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
On the basis of both the general theory[1,2]and the finite element method[4]of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are...On the basis of both the general theory[1,2]and the finite element method[4]of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are studied.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
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The Project supported by the State Education Commission of the People’s Republic of China
文摘On the basis of both the general theory[1,2]and the finite element method[4]of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are studied.
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.
