Residual-based a posteriori estimators for the A/phi magnetodynamic harmonic formulation of the Maxwell system

International audienceThis paper is devoted to the derivation of an a posteriori residual-based error estimator for the A/phi magnetodynamic harmonic formulation of the Maxwell system. The weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc Helmholtz decomposition is proven, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results

Corrigendum to "Overview: oxidant and particle photochemical processes above a south-east Asian tropical rainforest (the OP3 project): introduction, rationale, location characteristics and tools" published in Atmos. Chem. Phys., 10, 169–199, 2010

Author(s): Hewitt, CN; Lee, JD; MacKenzie, AR; Barkley, MP; Carslaw, N; Carver, GD; Chappell, NA; Coe, H; Collier, C; Commane, R; Davies, F; Davison, B; DiCarlo, P; Di Marco, CF; Dorsey, JR; Edwards, PM; Evans, MJ; Fowler, D; Furneaux, KL; Gallagher, M; Guenther, A; Heard, DE; Helfter, C; Hopkins, J; Ingham, T; Irwin, M; Jones, C; Karunaharan, A; Langford, B; Lewis, AC; Lim, SF; MacDonald, SM; Mahajan, AS; Malpass, S; McFiggans, G; Mills, G; Misztal, P; Moller, S; Monks, PS; Nemitz, E; Nicolas-Perea, V; Oetjen, H; Oram, DE; Palmer, PI; Phillips, GJ; Pike, R; Plane, JMC; Pugh, T; Pyle, JA; Reeves, CE; Robinson, NH; Stewart, D; Stone, D; Whalley, LK; Yang,

Towards long-term standardised carbon and greenhouse gas observations for monitoring Europe's terrestrial ecosystems : a review

Research infrastructures play a key role in launching a new generation of integrated long-term, geographically distributed observation programmes designed to monitor climate change, better understand its impacts on global ecosystems, and evaluate possible mitigation and adaptation strategies. The pan-European Integrated Carbon Observation System combines carbon and greenhouse gas (GHG; CO2, CH4, N2O, H2O) observations within the atmosphere, terrestrial ecosystems and oceans. High-precision measurements are obtained using standardised methodologies, are centrally processed and openly available in a traceable and verifiable fashion in combination with detailed metadata. The Integrated Carbon Observation System ecosystem station network aims to sample climate and land-cover variability across Europe. In addition to GHG flux measurements, a large set of complementary data (including management practices, vegetation and soil characteristics) is collected to support the interpretation, spatial upscaling and modelling of observed ecosystem carbon and GHG dynamics. The applied sampling design was developed and formulated in protocols by the scientific community, representing a trade-off between an ideal dataset and practical feasibility. The use of open-access, high-quality and multi-level data products by different user communities is crucial for the Integrated Carbon Observation System in order to achieve its scientific potential and societal value.Peer reviewe

Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering

This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the fast multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of hard obstacles in a bounded 3D acoustic domain, for configurations featuring nodal unknowns and sampling points, based on exact or noisy synthetic data

Identification d'obstacles en acoustique dans des domaines tridimensionnels bornés

International audienceThis communication addresses the identification of rigid scatterers in a three-dimensional acoustic medium of finite extent. The methodology is based on two main concepts. The first is a boundary element formulation of the relevant acoustic boundary value problems which is accelerated by means of the Fast Multipole Method, and thereby applicable to acoustic domains of relatively large size compared to the acoustic wavelength. The second is the topo-logical gradient of the cost function associated with the inverse problem, a distribution whose computation indicates the spatial regions in the acoustic medium where the virtual introduction of a rigid scatterer of very small size induces a decrease of the cost function, thereby allowing e.g. a better-informed choice of initial conditions for a subsequent optimization-based inversion algorithm. Both concepts are presented and demonstrated on numerical examples.Cette communication concerne l'identification d'obstacles dans un domaine acoustique tridimensionnel borné. L'approche présentée repose sur deux ingrédients essentiels. Le premier est l'utilisation d'une méthode d'équations intégrales rapide fondée sur la fast multi-pole method, grâce à laquelle il est possible d'aborder ce type de problème d'inversion sur des configurations tridimensionnelles bornées de longueurs caractéristiques relativement grandes par rapport à la longueur d'onde acoustique. Le second est le gradient topologique de la fonction coût associée au problème inverse, permettant de déterminer les zones du domaine acoustique dans lesquelles l'introduction virtuelle d'un obstacle infinitésimal induit une diminution de la fonction coût. Cela permet par exemple de guider le choix de conditions initiales pour la mise en œuvre ultérieure d'un algorithme d'inversion reposant sur l'optimisation de la fonction coût. Ces deux aspects sont présentés et illustrés sur des exemples numériques

FM-BEM and topological derivative applied to acoustic inverse scattering

This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally-small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the Fast Multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of a hard obstacle in a bounded acoustic domain, for configurations featuring O(105) nodal unknowns and O(106) sampling points

A posteriori error estimator for harmonic A‐φ formulation

International audiencePurpose :In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A‐φ formulation.Design/methodology/approach :The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency).Findings :This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A‐φ formulation.Originality/value :In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications