It is known in the computational electromagnetics (CEM) that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions...It is known in the computational electromagnetics (CEM) that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions, but usually produces an ill-conditioned matrix. Particularly, when the mesh is over dense, the iterative solution of the matrix equation from edge element converges very slowly. Based on the node element and edge element, a node-edge element is presented, which has no spurious solutions and better-conditioned matrix. Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.展开更多
The 3-dimension numerical simulation study on the electromagnetic dam used in the twin roll caster has been performed by using the edge element method. It was found that the materials and structures of the roll collar...The 3-dimension numerical simulation study on the electromagnetic dam used in the twin roll caster has been performed by using the edge element method. It was found that the materials and structures of the roll collars have great influence on the distribution of the magnetic flux density, eddy current density and the electromagnetic force in the molten pool. The conductive collars make the magnetic flux density decreased in the molten pool, but it also makes the magnetic force more uniformly, and the force in the low part of the molten pool where needs greater force have increased some what. The conductive collars make the EMD device more effective than the nonconductive collars.展开更多
We consider an Adaptive Edge Finite Element Method (AEFEM) for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and c...We consider an Adaptive Edge Finite Element Method (AEFEM) for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.展开更多
In this paper, we obtain optimal error estimates in both L^2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretize...In this paper, we obtain optimal error estimates in both L^2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L^2 error estimates into the L^2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.展开更多
The so-called surface Magneto-hydro-dynamic(MHD)propulsion relies on the Lorentz force induced in weak electrolyte solutions(such as seawater or plasma)by NdFeB Magnets.The Lorentz force plays an important role in suc...The so-called surface Magneto-hydro-dynamic(MHD)propulsion relies on the Lorentz force induced in weak electrolyte solutions(such as seawater or plasma)by NdFeB Magnets.The Lorentz force plays an important role in such dynamics as it directly affects the structures of flow boundary layers.Previous studies have mainly focused on the development of such boundary layers and related fluid-dynamic aspects.The main focus of the present study is the determination of electromagnetic field distributions around the propulsion units.In particular dedicated experiments and numerical simulations(based on the finite volume method)are conducted considering a NACA0012 airfoil immersed in seawater.The results show that,along the propulsion unit,the field strength undergoes a rapid attenuation in the direction perpendicular to the wall.展开更多
In this paper, we give the state of the art for the so called “mixed spectral elements” for Maxwell's equations. Several families of elements, such as edge elements and discon-tinuous Galerkin methods (DGM) are p...In this paper, we give the state of the art for the so called “mixed spectral elements” for Maxwell's equations. Several families of elements, such as edge elements and discon-tinuous Galerkin methods (DGM) are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.展开更多
In this paper,we first develop the mathematical modeling equations for wave propagation in several transformation optics devices,including electromagnetic concentrator,rotator and splitter.Then we propose the correspo...In this paper,we first develop the mathematical modeling equations for wave propagation in several transformation optics devices,including electromagnetic concentrator,rotator and splitter.Then we propose the corresponding finite element time-domain methods for simulating wave propagation in these transformation optics devices.We implement the proposed algorithms and our numerical results demonstrate the effectiveness of our modeling equations.To our best knowledge,this is the first work on time-domain finite element simulation carried out for the electromagnetic concentrator,rotator and splitter.展开更多
This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell’s equations with uncertain permittivity,perme-ability and initial conditions.We develop the mathematical...This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell’s equations with uncertain permittivity,perme-ability and initial conditions.We develop the mathematical analysis of the error estimate for single level Monte Carlo method,multi-level Monte Carlo method,and the quasi-Monte Carlo method.The theoretical results are supplemented by numerical experiments.展开更多
In this paper,we propose an iterative two-grid method for the edge finite element discretizations(a saddle-point system)of Perfectly Matched Layer(PML)equations to the Maxwell scattering problem in two dimensions.Firs...In this paper,we propose an iterative two-grid method for the edge finite element discretizations(a saddle-point system)of Perfectly Matched Layer(PML)equations to the Maxwell scattering problem in two dimensions.Firstly,we use a fine space to solve a discrete saddle-point system of H(grad)variational problems,denoted by auxiliary system 1.Secondly,we use a coarse space to solve the original saddle-point system.Then,we use a fine space again to solve a discrete H(curl)-elliptic variational problems,denoted by auxiliary system 2.Furthermore,we develop a regularization diagonal block preconditioner for auxiliary system 1 and use H-X preconditioner for auxiliary system 2.Hence we essentially transform the original problem in a fine space to a corresponding(but much smaller)problem on a coarse space,due to the fact that the above two preconditioners are efficient and stable.Compared with some existing iterative methods for solving saddle-point systems,such as PMinres,numerical experiments show the competitive performance of our iterative two-grid method.展开更多
