Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations

In this note we study the temporal convergence of a locally implicit discontinuous Galerkin (DG) method for Maxwell's equations modeling electromagnetic wave propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order reduction.Dans ce papier nous étudions la convergence temporelle d'une méthode Galerkin discontinue localement implicite pour la résolution des équations de Maxwell modélisant la propagation des ondes électromagnétiques. En particulier, nous nous demandons si pour un raffinement du maillage, simultané et stable en espace-temps, le second ordre de convergence au sens des EDO est conservé pour la solution exacte de l'EDP. Cela n'est pas à priori clair en raison de la décomposition des éléments qui peut introduire une réduction d'ordre

Temporal convergence analysis of a locally implicit discontinuous galerkin time domain method for electromagnetic wave propagation in dispersive media

International audienceThis paper is concerned with the approximation of the time domain Maxwell's equations in a dispersive propagation media by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the media. We adapt the locally implicit time integration method from [1] and derive a convergence analysis to prove that the locally implicit DGTD method for Maxwell's equations in dispersive media retains its second-order convergence

Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations

International audienceAn attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, locally refined meshes lead to severe stability constraints on explicit integration methods to numerically solve a time-dependent partial differential equation. If the region of refinement is small relative to the computational domain, the time step size restriction can be overcome by blending an implicit and an explicit scheme where only the solution variables living at fine elements are treated implicitly. The downside of this approach is having to solve a linear system per time step. But due to the assumed small region of refinement relative to the computational domain, the overhead will also be small while the solution can be advanced in time with step sizes determined by the coarse elements. In this paper, we present two locally implicit time integration methods for solving the time-domain Maxwell equations spatially discretized with a DG method. Numerical experiments for two-dimensional problems illustrate the theory and the usefulness of the implicit-explicit approaches in presence of local refinements

Locally implicit discontinuous Galerkin time domain method for electromagnetic wave propagation in dispersive media applied to numerical dosimetry in biological tissues

International audienceWe are concerned here with the numerical simulation of electromagnetic wave propagation in biological media. Because of their water content, these media are dispersive i.e. their electromagnetic material characteristics depend of the frequency. In the time-domain, this translates in a time dependency of these parameters that can be taken into account through and additional (auxiliary) differential equation for, e.g, the electric polarization, which is coupled to the system of Maxwell's equations. From the application point of view, the problems at hand most often involve irregularly shaped structures corresponding to biological tissues. Modeling realistically the interfaces between tissues is particularly important if one is interested in evaluating accurately the impact of field discontinuities at these interfaces. In this paper, we propose and study a locally implicit discon-tinuous Galerkin time-domain method formulated on an unstructured tetrahedral mesh for solving the resulting system of differential equations in the case of Debye-type media. Three-dimensional numerical simulations are presented concerning the exposure of head tissues to a localized source radiation. 1. Introduction. This article is concerned with the numerical simulation of electromagnetic wave propagation in dispersive media. These are materials in which either or both of the electromagnetic material parameters ε and µ are functions of frequency. Note that the conductivity σ may also be a function of frequency, but its effect can be rolled into the complex permittivity. In reality, all materials have frequency-dependent ε and µ, but many materials can be approximated as frequency-independent over a frequency band of interest, simplifying their analysis and simulation. Here, we will focus on the much more common case of frequency-dependent permittivity. A lot of practical electromagnetic wave propagation problems involve such propagation media, such as those involving the interaction of an electromagnetic wave with biological tissues. The numerical modeling of the propagation of electromagnetic waves through human tissues is at the heart of many biomedical applications such as the microwave imaging of cancer tumors or the treatment of the latter by hy-perthermia. For example, microwave imaging for breast cancer detection is expected to be safe for the patient and has the potential to detect very small cancerous tumors in the breast [3, 14, 24]. Beside, the definition of microwave-based hyperthermia as an immunotherapy strategy for cancer can also be cited [2, 11]. The electroporation technique can also be an application, which consists of applying nanopulses to the tissues, enabling only intracellular membranes to be affected, and then opening the route to therapeutic strategies such as electrochemotherapy or gene transfer [21, 30, 25, 26, 28]. Because for all these biomedical applications experimental modeling is almost impossible , computer simulation is the approach of choice for understanding the underlyin

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase 1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age  6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score  652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc = 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N = 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701

Research and Design of a Routing Protocol in Large-Scale Wireless Sensor Networks

无线传感器网络，作为全球未来十大技术之一，集成了传感器技术、嵌入式计算技术、分布式信息处理和自组织网技术，可实时感知、采集、处理、传输网络分布区域内的各种信息数据，在军事国防、生物医疗、环境监测、抢险救灾、防恐反恐、危险区域远程控制等领域具有十分广阔的应用前景。 本文研究分析了无线传感器网络的已有路由协议，并针对大规模的无线传感器网络设计了一种树状路由协议，它根据节点地址信息来形成路由，从而简化了复杂繁冗的路由表查找和维护，节省了不必要的开销，提高了路由效率，实现了快速有效的数据传输。 为支持此路由协议本文提出了一种自适应动态地址分配算——ADAR（AdaptiveDynamicAddre...As one of the ten high technologies in the future, wireless sensor network, which is the integration of micro-sensors, embedded computing, modern network and Ad Hoc technologies, can apperceive, collect, process and transmit various information data within the region. It can be used in military defense, biomedical, environmental monitoring, disaster relief, counter-terrorism, remote control of haz...学位：工学硕士院系专业：信息科学与技术学院通信工程系_通信与信息系统学号：2332007115216

Locally implicit discontinuous Galerkin time-domain methods for electromagnetic wave propagation in biological tissues

Cette thèse traite des équations de Maxwell en domaine temporel. Le principal objectif est de proposer des méthodes de type éléments finis d'ordre élevé pour les équations de Maxwell et des schémas d'intégration en temps efficaces sur des maillages localement raffinés. Nous considérons des méthodes GDDT (Galerkine Discontinues en Domaine Temporel) s'appuyant sur une interpolation polynomiale d'ordre arbitrairement élevé des composantes du champ électromagnétique. Les méthodes GDDT pour les équations de Maxwell s'appuient le plus souvent sur des schémas d'intégration en temps explicites dont la condition de stabilité peut être très restrictive pour des maillages raffinés. Pour surmonter cette limitation, nous considérons des schémas en temps qui consistent à appliquer un schéma implicite localement, dans les régions raffinées, tout en préservant un schéma explicite sur le reste du maillage. Nous présentons une étude théorique complète et une comparaison de deux méthodes GDDT localement implicites. Des expériences numériques en 2D et 3D illustrent l'utilité des schémas proposés. Le traitement numérique de milieux de propagation complexes est également l'un des objectifs. Nous considérons l'interaction des ondes électromagnétiques avec les tissus biologiques qui est au cœur de nombreuses applications dans le domaine biomédical. La modélisation numérique nécessite alors de résoudre le système de Maxwell avec des modèles appropriés de dispersion. Nous formulons une méthode GDDT localement implicite pour le modèle de Debye et proposons une analyse théorique et numérique complète du schéma.This work deals with the time-domain formulation of Maxwell's equations. The main objective is to propose high-order finite element type methods for the discretization of Maxwell's equations and efficient time integration methods on locally refined meshes. We consider Discontinuous Galerkin Time-Domain (DGTD) methods relying on an arbitrary high-order polynomial interpolation of the components of the electromagnetic field. Existing DGTD methods for Maxwell's equations often rely on explicit time integration schemes and are constrained by a stability condition that can be very restrictive on highly refined meshes. To overcome this limitation, we consider time integration schemes that consist in applying an implicit scheme locally i.e. in the refined regions of the mesh, while preserving an explicit scheme in the complementary part. We present a full theoretical study and a comparison of two locally implicit DGTD methods. Numerical experiments for 2D and 3D problems illustrate the usefulness of the proposed time integration schemes. The numerical treatment of complex propagation media is also one of the objectives. We consider the interaction of electromagnetic waves with biological tissues that is of interest to applications in biomedical domain. Numerical modeling then requires to solve the system of Maxwell's equations coupled to appropriate models of physical dispersion. We derive a locally implicit DGTD method for the Debye model and we achieve a full theoretical and numerical analysis of the resulting scheme

Méthodes Galerkine discontinues localement implicites en domaine temporel pour la propagation des ondes électromagnétiques dans les tissus biologiques

This work deals with the time-domain formulation of Maxwell's equations. The main objective is to propose high-order finite element type methods for the discretization of Maxwell's equations and efficient time integration methods on locally refined meshes. We consider Discontinuous Galerkin Time-Domain (DGTD) methods relying on an arbitrary high-order polynomial interpolation of the components of the electromagnetic field. Existing DGTD methods for Maxwell's equations often rely on explicit time integration schemes and are constrained by a stability condition that can be very restrictive on highly refined meshes. To overcome this limitation, we consider time integration schemes that consist in applying an implicit scheme locally i.e. in the refined regions of the mesh, while preserving an explicit scheme in the complementary part. We present a full theoretical study and a comparison of two locally implicit DGTD methods. Numerical experiments for 2D and 3D problems illustrate the usefulness of the proposed time integration schemes. The numerical treatment of complex propagation media is also one of the objectives. We consider the interaction of electromagnetic waves with biological tissues that is of interest to applications in biomedical domain. Numerical modeling then requires to solve the system of Maxwell's equations coupled to appropriate models of physical dispersion. We derive a locally implicit DGTD method for the Debye model and we achieve a full theoretical and numerical analysis of the resulting scheme.Cette thèse traite des équations de Maxwell en domaine temporel. Le principal objectif est de proposer des méthodes de type éléments finis d'ordre élevé pour les équations de Maxwell et des schémas d'intégration en temps efficaces sur des maillages localement raffinés. Nous considérons des méthodes GDDT (Galerkine Discontinues en Domaine Temporel) s'appuyant sur une interpolation polynomiale d'ordre arbitrairement élevé des composantes du champ électromagnétique. Les méthodes GDDT pour les équations de Maxwell s'appuient le plus souvent sur des schémas d'intégration en temps explicites dont la condition de stabilité peut être très restrictive pour des maillages raffinés. Pour surmonter cette limitation, nous considérons des schémas en temps qui consistent à appliquer un schéma implicite localement, dans les régions raffinées, tout en préservant un schéma explicite sur le reste du maillage. Nous présentons une étude théorique complète et une comparaison de deux méthodes GDDT localement implicites. Des expériences numériques en 2D et 3D illustrent l'utilité des schémas proposés. Le traitement numérique de milieux de propagation complexes est également l'un des objectifs. Nous considérons l'interaction des ondes électromagnétiques avec les tissus biologiques qui est au cœur de nombreuses applications dans le domaine biomédical. La modélisation numérique nécessite alors de résoudre le système de Maxwell avec des modèles appropriés de dispersion. Nous formulons une méthode GDDT localement implicite pour le modèle de Debye et proposons une analyse théorique et numérique complète du schéma

Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations

In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order reductio