Optical and microwave devices with nonlinear materials offer a series of novel phenomena and have many potential applications, so they have received more and more attention. There have been many papers which investiga...Optical and microwave devices with nonlinear materials offer a series of novel phenomena and have many potential applications, so they have received more and more attention. There have been many papers which investigated wave propagation in uniform optical waveguides with nonlinear materials and discovered that they possess the properties of self-focusing and bistability. However, there have rarely been reports on studying the 3-D nonlinear electromagnetic cavities. In the meantime among the methods used to analyze nonlinear optical waveguides, the most commonly used展开更多
In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's equations.We present the preconditioners for the first family and second family of higher orde...In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's equations.We present the preconditioners for the first family and second family of higher order N′ed′elec element equations,respectively.By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.We also present some numerical experiments to demonstrate the theoretical results.展开更多
基金Project supported by the State Education Commission of Chinathe Grant of Natural Science of Peking University.
文摘Optical and microwave devices with nonlinear materials offer a series of novel phenomena and have many potential applications, so they have received more and more attention. There have been many papers which investigated wave propagation in uniform optical waveguides with nonlinear materials and discovered that they possess the properties of self-focusing and bistability. However, there have rarely been reports on studying the 3-D nonlinear electromagnetic cavities. In the meantime among the methods used to analyze nonlinear optical waveguides, the most commonly used
基金the National Natural Science Foundation of China(Grant Nos.10771178,10676031)the National Key Basic Research Program of China(973Program)(Grant No.2005CB321702)the Key Project of Chinese Ministry of Education and Scientific Research Fund of Hunan Provincial Education Department(Grant Nos.208093,07A068)
文摘In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's equations.We present the preconditioners for the first family and second family of higher order N′ed′elec element equations,respectively.By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.We also present some numerical experiments to demonstrate the theoretical results.