In this paper,we study high order discretization methods for solving the Maxwell equations on hybrid triangle-quad meshes.We have developed high order finite edge element methods coupled with different high order time...In this paper,we study high order discretization methods for solving the Maxwell equations on hybrid triangle-quad meshes.We have developed high order finite edge element methods coupled with different high order time schemes and we compare results and efficiency for several schemes.We introduce in particular a class of simple high order low dissipation time schemes based on a modified Taylor expansion.展开更多
We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator fun...We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.展开更多
In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. We discuss the para...In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. We discuss the parallel implementation of the most promising of these methods, the ones derived from the recent Hiptmair-Xu (HX) auxiliary space decomposition [Hiptmair and Xu, SIAM J. Numer. Anal., 45 (2007), pp. 2483-2509]. An extensive set of numerical experiments demonstrate the scalability of our implementation on large-scale H(curl) problems.展开更多
We consider H(curl, Ω)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral...We consider H(curl, Ω)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 (Ω)-context along with local discrete Helmholtz-type decompositions of the edge element space.展开更多
This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated...This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms: the Current Projection method, the MUltiple Signal Classification (MUSIC) algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.展开更多
This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell's equations on unstructured ...This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell's equations on unstructured 3D tetrahedral grids. Spatial mesh re- finement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral H(curl)-conforming edge elements in space with linearly implicit Rosenbrock methods in time. An embedding technique is applied to get efficiency in time through variable time steps. Finally, we present numerical results for the magnetic recording write head benchmark problem proposed by the Storage Research Consortium in Japan.展开更多
From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric...From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes: the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.展开更多
Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmi...Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.展开更多
We are concerned, in a static regime, with a three-dimensional bounded domain of certain an imaging approach of the locations in electromagnetic imperfections. This approach is related to Electrical Impedance Tomograp...We are concerned, in a static regime, with a three-dimensional bounded domain of certain an imaging approach of the locations in electromagnetic imperfections. This approach is related to Electrical Impedance Tomography and makes use of a new perturbation formula in the electric fields. We present two localization procedures, from a Current Pro- jection method that deals with the single imperfection context and an inverse Fourier process that is devoted to multiple imperfections configurations. These procedures extend those that were described in our previous work, since operating for a broader class of settings. Namely, the localization is additionally performed for certain purely electric imperfections, as established from numerical simulations.展开更多
We consider the convergence theory of adaptive multigrid methods for secondorder elliptic problems and Maxwell’s equations.The multigrid algorithm only performs pointwise Gauss-Seidel relaxations on new degrees of fr...We consider the convergence theory of adaptive multigrid methods for secondorder elliptic problems and Maxwell’s equations.The multigrid algorithm only performs pointwise Gauss-Seidel relaxations on new degrees of freedom and their“immediate”neighbors.In the context of lowest order conforming finite element approximations,we present a unified proof for the convergence of adaptive multigrid V-cycle algorithms.The theory applies to any hierarchical tetrahedral meshes with uniformly bounded shape-regularity measures.The convergence rates for both problems are uniform with respect to the number of mesh levels and the number of degrees of freedom.We demonstrate our convergence theory by two numerical experiments.展开更多
We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer.These models appear as first order approximations of the electromagnetic field.Th...We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer.These models appear as first order approximations of the electromagnetic field.They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer,that makes possible to replace the thin layer by approximate conditions.We present the advantages and the drawbacks of several approximations together with numerical validations and simulations.The main motivation of this work concerns the computation of electromagnetic field in biological cells.The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane,which provides a specific behavior of the electromagnetic field at low frequencies.展开更多
文摘It is known in the computational electromagnetics (CEM) that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions, but usually produces an ill-conditioned matrix. Particularly, when the mesh is over dense, the iterative solution of the matrix equation from edge element converges very slowly. Based on the node element and edge element, a node-edge element is presented, which has no spurious solutions and better-conditioned matrix. Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.
基金This study was financially supported by the National Natural Science Foundation of China under the Grant No.59995440 and the Natural Science Foundation of Liaoning Province under the Grant No.2001101021.
文摘The 3-dimension numerical simulation study on the electromagnetic dam used in the twin roll caster has been performed by using the edge element method. It was found that the materials and structures of the roll collars have great influence on the distribution of the magnetic flux density, eddy current density and the electromagnetic force in the molten pool. The conductive collars make the magnetic flux density decreased in the molten pool, but it also makes the magnetic force more uniformly, and the force in the low part of the molten pool where needs greater force have increased some what. The conductive collars make the EMD device more effective than the nonconductive collars.
基金The work of the first author was supported by the NSF under Grant No.DMS-0411403 and Grant No.DMS-0511611The second author acknowledges the support from the Austrian Science Foundation(FWF)under Grant No.Start Y-192Both authors acknowledge support and the inspiring athmosphere at the Johann Radon Institute for Computational and Applied Mathematics(RICAM),Linz,Austria,during the special semester on computational mechanics
文摘We consider an Adaptive Edge Finite Element Method (AEFEM) for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.
基金supported in part by National Natural Science Foundation of China(Grant Nos.10771178 and 10676031)National Key Basic Research Program of China(973 Program)(Grant No.2005CB321702)+3 种基金the Key Proiect of Chinese Ministry of Education and Scientific Research Fund of Hunan Provincial Education Department(Grant Nos.208093 and 07A068)Especially,the first author was also supported in part by Hunan Provincial Innovation Foundation for Postgraduatesupported by Alexander von Humboldt Research Award for Senior US Scientists,NSF DMS-0609727,NSFC-10528102Furong Professor Scholar Program of Hunan Province of China through Xiangtan University
文摘In this paper, we obtain optimal error estimates in both L^2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L^2 error estimates into the L^2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.
基金the National Natural Science Foundation of China[Grant No.11702139].
文摘The so-called surface Magneto-hydro-dynamic(MHD)propulsion relies on the Lorentz force induced in weak electrolyte solutions(such as seawater or plasma)by NdFeB Magnets.The Lorentz force plays an important role in such dynamics as it directly affects the structures of flow boundary layers.Previous studies have mainly focused on the development of such boundary layers and related fluid-dynamic aspects.The main focus of the present study is the determination of electromagnetic field distributions around the propulsion units.In particular dedicated experiments and numerical simulations(based on the finite volume method)are conducted considering a NACA0012 airfoil immersed in seawater.The results show that,along the propulsion unit,the field strength undergoes a rapid attenuation in the direction perpendicular to the wall.
文摘In this paper, we give the state of the art for the so called “mixed spectral elements” for Maxwell's equations. Several families of elements, such as edge elements and discon-tinuous Galerkin methods (DGM) are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.
基金supported by NSFC Projects(11771371,11671340)Hunan Education Department Projects(15B236,YB2015B027)+2 种基金Hunan NSF(2017jj3304)NSFC Key Projects(91430213,91630205)NSF grant(DMS-1416742),Guangdong Provincial Engineering Technology Research Center for Data Science.
文摘In this paper,we first develop the mathematical modeling equations for wave propagation in several transformation optics devices,including electromagnetic concentrator,rotator and splitter.Then we propose the corresponding finite element time-domain methods for simulating wave propagation in these transformation optics devices.We implement the proposed algorithms and our numerical results demonstrate the effectiveness of our modeling equations.To our best knowledge,this is the first work on time-domain finite element simulation carried out for the electromagnetic concentrator,rotator and splitter.
基金supported by National Natural Science Foundation of China under grants No.11961048,No.11671340NSF of Jiangxi Province with No.20181ACB20001.
文摘This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell’s equations with uncertain permittivity,perme-ability and initial conditions.We develop the mathematical analysis of the error estimate for single level Monte Carlo method,multi-level Monte Carlo method,and the quasi-Monte Carlo method.The theoretical results are supplemented by numerical experiments.
基金This work was partially supported by NSFC Project(Grant No.11031006,91130002,11171281,10971059,11026091)the Key Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(Grant No.2011FJ2011)Hunan Provincial Innovation Foundation for Postgraduate(CX2010B245,CX2010B246).
文摘In this paper,we propose an iterative two-grid method for the edge finite element discretizations(a saddle-point system)of Perfectly Matched Layer(PML)equations to the Maxwell scattering problem in two dimensions.Firstly,we use a fine space to solve a discrete saddle-point system of H(grad)variational problems,denoted by auxiliary system 1.Secondly,we use a coarse space to solve the original saddle-point system.Then,we use a fine space again to solve a discrete H(curl)-elliptic variational problems,denoted by auxiliary system 2.Furthermore,we develop a regularization diagonal block preconditioner for auxiliary system 1 and use H-X preconditioner for auxiliary system 2.Hence we essentially transform the original problem in a fine space to a corresponding(but much smaller)problem on a coarse space,due to the fact that the above two preconditioners are efficient and stable.Compared with some existing iterative methods for solving saddle-point systems,such as PMinres,numerical experiments show the competitive performance of our iterative two-grid method.
