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We present impedance boundary conditions for the viscoacoustic equations for approximative models that are in terms of the acoustic pressure or in terms of the macroscropic acoustic velocity. The approximative models are derived by the method of multiple scales up to order 2 in the boundary layer thickness. The boundary conditions are stable and asymptotically exact, which is justified by a complete mathematical analysis. The models can be discretized by finite element methods without resolving boundary layers. In difference to an approximation by asymptotic expansion for which for each order 1 PDE system has to be solved, the proposed approximative are solutions to one PDE system only. The impedance boundary conditions for the pressure of first and second orders are of Wentzell type and include a second tangential derivative of the pressure proportional to the square root of the viscosity and take thereby absorption inside the viscosity boundary layer of the underlying velocity into account. The conditions of second order incorporate with curvature the geometrical properties of the wall. The velocity approximations are described by Helmholtz‐like equations for the velocity, where the Laplace operator is replaced by ∇div, and the local boundary conditions relate the normal velocity component to its divergence. The velocity approximations are for the so‐called far field and do not exhibit a boundary layer. Including a boundary corrector, the so‐called near field, the velocity approximation is accurate even up to the domain boundary. The results of numerical experiments illustrate the theoretical foundations.

Contour integration methods are claimed to be the methods of choice for computing many (several hundred) eigenvalues of a nonlinear eigenvalue problem inside a closed region of the complex plane. Typically, contour integration methods are designed for circular (or more generally elliptic) shaped contours and rely on the exponential convergence of the trapezoidal rule applied to periodic functions. In this article, the curl–curl eigenvalue problem in a resonator coupled with a waveguide boundary in a way that allows outgoing waves along longitudinally homogeneous waveguide structures is considered. This problem has a square root dependence on the frequency, and thus, adapted integration contours are required to reliably find eigenvalues in the vicinity of branch cuts. The filter function-based analysis of the quadrature rules has been used and improved to reduce the problem to consider the behavior of filter functions on eigenvalues and singular points only. First, conformally mapped circular contours are considered for problems with one branch cut. For problems where there are several branch cuts necessary, the Gauß–Legendre quadrature rules on closed polygonal contours had been analyzed. In both cases, exponential convergence rates were obtained. The estimates are validated numerically using the example of the TESLA cavity.

PurposeMotivated by the acoustics of motor vehicles, a coupled fluid–solid system is considered. The air pressure is modeled by the Helmholtz equation, and the structure displacement is described by elastodynamic equations. The acoustic–structure interaction is modeled by coupling conditions on the common interface. First, the existence and uniqueness of solutions are investigated, and then, after recalling fundamental notions of shape optimization, the tensor form of the distributed shape derivative is obtained for the coupled problem. It is then applied to the minimization of the sound pressure by variation of the structure shape through the positioning of beads.Design/methodology/approachThe existence and uniqueness of solutions up to eigenfrequencies are shown by the Fredholm–Riesz–Schauder theory using a novel decomposition into an isomorphism and a compact operator. For the design optimization, the distributed shape derivative is obtained using the averaged adjoint method. It is then used in a closed 3D optimization process of the position of a bead for noise reduction. In this process, the C++ library concepts are used to solve the differential equations on hexahedral meshes with the finite element method of higher order.FindingsThe existence and uniqueness of solutions have been shown for the case without absorption, where the given proof allows for extension to the case with absorption in the domain or via boundary conditions. The theoretical results show that the averaged adjoint can be applied to compute distributed shape derivatives in the context of acoustic–structure interaction. The numerical results show that the distributed shape derivative can be used to reduce the sound pressure at a chosen frequency via rigid motions of a nonsmooth shape.Originality/valueThe proof of shape differentiability and the calculation of the distributed shape derivative in tensor form allows to consider nonsmooth shapes for the optimization, which is particularly relevant for the optimal placement of beads or stampings in a structural-acoustic system.

In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction condition is applied at all (inner) vertices. Using the two-scale convergence adapted to homogenization of lower-dimensional problems we obtain the limit homogenized problem defined on a two-dimensional domain that is occupied by the mesh when the mesh period δ tends to 0. The homogenized model is given by the classical heat equation with the conductivity tensor depending on the unit cell graph only through the topology of the graph and lengthes of its edges. We show the well-posedness of the limit problem and give a purely algebraic formula for the computation of the homogenized conductivity tensor. The analysis is completed by numerical experiments showing a convergence to the limit problem where the convergence order in δ depends on the unit cell pattern.

In the framework of the EU/ESA co-funded Copernicus program [RD-1] (formerly known as Global Monitoring for Environment and Security - GMES). ESA is developing and operating a series of Sentinel missions with the objective to provide routinely Earth Observation data for supporting the implementation of operational Copernicus services and for existing or future national service initiatives.

Radiometric calibration adjusts the measured pixel intensity to a physical property, the radar cross section (RCS). After calibration, this relationship is defined over the entire backscatter range: from low image power (near noise) up to high reflections (below saturation). Based on a proper radiometric calibration, the measured radar backscatter for the Sentinel-1 synthetic aperture radar (SAR) satellite constellation is validated over a wide backscatter range using different target types. Therefore, the RCS derived from point targets and radar brightness from distributed targets are compared between Sentinel-1A (S-1A) and Sentinel-1B (S-1B) acquisitions over the same observation area for regions where a stable target backscatter is expected for a certain period of time. Low differences (in the order of 0.3 dB) are found between S-1A and S-1B for high and medium backscatter derived from point targets or rainforest regions, but higher differences for low backscattering regions like ice areas and lakes. For comparing radar brightness containing low backscatter targets, an accurate derived noise level has to be taken into account. In addition to the measured lower noise equivalent beta zero (NEBZ) level, higher transmit power was detected for S-1B compared to S-1A. The higher antenna gain of S-1B leads finally to a higher sensitivity for low backscattering areas of S-1B compared to S-1A and explains the found differences.

We consider the efficient numerical solution of coupled dynamical systems, consisting of a low dimensional nonlinear part and a high dimensional linear time invariant part, e.g., stemming from spatial discretization of an underlying partial differential equation. The linear subsystem can be eliminated in frequency domain and for the numerical solution of the resulting integro-differential algebraic equations, we propose a combination of Runge–Kutta or multistep time stepping methods with appropriate convolution quadrature to handle the integral terms. The resulting methods are shown to be algebraically equivalent to a Runge–Kutta or multistep solution of the coupled system and thus automatically inherit the corresponding stability and accuracy properties. After a computationally expensive pre-processing step, the online simulation can, however, be performed at essentially the same cost as solving only the low dimensional nonlinear subsystem. The proposed method is, therefore, particularly attractive, if repeated simulation of the coupled dynamical system is required.

The present work deals with the resolution of the Poisson equation in a bounded domain made of a thin and periodic layer of finite length placed into a homogeneous medium. We provide and justify a high order asymptotic expansion which takes into account the boundary layer effect occurring in the vicinity of the periodic layer as well as the corner singularities appearing in the neighborhood of the extremities of the layer. Our approach combines the method of matched asymptotic expansions and the method of periodic surface homogenization.

We consider different acoustic models with viscosity in a semi-infinite waveguide with rigid walls, for which we propose and analyse absorbing boundary conditions on a truncated subdomain. The considered models are (i) the viscous acoustic equations in a stagnant mean flow, which exhibit for small viscosities boundary layers on the infinite walls, (ii) the limit equations for vanishing viscosity and (iii) a first-order approximation for low viscosity. The limit model (i) is well known as the Helmholtz equation for the pressure with homogeneous Neumann boundary conditions. For each of these models, the absorbing conditions appear as Dirichlet-to-Neumann (DtN) maps. The DtN boundary conditions for the singularly perturbed model (i) and the approximative model (iii) tend to the DtN boundary conditions of the limit problem (ii) if the viscosity approaches zero, and, hence, provide a uniform accuracy in the viscosity. The convergence of truncated DtN boundary conditions and the behaviour for viscosities tending to zero are shown in numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.

We propose equivalent transmission conditions of order 1 and 2 for thin and highly conducting sheets for the time-harmonic Maxwell's equation in three dimensions. The transmission conditions are derived asymptotically for vanishing sheet thickness $\varepsilon$ where the skin depth is kept proportional to $\varepsilon$. The condition of order 1 turns out to be the perfect electric conductor boundary condition. The conditions of order 2 appear as generalized Poincareź--Steklov maps between tangential components of the magnetic field and the electric field, and they are of Wentzell type involving second order surface differential operators. Numerical results with finite elements of higher order validate the asymptotic convergence for $\varepsilon\to0$ and the robustness of the equivalent transmission condition of order 2.

