model for the SAE 90 and SAE 250 oils were 5.0% and 15.7%, respectively.©2008 IEEE.

Visualisierung vergrabener Objekte: Ein Sampling-Verfahren für die Maxwell-Gleichungen

Wir untersuchen die numerische Lösung des inversen Streuproblems der Rekonstruktion der Form, Position und Anzahl endlich vieler perfekt leitender Objekte durch Nahfeldmessungen zeitharmonischer elektromagnetischer Wellen mit Hilfe von Metalldetektoren. Wir nehmen an, dass sich die Objekte gänzlich im unteren Halbraum eines unbeschränkten zweischichtigen Hintergrundmediums befinden. Wir nehmen weiter an, dass der obere Halbraum mit Luft und der untere Halbraum mit Erde gefüllt ist. Wir betrachten zuerst die physikalischen Grundlagen elektromagnetischer Wellen, aus denen wir zunächst ein vereinfachtes mathematisches Modell ableiten, in welchem wir direkt das elektromagnetische Feld messen. Dieses Modell erweitern wir dann um die Messung des elektromagnetischen Feldes von Sendespulen mit Hilfe von Empfangsspulen. Für das vereinfachte Modell entwickeln wir, unter Verwendung der Theorie des zugehörigen direkten Streuproblems, ein nichtiteratives Verfahren, das auf der Idee der sogenannten Faktorisierungsmethode beruht. Dieses Verfahren übertragen wir dann auf das erweiterte Modell. Wir geben einen Implementierungsvorschlag der Rekonstruktionsmethode und demonstrieren an einer Reihe numerischer Experimente die Anwendbarkeit des Verfahrens. Weiterhin untersuchen wir mehrere Abwandlungen der Methode zur Verbesserung der Rekonstruktionen und zur Verringerung der Rechenzeit.

Stability of higher dimensional Reissner-Nordstrom-anti-de Sitter black holes

We investigate stability of the D-dimensional Reissner-Nordstrom-anti-de Sitter metrics as solutions of the Einstein-Maxwell equations. We have shown that asymptotically anti-de Sitter (AdS) black holes are dynamically stable for all values of charge and anti-de Sitter radius in D=5,6...11 dimensional space-times. This does not contradict dynamical instability of RNAdS black holes found by Gubser in N=8 gauged supergravity, because the latter instability comes from the tachyon mode of the scalar field, coupled to the system. Asymptotically AdS black holes are known to be thermodynamically unstable for some region of parameters, yet, as we have shown here, they are stable against gravitational perturbations.

SAR calculation using FDTD simulations

The main intend of this work, is to determinate the Specific Absorption Rate (SAR) on human head tissues exposed to radiation caused by sources of 900 and 1800MHz, since those are the typical frequencies for mobile communications systems nowadays. In order to determinate the SAR, has been used the FDTD (Finite Difference Time Domain), which is a numeric method in time domain, obtained from the Maxwell equations in differential mode. In order to do this, a computational model from the human head in two dimensions made with cells of the smallest possible size was implemented, respecting the limits from computational processing. It was possible to verify the very good efficiency of the FDTD method in the resolution of those types of problems.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Application of fractional order concepts in the study of electrical potential

The Maxwell equations, expressing the fundamental laws of electricity and magnetism, only involve the integer-order calculus. However, several effects present in electromagnetism, motivated recently an analysis under the fractional calculus (FC) perspective. In fact, this mathematical concept allows a deeper insight into many phenomena that classical models overlook. On the other hand, genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. In this work we use FC and GA to implement the electrical potential of fractional order. The performance of the GA scheme and the convergence of the resulting approximations are analyzed.

Fractional order electromagnetics

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.