基金This work was partially supported by the Agence Nationale de la Recherche,ANR-06-CIS6-0013.
文摘In this paper,we study high order discretization methods for solving the Maxwell equations on hybrid triangle-quad meshes.We have developed high order finite edge element methods coupled with different high order time schemes and we compare results and efficiency for several schemes.We introduce in particular a class of simple high order low dissipation time schemes based on a modified Taylor expansion.
基金China Postdoctoral Science Foundation Grant 2019M650460the NSF grant DMS-2011148.The research of J.Sun is supported partially by the Simons Foundation Grant 711922.
文摘We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.
基金This work performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.UCRL-JRNL-237306
文摘In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. We discuss the parallel implementation of the most promising of these methods, the ones derived from the recent Hiptmair-Xu (HX) auxiliary space decomposition [Hiptmair and Xu, SIAM J. Numer. Anal., 45 (2007), pp. 2483-2509]. An extensive set of numerical experiments demonstrate the scalability of our implementation on large-scale H(curl) problems.
基金supported in part by China NSF under the grant 60873177by the National Basic Research Project under the grant 2005CB321702
文摘We consider H(curl, Ω)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 (Ω)-context along with local discrete Helmholtz-type decompositions of the edge element space.
基金supported by ACI NIM (171) from the French Ministry of Education and Scientific Research
文摘This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms: the Current Projection method, the MUltiple Signal Classification (MUSIC) algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.
基金supported by the Deutsche Forschungsgemeinschaft(DFG)within the project"Space-time adaptive magnetic field computation"(grants CL143/3-1,CL143/3-2,LA1372/3-1,LA1372/3-2)
文摘This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell's equations on unstructured 3D tetrahedral grids. Spatial mesh re- finement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral H(curl)-conforming edge elements in space with linearly implicit Rosenbrock methods in time. An embedding technique is applied to get efficiency in time through variable time steps. Finally, we present numerical results for the magnetic recording write head benchmark problem proposed by the Storage Research Consortium in Japan.
基金supported by ACI NIM(171)from the French Ministry of Education and Scientific Research
文摘From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes: the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.
文摘Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.
文摘We are concerned, in a static regime, with a three-dimensional bounded domain of certain an imaging approach of the locations in electromagnetic imperfections. This approach is related to Electrical Impedance Tomography and makes use of a new perturbation formula in the electric fields. We present two localization procedures, from a Current Pro- jection method that deals with the single imperfection context and an inverse Fourier process that is devoted to multiple imperfections configurations. These procedures extend those that were described in our previous work, since operating for a broader class of settings. Namely, the localization is additionally performed for certain purely electric imperfections, as established from numerical simulations.
基金supported in part by the National Magnetic Confinement Fusion Science Program(Grant No.2011GB105003)the NSF of China under the grants 91130004,11071116,and 10971096+1 种基金supported in part by China NSF under the grants 11031006 and 11171334the Funds for Creative Research Groups of China(Grant No.11021101).
文摘We consider the convergence theory of adaptive multigrid methods for secondorder elliptic problems and Maxwell’s equations.The multigrid algorithm only performs pointwise Gauss-Seidel relaxations on new degrees of freedom and their“immediate”neighbors.In the context of lowest order conforming finite element approximations,we present a unified proof for the convergence of adaptive multigrid V-cycle algorithms.The theory applies to any hierarchical tetrahedral meshes with uniformly bounded shape-regularity measures.The convergence rates for both problems are uniform with respect to the number of mesh levels and the number of degrees of freedom.We demonstrate our convergence theory by two numerical experiments.
基金the Investments for the Future Programme IdEx Bordeaux CPU(ANR-10-IDEX-03-02).C.P.is partly funded by ANR projects INTCELL(ANR 2010-BLAN-916)MEMOVE(ANR 2011 BS0100601)。
文摘We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer.These models appear as first order approximations of the electromagnetic field.They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer,that makes possible to replace the thin layer by approximate conditions.We present the advantages and the drawbacks of several approximations together with numerical validations and simulations.The main motivation of this work concerns the computation of electromagnetic field in biological cells.The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane,which provides a specific behavior of the electromagnetic field at low frequencies.