The TerraSAR-X mission, based on two satellites, has produced SAR data products of high quality for a number of scientific and commercial applications for more than ten years. To guarantee the stability and the reliability of these highly accurate SAR data products, both systems were first accurately calibrated during their respective commissioning phases and have been permanently monitored since then. Based on a short description of the methods applied, this paper focuses on the radiometric performance including the gain and phase properties of the transmit/receiver modules, the antenna pattern checked by evaluating scenes acquired over uniformly distributed targets and the radiometric stability derived from permanently deployed point targets. The outcome demonstrates the remarkable performance of both systems since their respective launch.

The geometric accuracy of synthetic aperture radar (SAR) data is usually derived from level-1 products using accurately surveyed corner reflector positions. This paper introduces a novel approach that derives the range delay and azimuth shift from acquired SAR raw data (level-0 products). Therefore, the propagation path is completely retrieved from SAR pulse transmission up to the reception of the point target’s backscatter. The procedure includes simple pulse compression in range and azimuth instead of full SAR data processing. By applying this method, the geometric accuracy of ESA’s Sentinel-1 SAR satellites (Sentinel-1A and Sentinel-1B) is derived for each satellite overpass by using corner reflectors with precisely surveyed GPS positions. The results show that the azimuth bias of about 2 m found in level-1 products for Stripmap acquisitions is reduced to about 15 cm. This indicates an artificial bias arising from operational Sentinel-1 SAR data processing. The remaining range bias of about 1.0 m, observed in L0-products, is interpreted as the offset between the SAR antenna phase center and the spacecraft’s center of gravity. The relative pixel localization accuracy derived with the proposed method is about 12 cm for the evaluated acquisitions. Compared to the full processed level-1 SAR data products, this accuracy is similar in the range direction, but, for the azimuth direction, it is improved by about 50% with the proposed method.

International audience; We introduce a novel method to compute approximations of integrals over implicitly defined hyper-surfaces. The new method is based on a weak formulation in L 2 (0, 1), that uses the coarea formula to circumvent an explicit integration over the hypersurfaces. As such it is possible to use standard quadrature rules in the spirit of hp/spectral finite element methods, and the expensive computation of explicit hypersurface parametrizations is avoided. We derive error estimates showing that high order convergence can be achieved provided the integrand and the hypersurface defining function are sufficiently smooth. The theoretical results are supplemented by numerical experiments including an application for plasma modeling in nuclear fusion.

Ocean circulation on the continental slope and Sao Paulo Plateau in the Campos Basin is governed by the so-called “Brazil Current System” which is formed by the Brazil Current (BC), the Intermediate Western Boundary Current (IWBC) and by the meanders and eddies associated with both flows. The water column of this current system is formed by a stacking of water masses, whose depths and interfaces vary due to the baroclinic adjustment of these flows. A multiparametric, physical and hydrochemical analysis of water masses, unprecedented in the Brazilian continental margin, was conducted to identify the composition of both, BC and IWBC. We found that BC carries Tropical Water and South Atlantic Central Water towards south-southwest, while IWBC carries essentially Antarctic Intermediate Water and Upper Circumpolar Deep Water (UCDW) towards the north-northeast. BC has a typical thickness of 450-500 m, whereas IWBC extends from the BC base to more than 1,150 m deep. Typical volume transport of BC is 6 Sv and of IWBC is 4 Sv. The core of BC’s speeds, whose instantaneous value may reach 1 m.s –1 , is always located on the surface. On the other hand, IWBC’s core is between 800 and 900 m and is apparently associated to the minimum salinity of the entire water column.

Highlights • Statistics of data quality parameters are used for KLDN performance evaluation. • Spatiotemporal distributions of lightning parameters are investigated for the evaluation of data quality. • Simulation of data uncertainty due to network geometry and topography is not significant compared with observation data. • The NFDF (Normalized Frequency Distribution Function) method is proposed to evaluate lightning detection performance

