A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations

International audienceTrefftz methods are known to be very efficient to reduce the numerical pollution when associated to plane wave basis. However, these local basis functions are not adapted to the computation of evanescent modes or corner singularities. In this article, we consider a two dimensional time-harmonic Maxwell system and we propose a formulation which allows to design an electromagnetic Trefftz formulation associated to local Galerkin basis computed thanks to an auxiliary Nédélec finite element method. The results are illustrated with numerous numerical examples. The considered test cases reveal that the short range and long range propagation phenomena are both well taken into account

Discontinuous Galerkin Method based on Riemann fluxes for the time domain Maxwell System

In this report, we devise a discontinuous Galerkin method for the propagation of electromagnetic waves in a homogeneous medium. The numerical fluxes are deduced from the solution of a 1D electromagnetic problem. Numerical simulations illustrate the accuracy of the method

Interior penalty discontinuous Galerkin method for coupled elasto-acoustic media

We introduce a high order interior penalty discontinuous Galerkin scheme for the nu- merical solution of wave propagation in coupled elasto-acoustic media. A displacement formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same framework. Weakly imposing the correct transmission condition is achieved by the derivation of adapted numerical fluxes. This generalization does not weaken the discontinuous Galerkin method, thus hp-non-conforming meshes are supported. Interior penalty discontinuous Galerkin methods were originally developed for scalar equations. Therefore, we propose an optimized formulation for vectorial equations more suited than the straightforward standard transposition. We prove consis- tency and stability of the proposed schemes. To study the numerical accuracy and convergence, we achieve a classic plane wave analysis. Finally, we show the relevance of our method on numerical experiments

Prognostic Accuracy of Sepsis-3 Criteria for In-Hospital Mortality Among Patients With Suspected Infection Presenting to the Emergency Department.

An international task force recently redefined the concept of sepsis. This task force recommended the use of the quick Sequential Organ Failure Assessment (qSOFA) score instead of systemic inflammatory response syndrome (SIRS) criteria to identify patients at high risk of mortality. However, these new criteria have not been prospectively validated in some settings, and their added value in the emergency department remains unknown. To prospectively validate qSOFA as a mortality predictor and compare the performances of the new sepsis criteria to the previous ones. International prospective cohort study, conducted in France, Spain, Belgium, and Switzerland between May and June 2016. In the 30 participating emergency departments, for a 4-week period, consecutive patients who visited the emergency departments with suspected infection were included. All variables from previous and new definitions of sepsis were collected. Patients were followed up until hospital discharge or death. Measurement of qSOFA, SOFA, and SIRS. In-hospital mortality. Of 1088 patients screened, 879 were included in the analysis. Median age was 67 years (interquartile range, 47-81 years), 414 (47%) were women, and 379 (43%) had respiratory tract infection. Overall in-hospital mortality was 8%: 3% for patients with a qSOFA score lower than 2 vs 24% for those with qSOFA score of 2 or higher (absolute difference, 21%; 95% CI, 15%-26%). The qSOFA performed better than both SIRS and severe sepsis in predicting in-hospital mortality, with an area under the receiver operating curve (AUROC) of 0.80 (95% CI, 0.74-0.85) vs 0.65 (95% CI, 0.59-0.70) for both SIRS and severe sepsis (P < .001; incremental AUROC, 0.15; 95% CI, 0.09-0.22). The hazard ratio of qSOFA score for death was 6.2 (95% CI, 3.8-10.3) vs 3.5 (95% CI, 2.2-5.5) for severe sepsis. Among patients presenting to the emergency department with suspected infection, the use of qSOFA resulted in greater prognostic accuracy for in-hospital mortality than did either SIRS or severe sepsis. These findings provide support for the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3) criteria in the emergency department setting. clinicaltrials.gov Identifier: NCT02738164

Testing for the Dual-Route Cascade Reading Model in the Brain: An fMRI Effective Connectivity Account of an Efficient Reading Style

Neuropsychological data about the forms of acquired reading impairment provide a strong basis for the theoretical framework of the dual-route cascade (DRC) model which is predictive of reading performance. However, lesions are often extensive and heterogeneous, thus making it difficult to establish precise functional anatomical correlates. Here, we provide a connective neural account in the aim of accommodating the main principles of the DRC framework and to make predictions on reading skill. We located prominent reading areas using fMRI and applied structural equation modeling to pinpoint distinct neural pathways. Functionality of regions together with neural network dissociations between words and pseudowords corroborate the existing neuroanatomical view on the DRC and provide a novel outlook on the sub-regions involved. In a similar vein, congruent (or incongruent) reliance of pathways, that is reliance on the word (or pseudoword) pathway during word reading and on the pseudoword (or word) pathway during pseudoword reading predicted good (or poor) reading performance as assessed by out-of-magnet reading tests. Finally, inter-individual analysis unraveled an efficient reading style mirroring pathway reliance as a function of the fingerprint of the stimulus to be read, suggesting an optimal pattern of cerebral information trafficking which leads to high reading performance

