Frequency-explicit a posteriori error estimates for finite element discretizations of Maxwell's equations

International audienceWe consider residual-based {\it a posteriori} error estimators for Galerkin discretizations of time-harmonic Maxwell's equations. We focus on configurations where the frequency is high, or close to a resonance frequency, and derive reliability and efficiency estimates. In contrast to previous related works, our estimates are frequency-explicit. In particular, our key contribution is to show that even if the constants appearing in the reliability and efficiency estimates may blow up on coarse meshes, they become independent of the frequency for sufficiently refined meshes. Such results were previously known for the Helmholtz equation describing scalar wave propagation problems, and we show that they naturally extend, at the price of many technicalities in the proofs, to Maxwell's equations. Our mathematical analysis is performed in the 3D case and covers conforming Nédélec discretizations of the first and second family. We also present numerical experiments in the 2D case, where Maxwell's equations are discretized with Nédélec elements of the first family. These illustrating examples perfectly fit our key theoretical findings and suggest that our estimates are sharp

Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations

We propose a new residual-based a posteriori error estimator for discontinuous Galerkin discretizations of time-harmonic Maxwell's equations in first-order form. We establish that the estimator is reliable and efficient, and the dependency of the reliability and efficiency constants on the frequency is analyzed and discussed. The proposed estimates generalize similar results previously obtained for the Helmholtz equation and conforming finite element discretization of Maxwell's equations. In addition, for the discontinuous Galerkin scheme considered here, we also show that the proposed estimator is asymptotically constantfree for smooth solutions. We also present two-dimensional numerical examples that highlight our key theoretical findings and suggest that the proposed estimator is suited to drive h and hp-adaptive iterative refinements

Frequency-explicit approximability estimates for time-harmonic Maxwell's equations

We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate measuring the difference between the corresponding solution and its best approximation by high-order Nédélec finite elements. Such an approximability estimate is crucial in both the a priori and a posteriori error analysis of finite element discretizations of Maxwell's equations, but the derivation is not trivial. Indeed, it is hard to take advantage of high-order polynomials given that the righthand side only exhibits $L^2$ regularity. We proceed in line with previously obtained results for the simpler setting of the scalar Helmholtz equation, and propose a regularity splitting of the solution. In turn, this splitting yields sharp approximability estimates generalizing known results for the scalar Helmoltz equation and showing the interest of high-order methods

A posteriori error estimates for finite element discretizations of time-harmonic Maxwell's equations coupled with a non-local hydrodynamic Drude model

We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error estimation and mesh adaptivity, which is of particular interest since the electromagnetic field usually exhibits strongly localized features near the interface between metals and their surrounding media. We propose a novel residual-based error estimator that is shown to be reliable and efficient. We also present a set of numerical examples where the estimator drives a mesh adaptive process. These examples highlight the quality of the proposed estimator, and the potential computational savings offered by mesh adaptivity

Report on the NSF Workshop on Formal Methods for Security

The NSF workshop on Security and Formal Methods, held 19--20 November 2015, brought together developers of formal methods, researchers exploring how to apply formal methods to various kinds of systems, and people familiar with the security problem space.Engineering and Applied Science

MIPModDB: a central resource for the superfamily of major intrinsic proteins

The channel proteins belonging to the major intrinsic proteins (MIP) superfamily are diverse and are found in all forms of life. Water-transporting aquaporin and glycerol-specific aquaglyceroporin are the prototype members of the MIP superfamily. MIPs have also been shown to transport other neutral molecules and gases across the membrane. They have internal homology and possess conserved sequence motifs. By analyzing a large number of publicly available genome sequences, we have identified more than 1000 MIPs from diverse organisms. We have developed a database MIPModDB which will be a unified resource for all MIPs. For each MIP entry, this database contains information about the source, gene structure, sequence features, substitutions in the conserved NPA motifs, structural model, the residues forming the selectivity filter and channel radius profile. For selected set of MIPs, it is possible to derive structure-based sequence alignment and evolutionary relationship. Sequences and structures of selected MIPs can be downloaded from MIPModDB database which is freely available at http://bioinfo.iitk.ac.in/MIPModDB

Ethical Challenges and Lessons Learned During the Clinical Development of a Group A Meningococcal Conjugate Vaccine.

BACKGROUND: The group A meningococcal vaccine (PsA-TT) clinical development plan included clinical trials in India and in the West African region between 2005 and 2013. During this period, the Meningitis Vaccine Project (MVP) accumulated substantial experience in the ethical conduct of research to the highest standards. METHODS: Because of the public-private nature of the sponsorship of these trials and the extensive international collaboration with partners from a diverse setting of countries, the ethical review process was complex and required strategic, timely, and attentive communication to ensure the smooth review and approval for the clinical studies. Investigators and their site teams fostered strong community relationships prior to, during, and after the studies to ensure the involvement and the ownership of the research by the participating populations. As the clinical work proceeded, investigators and sponsors responded to specific questions of informed consent, pregnancy testing, healthcare, disease prevention, and posttrial access. RESULTS: Key factors that led to success included (1) constant dialogue between partners to explore and answer all ethical questions; (2) alertness and preparedness for emerging ethical questions during the research and in the context of evolving international ethics standards; and (3) care to assure that approaches were acceptable in the diverse community contexts. CONCLUSIONS: Many of the ethical issues encountered during the PsA-TT clinical development are familiar to groups conducting field trials in different cultural settings. The successful approaches used by the MVP clinical team offer useful examples of how these problems were resolved. CLINICAL TRIALS REGISTRATION: ISRCTN17662153 (PsA-TT-001); ISRTCN78147026 (PsA-TT-002); ISRCTN87739946 (PsA-TT-003); ISRCTN46335400 (PsA-TT-003a); ISRCTN82484612 (PsA-TT-004); CTRI/2009/091/000368 (PsA-TT-005); PACTR ATMR2010030001913177 (PsA-TT-006); PACTR201110000328305 (PsA-TT-007)