In this paper we present an efficient algorithm for the calculation of photonic crystal band structures and band structures of photonic crystal waveguides. Our method relies on the fact that the dispersion curves of the band structure are smooth functions of the quasi-momentum in the one-dimensional Brillouin zone. We show the derivation and computation of the group velocity, the group velocity dispersion, and any higher derivative of the dispersion curves. These derivatives are then employed in a Taylor expansion of the dispersion curves. We control the error of the Taylor expansion with the help of a residual estimate and introduce an adaptive scheme for the selection of nodes in the one-dimensional Brillouin zone at which we solve the underlying eigenvalue problem and compute the derivatives of the dispersion curves. These derivatives are then employed in a Taylor expansion of the dispersion curves. We control the error of the Taylor expansion with the help of a residual estimate and introduce an adaptive scheme for the selection of nodes in the one-dimensional Brillouin zone at which we solve the underlying eigenvalue problem and compute the derivatives of the dispersion curves. The proposed algorithm is not only advantageous as it decreases the computational effort to compute the band structure but also because it allows for the identification of crossings and anti-crossings of dispersion curves, respectively. This identification is not possible with the standard approach of solving the underlying eigenvalue problem at a discrete set of values of the quasi-momentum without taking the mode parity into account.

The computation of guided modes in photonic crystal wave-guides is a key issue in the process of designing devices in photonic communications. Existing methods, such as the super-cell method, provide an efficient computation of well-confined modes. However, if the modes are not well-confined, the modelling error of the super-cell method becomes prohibitive and advanced methods applying transparent boundary conditions for periodic media are needed. In this work we demonstrate the numerical realization of a recently proposed Dirichlet-to-Neumann approach and compare the results with those of the super-cell method. For the resulting non-linear eigenvalue problem we propose an iterative solution based on Newton's method and a direct solution using Chebyshev interpolation of the non-linear operator. Based on the Dirichlet-to-Neumann approach, we present a formula for the group velocity of guided modes that can serve as an objective function in the optimization of photonic crystal wave-guides.

Resolving thin conducting sheets for shielding or even skin layers inside by the mesh of numerical methods like the finite-element method can be avoided using impedance transmission conditions (ITCs). Those ITCs shall provide an accurate approximation for small sheet thicknesses d, where the accuracy is best possible independent of the conductivity or the frequency being small or large-this we will call robustness. We investigate the accuracy and robustness of popular and recently developed ITCs, and propose robust ITCs, which are accurate up to O(d2).

Shielding sheets are commonly used in the protection of electronic devices. With their large aspect ratios they become a serious issue for the direct application of BEMs due to the occurring almost singular integrals. Impedance transmission conditions (ITCs) allow for boundary element formulations where only sheet midline has to be triangulated. We propose and analyze BEMs of second kind for ITCs of two different types for the time-harmonic eddy-current problem in 2-D. In numerical experiments, we study the effect on the magnetic shielding efficiency of the discretization error due the boundary element discretization and the modeling error due to the impedance transmission condition.

In this paper, we present a complete algorithm for the exact computation of the guided mode band structure in photonic crystal (PhC) waveguides. In contrast to the supercell method, the used approach does not introduce any modeling error and is hence independent of the confinement of the modes. The approach is based on Dirichlet-to-Neumann transparent boundary conditions that yield a nonlinear eigenvalue problem. For the solution of this nonlinear eigenvalue problem, we present a direct technique using Chebyshev interpolation that requires a bandgap calculation of the PhC in advance. For this bandgap calculation, we introduce as a very efficient tool a Taylor expansion of the PhC band structure. We show that our algorithm-like the supercell method-converges exponentially, however, its computational costs-in comparison with the supercell method-only increase moderately since the size of the matrix to be inverted remains constant.

A synthetic aperture radar (SAR) system requires external absolute calibration so that radiometric measurements can be exploited in numerous scientific and commercial applications. Besides estimating a calibration factor, metrological standards also demand the derivation of a respective calibration uncertainty. This uncertainty is currently not systematically determined. Here for the first time it is proposed to use hierarchical modeling and Bayesian statistics as a consistent method for handling and analyzing the hierarchical data typically acquired during external calibration campaigns. Through the use of Markov chain Monte Carlo simulations, a joint posterior probability can be conveniently derived from measurement data despite the necessary grouping of data samples. The applicability of the method is demonstrated through a case study: The radar reflectivity of DLR’s new C-band Kalibri transponder is derived through a series of RADARSAT-2 acquisitions and a comparison with reference point targets (corner reflectors). The systematic derivation of calibration uncertainties is seen as an important step toward traceable radiometric calibration of synthetic aperture radars.