Opposite Modulation of RAC1 by Mutations in TRIO Is Associated with Distinct, Domain-Specific Neurodevelopmental Disorders

The Rho-guanine nucleotide exchange factor (RhoGEF) TRIO acts as a key regulator of neuronal migration, axonal outgrowth, axon guidance, and synaptogenesis by activating the GTPase RAC1 and modulating actin cytoskeleton remodeling. Pathogenic variants in TRIO are associated with neurodevelopmental diseases, including intellectual disability (ID) and autism spectrum disorders (ASD). Here, we report the largest international cohort of 24 individuals with confirmed pathogenic missense or nonsense variants in TRIO. The nonsense mutations are spread along the TRIO sequence, and affected individuals show variable neurodevelopmental phenotypes. In contrast, missense variants cluster into two mutational hotspots in the TRIO sequence, one in the seventh spectrin repeat and one in the RAC1-activating GEFD1. Although all individuals in this cohort present with developmental delay and a neuro-behavioral phenotype, individuals with a pathogenic variant in the seventh spectrin repeat have a more severe ID associated with macrocephaly than do most individuals with GEFD1 variants, who display milder ID and microcephaly. Functional studies show that the spectrin and GEFD1 variants cause a TRIO-mediated hyper- or hypo-activation of RAC1, respectively, and we observe a striking correlation between RAC1 activation levels and the head size of the affected individuals. In addition, truncations in TRIO GEFD1 in the vertebrate model X. tropicalis induce defects that are concordant with the human phenotype. This work demonstrates distinct clinical and molecular disorders clustering in the GEFD1 and seventh spectrin repeat domains and highlights the importance of tight control of TRIO-RAC1 signaling in neuronal development.<br/

Extracorporeal Membrane Oxygenation for Severe Acute Respiratory Distress Syndrome associated with COVID-19: An Emulated Target Trial Analysis.

RATIONALE: Whether COVID patients may benefit from extracorporeal membrane oxygenation (ECMO) compared with conventional invasive mechanical ventilation (IMV) remains unknown. OBJECTIVES: To estimate the effect of ECMO on 90-Day mortality vs IMV only Methods: Among 4,244 critically ill adult patients with COVID-19 included in a multicenter cohort study, we emulated a target trial comparing the treatment strategies of initiating ECMO vs. no ECMO within 7 days of IMV in patients with severe acute respiratory distress syndrome (PaO2/FiO2 <80 or PaCO2 ≥60 mmHg). We controlled for confounding using a multivariable Cox model based on predefined variables. MAIN RESULTS: 1,235 patients met the full eligibility criteria for the emulated trial, among whom 164 patients initiated ECMO. The ECMO strategy had a higher survival probability at Day-7 from the onset of eligibility criteria (87% vs 83%, risk difference: 4%, 95% CI 0;9%) which decreased during follow-up (survival at Day-90: 63% vs 65%, risk difference: -2%, 95% CI -10;5%). However, ECMO was associated with higher survival when performed in high-volume ECMO centers or in regions where a specific ECMO network organization was set up to handle high demand, and when initiated within the first 4 days of MV and in profoundly hypoxemic patients. CONCLUSIONS: In an emulated trial based on a nationwide COVID-19 cohort, we found differential survival over time of an ECMO compared with a no-ECMO strategy. However, ECMO was consistently associated with better outcomes when performed in high-volume centers and in regions with ECMO capacities specifically organized to handle high demand. This article is open access and distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives License 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/)