In this paper, we introduce a high order flnite element (FEM) implementation using perfectly matched layer (PML) for the scattering by plasmonic structures inside layered media. The PML is proven to be very accurate and e-cient by a comparative analysis with a commercial FEM software and the Multiple Multipole Program (MMP). A convergence analysis using hp-adaptive reflnement inside the PML layer shows that adaptive mesh reflnement inside the PML layer is most e-cient. Based on this convergence analysis an hp- strategy is proposed, which shows a remarkable error reduction for small additional computational costs.

We introduce tools for a unified analysis and a comparison of impedance transmission conditions (ITCs) for thin conducting sheets within the time-harmonic eddy current model in two dimensions. The first criterion is the robustness with respect to the frequency or skin depth, which means whether they give meaningful results for small and for large frequencies or conductivities. As a second tool we study the accuracy for a range of sheet thicknesses and frequencies for a relevant example and finally analyze their asymptotic order in different asymptotic regimes. For the latter we write all the ITCs in a common form and show how they can be realized within the finite element method. Two new conditions, which we call ITC-2-0 and ITC-2-1, are introduced in this article, which appear in a symmetric form. They are derived by asymptotic expansions in the asymptotic regime of constant ratio between skin depth and thickness like those in [K. Schmidt and A. Chernov, Technical report 1102, Institut for Numerical Simu...

Optical nano antennas are currently promising key elements for sensing and optical communication [1, 2]. They may resonate even when they are much smaller than the wavelength. However, this extraordinary behaviour makes the design and simulation very difficult. Traditional RF antennas are essentially scalable, which implies relatively simple design rules [3]. In contrast to this, plasmonic nano antennas are not scalable, thus it is very hard or even impossible to obtain simple design rules.

In the frame of the GMES program, the main objective of the Sentinel-1 mission is to ensure the continuity of SAR data acquisitions in C-band for global earth monitoring. Sentinel-1A is the first of two C-band satellites launched in April 2014. In addition to the commissioning of Sentienl-1A executed by ESA, an independent verification of the system calibration is executed for the first time by an external institution. For this purpose, the complete calibration chain was developed and established by DLR, starting with an efficient calibration concept, a detailed in-orbit calibration plan, the SW-tools for analyzing and evaluating all the measurements up to the calibration targets serving as accurate reference. Based on an efficient calibration strategy, this paper describes the different activities performed by DLR and presents first results obtained from real in-orbit data. As Sentinel-1A had not achieved the reference orbit at the time of uploading the full paper, a discussion of radiometric and geometric calibration results will be presented at the conference on July 2014.

In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the material coefficients or it is a wall modelled by boundary conditions with an periodic array of small perforations. We consider the periodicity in the layer as the small variable $\delta$ and the thickness of the layer to be at the same order. Moreover we assume the thin layer to terminate at re-entrant corners leading to a singular behaviour in the asymptotic expansion of the solution representation. This singular behaviour becomes visible in the asymptotic expansion in powers of $\delta$ where the powers depend on the opening angle. We construct the asymptotic expansion order by order. It consists of a macroscopic representation away from the layer, a boundary layer corrector in the vicinity of the layer, and a near field corrector in the vicinity of the end-points. The boundary layer correctors and the near field correctors are obtained by the solution of canonical problems based, respectively, on the method of periodic surface homogenization and on the method of matched asymptotic expansions. This will lead to transmission conditions for the macroscopic part of the solution on an infinitely thin interface and corner conditions to fix the unbounded singular behaviour at its end-points. Finally, theoretical justifications of the second order expansion are given and illustrated by numerical experiments. The solution representation introduced in this article can be used to compute a highly accurate approximation of the solution with a computational effort independent of the small periodicity $\delta$., Comment: arXiv admin note: text overlap with arXiv:1506.06964

The three-hour life-cycle of the isolated thunderstorm on 15 July 2007 during the Convective and Orographically-induced Precipitation Study (COPS) is documented in detail, with a special emphasis on the rapid development and mature phases. Remote sensing techniques as 5-min rapid scans from geostationary satellites, combined velocity retrievals from up to four Doppler-radars, the polarimetric determination of hydrometeors and spatio-temporal occurrences of lightning strokes are employed to arrive at a quantification of the physical parameters of this, during the COPS period, singular event. Inner cloud flow fields are available from radar multiple Doppler analyses at four consecutive times separated by 15 min-intervals. They contain horizontal winds of around 15 m s−1 and updrafts exceeding 5 m s−1, the latter collocated with lightning strokes. Reflectivity and polarimetric data indicate the existence of hail at the 2 km level around 14:40. Furthermore, polarimetric and Doppler radar variables indicate intense hydrometeor variability and turbulence corresponding to an enhanced variance of the retrieved 3-D wind fields. Profiles of flow and hydrometeor statistics over the entire cloud volume provide reference data for high-resolution numerical weather prediction runs in research mode. The study embarks from two movie-loops of geostationary satellite imagery (as Supplement), which provide an intuitive distinction of six phases making up the entire life-cycle of the thunderstorm. It concludes with a triple-image loop, juxtaposing a close-up of the cloud motion as seen by Meteosat, simulated brightness temperature (as a proxy for clouds seen by the infrared satellite channel), and a perspective view on the model generated system of cloud cells. The simulation suggests that several updrafts fed from a low level convergence line eventually removed the convective inhibition and set deep convection in motion. A shear line in the radial velocity relative to the Feldberg radar site shows good agreement beween observation and simulation, whereas the onset location of deep convection exhibits a horizontal discrepancy of 15 km. A quantitative schematic of the isolated thunderstorm synthesizes all retrieved characteristics.

In this paper a high-order finite element method with curvilinear elements is proposed for the simulation of plasmonic structures. Most finite element packages use low order basis functions and non ...

During the "African Monsoon Multidisciplinary Analysis" (AMMA) field phase in August 2006, a variety of measurements focusing on deep convection were performed over West Africa. The German research aircraft Falcon based in Ouagadougou (Burkina Faso) investigated the chemical composition in the outflow of large mesoscale convective systems (MCS). Here we analyse two different types of MCS originating north and south of the intertropical convergence zone (ITCZ, ~10° N), respectively. In addition to the airborne trace gas measurements, stroke measurements from the Lightning Location Network (LINET), set up in Northern Benin, are analysed. The main focus of the present study is 1) to analyse the trace gas composition (CO, O3, NO, NOx, NOy, and HCHO) in the convective outflow as a function of distance from the convective core, 2) to investigate how different trace gas compositions in the boundary layer (BL) and ambient air may influence the O3 concentration in the convective outflow, and 3) to estimate the rate of lightning-produced nitrogen oxides per flash in selected thunderstorms and compare it to our previous results for the tropics. The MCS outflow was probed at different altitudes (~10–12 km) and distances from the convective core (

In the mid-afternoon of 15 July 2007, during the Convective and Orographically-induced Precipitation Study (COPS), in a very warm and dry environment, an isolated, short-lived, deep convective system developed over the southern Black Forest. Most of the high-resolution, convection-permitting models involved in COPS were unable to capture this event whereas the Meso-NH forecast was quite skilful. To assess the Meso-NH performance further, the model results were carefully checked against the various and numerous COPS observations. In full agreement with clear-air radar observations, model results underlined the triggering role of a low-level convergence line that developed in the lee of the Feldberg. The main departure from the observations was found to be in the low-level moisture fields, which appeared significantly moister in the model than in the observations and also slightly moister than in the other models. Sensitivity studies showed that this departure from the observations was strongly controlled by the initial surface moisture conditions. When the surface moisture was reduced by 20% or replaced by the value derived from a different analysis, the evolution of the planetary boundary layer was more accurately represented while the storm evolution was still correctly captured. These results demonstrate that the quality of the initial forecast cannot be ascribed to the moist bias of the model. It could therefore be hypothesized that the key parameters for a satisfactory forecast of this event lie more in the ability of the model to reproduce the dynamical forcing accurately than in the characteristics of the air-mass instability. Copyright © 2011 Royal Meteorological Society

Geophysical Journal International, 176 (3), ISSN:0956-540X, ISSN:1365-246X

International audience; A new non-conforming finite element discretization methodology for second order elliptic partial dif-ferential equations involving higher order local absorbing boundary conditions in 2D and 3D is proposed.The novelty of the approach lies in the application of C 0 -continuous finite element spaces, which is thestandard discretization of second order operators, to the discretization of boundary differential operatorsof order four and higher. For each of these boundary operators, additional terms appear on the bound-ary nodes in 2D and on the boundary edges in 3D, similarly to interior penalty discontinuous Galerkinmethods, which leads to a stable and consistent formulation. In this way, no auxiliary variables on theboundary have to be introduced and trial and test functions of higher smoothness along the boundary arenot required. As a consequence, the method leads to lower computational costs for discretizations withhigher order elements and is easily integrated in high-order finite element libraries. A priori h-conver-gence error estimates show that the method does not reduce the order of convergence compared to usualDirichlet, Neumann or Robin boundary conditions if the polynomial degree on the boundary is increasedsimultaneously. A series of numerical experiments illustrates the utility of the method and validates thetheoretical convergence results.