A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation

Trefftz iterative method for three-dimensional electromagnetic waves propagation

International audienceThree-dimensional electromagnetic waves simulation is used in several civil and military applications. It often involves large linear systems leading to memory cost and computation time issues. When using a LU factorisation, the memory needed to invert the matrix increases very quickly with the domain size. In this thesis, we develop GoTEM3 : a HPC Trefftz iterative solver.Trefftz methods can be interpreted as Discontinuous Galerkin methods whose basis functions are local solutions of the studied partial differential equations. Trefftz variational formulations are presented following either the consistant forms or the numerical traces point of view. The latter are obtained, in the homogeneous case, thanks to a Riemann solver, and in the heterogeneous case, thanks to a Cessenat-Després or an upwind problem. They all lead to equivalent and coercive variational formulations. A fixed point algorithm based on Cessenat-Després UWVF is written and uses a contractant matrix. However, this property might not be numerically satisfied due to rounding errors. We then derive two Trefftz iterative solvers based on Krylov spaces : a GMRES solver and a Krylov Galerkin solver. In this thesis, basis functions are plane waves and can become numerically dependant. A new global preconditioner, implying the three directions of the domain, outperforms the Cessenat-Després preconditioner by using significantly fewer iterations. Conditioning enhancement is also performed thanks to a plane waves basis reduction, leading to both time and memory gains. This latter aspect is strongly improved by the use of a free-matrix strategy achieved thanks to the cartesian structure of the mesh. GoTEM3 is therefore a code simulating electromagnetic waves on domains containing more than one billion of degrees of freedom.La simulation d'ondes électromagnétiques en trois dimensions intervient dans de nombreuses applications civiles et militaires et met très souvent en jeu la résolution de très grands systèmes linéaires. La mémoire nécessaire pour la factorisation LU de la matrice croît très rapidement avec la taille du domaine de calcul de telles sortes que les méthodes de type EF ou GD classiques sont inutilisables. Cela conduit naturellement à employer une méthode itérative. Dans cette thèse, nous développons GoTEM3, un solveur Trefftz itératif HPC basé sur des espaces de Krylov.Les méthodes de Trefftz peuvent être interprétées comme des méthodes de Galerkin Discontinues dont les fonctions de base sont des solutions locales des équations aux dérivées partielles étudiées. Les formulations variationnelles Trefftz sont présentées sous le point de vue de formes consistantes ou de traces numériques. Ces dernières sont obtenues alternativement, pour les milieux homogènes, par un solveur de Riemann, et dans le cas général des milieux hétérogènes, par un problème de Cessenat-Després ou upwind. Elles conduisent toutes à des formulations équivalentes et coercives. Un algorithme itératif reposant sur l'UWVF de Cessenat-Després mène à un problème de point fixe dont la matrice est contractante. Toutefois, cette propriété n'est parfois plus vérifiée numériquement à cause des erreurs d'arrondis. Nous mettons alors en place un solveur GMRES et un solveur de type Krylov Galerkin dans GoTEM3. Les fonctions de base employées sont des ondes planes et peuvent devenir linéairement dépendantes numériquement. Un nouveau préconditionneur global, au sens où il implique les trois dimensions du domaine, permet d'obtenir une solution numérique précise avec nettement moins d'itérations qu'un préconditionneur de Cessenat-Després. L'amélioration du conditionnement passe aussi par une stratégie de réduction de la base d'ondes planes, conduisant à des diminutions du temps d'exécution et du coût mémoire. Ce dernier aspect est particulièrement optimisé avec un désassemblage de la matrice, rendu possible grâce au caractère cartésien du maillage. Ainsi, GoTEM3 simule les ondes électromagnétiques sur des domaines contenant plus d'un milliard de degrés de liberté

Flux reconstruction method for time-harmonic linear propagation problems: 1D a priori error analysis

International audienceThe Flux Reconstruction (FR) method is well established for hyperbolic equations in the Computational Fluid Dynamics field, but has barely been studied for electromagnetism. In this article, we propose to describe the FR formulation for time-harmonic linear hyperbolic problems. In particular, this formalism includes the Maxwell's equations and the unidimensional wave equations, for which the method is detailed. We then focus on the wave equations for incoming boundary conditions, and prove the well-posedness of the associated FR method and quasi-optimal a priori error estimates, which are explicit in terms of the flux correction polynomials and discretisation parameters. Numerical experiments finally validate the main behaviours of the estimates, and confirm the good properties of the method for the Maxwell problem.La méthode Flux Reconstruction (FR) est largement établie pour les équations hyperboliques de la mécanique des fluides, mais n'a été encore que peu étudiée dans le cadre de l'électromagnétisme. Dans cet article, nous nous proposons donc de décrire la formulation FR pour des problèmes hyperboliques linéaires harmoniques. Ce formalisme général contient en particulier le problème de Maxwell et l'équation des ondes unidimensionnelle, pour lesquelles la méthode est détaillée. Nous nous concentrons ensuite sur l'équation des ondes pour des conditions de bord entrantes, et prouvons le caractère bien posé de la méthode FR associée, ainsi que des estimations d'erreur a priori quasi-optimales et explicites en les polynômes de correction de flux et les paramètres de discrétisation. Finalement, des expériences numériques permettent de valider les principaux comportements de ces estimations, et confirment les bonnes propriétés de la méthode pour les équations de Maxwell