A SAR system has to be calibrated for quantitative measurement. During this process all essential parameters of a SAR image are linked to their geophysical quantity. This includes the location of the image pixel, its backscattering characteristics (in amplitude and in phase) and polarimetric information. The Microwave and Radar Institute of the DLR has gained a lot of experience in these calibration procedures during the last decades and has developed special methods and dedicated reference targets for spaceborne SAR system calibration. In example of calibration results obtained for different spaceborne SAR systems the DLR SAR Calibration Center is presented.

RESUMO A circulacao oceânica, sobre o talude continental e o Plato de Sao Paulo, na Bacia de Campos e dominada pelo chamado “Sistema Corrente do Brasil”. Este e formado pela Corrente do Brasil (CB), pela Corrente de Contorno Intermediaria (CCI) e pelos meandros e vortices associados a ambos escoamentos. A coluna d’agua deste sistema de correntes e formada por um empilhamento de massas de agua, cujas profundidades e interfaces variam devido ao ajustamento baroclinico destes fluxos. Analise multiparametrica fisico-hidroquimica de massas de agua, de inedita aplicacao na margem continental brasileira, foi conduzida para identificar a composicao tanto da CB quanto da CCI. Encontrou-se que a CB transporta Agua Tropical e Agua Central do Atlântico Sul para sul-sudoeste, enquanto a CCI transporta essencialmente Agua Intermediaria Antartica e Agua Circumpolar Superior para norte-nordeste. A CB tem uma tipica espessura de 450-500 m, enquanto a CCI se estende desde a base da CB ate mais de 1.150 m de profundidade. O transporte de volume caracteristico da CB e de 6 Sv e o da CCI, de 4 Sv. O nucleo de velocidades da CB, cujos valores instantâneos podem atingir 1 m.s−1, esta localizado sempre em superficie. Ja o nucleo da CCI se encontra entre 800-900 m e aparentemente esta associado ao minimo de salinidade de toda coluna d’agua. Analise de 11 meses de series correntograficas sobre o poco Marlim revelam que CB e CCI formam um jato baroclinico medio, sem componente barotropica relevante. Esta caracteristica e crucial para explicar a natureza dinâmica dos amplos e recorrentes meandros e vortices formados na Bacia de Campos: tratam-se de meandros instaveis com propagacao horizontal virtualmente nula. Ou seja, as duas correntes eventualmente se acoplam durante a formacao do meandro. O meandro passa entao a crescer em amplitude em direcao ao oceano aberto, drenando energia potencial da CB e CCI e a transformando em cinetica na estrutura vortical. O perfil vertical caracteristico destes meandros decai exponencialmente com a profundidade, o que indica que a CB deve apresentar uma variabilidade subinercial bastante mais rica que a da CCI. Tambem e mostrado pela analise que os meandros, que sao cristas ou cavados de ondas de vorticidade baroclinicas, nao apresentam periodos dominantes. Seus comprimentos de onda, no entanto, sao tipicamente na faixa de 200-350 km.

International audience; The efficient and reliable computation of guided modes in photonic crystal wave-guides is of great importance for designing optical devices. Transparent boundary conditions based on Dirichlet-to-Neumann operators allow for an exact computation of well-confined modes and modes close to the band edge in the sense that no modelling error is introduced. The well-known super-cell method, on the other hand, introduces a modelling error which may become prohibitively large for guided modes that are not well-confined. The Dirichlet-to-Neumann transparent boundary conditions are, however, not applicable for all frequencies as they are not uniquely defined and their computation is unstable for a countable set of frequencies that correspond to so called Dirichlet eigenvalues. In this work we describe how to overcome this theoretical difficulty introducing Robin-to-Robin transparent boundary conditions whose construction do not exhibit those forbidden frequencies. They seem, hence, well suited for an exact and reliable computation of guided modes in photonic crystal wave-guides.