This paper formulates the light timing calculations for each interferometer arm;one that is parallel to the direction of motion of the interferometer through space and the other that is perpendicular. The calculations...This paper formulates the light timing calculations for each interferometer arm;one that is parallel to the direction of motion of the interferometer through space and the other that is perpendicular. The calculations are done for a vacuum-mode interferometer and then for a gas-mode interferometer. The calculations show that no light timing difference is detectable in a vacuum-mode interferometer, but once an optical medium is present in the light path down the arms of the interferometer, this is no longer the case and a timing difference is detectable. Further to this, the timing equations obtained from the analysis are used to model the historical experiments of Michelson-Morley and Miller (Mt Wilson) and predictions are made by the model that accurately match the actual recorded results from those experiments. Thus, this timing analysis confirms that there is a light speed anisotropy in a reference frame that is moving through space, indicating the presence of a preferred Aether reference frame through which the Earth is moving.展开更多
In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using...In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using a conforming interpolation operator and construct a uniformly bounded decomposition for the finite element space. Both coarse and fine grid spaces are nonconforming. We get optimal convergence properties of the additive Schwarz algorithm that is constructed on nonnested meshes and with a not necessarily shape regular subdomain partitioning. Our analysis is based on the theory of Dryja and Widlund.It is interesting to mention that when coarse and fine spaces are all nonconforming, a natural intergrid operator seems to be one defined by taking averages of the nodal parameters. In this way, we obtain the stable factor (H/h)3/2, and show that this factor can not be improved. However, to get an optimal preconditioner,we need in general the stability with a factor C independent of mesh parameters.Therefore. the latter can not be used in this case.展开更多
This paper proposes a modified Morley element method for a fourth order elliptic singular perturbation problem. The method also uses Morley element or rectangle Morley element, but linear or bilinear approximation of ...This paper proposes a modified Morley element method for a fourth order elliptic singular perturbation problem. The method also uses Morley element or rectangle Morley element, but linear or bilinear approximation of finite element functions is used in the lower part of the bilinear form. It is shown that the modified method converges uniformly in the perturbation parameter.展开更多
This paper presents an optimal solver for the Morley element problem for the boundaryvalue problem of the biharmonic equation by decomposing it into several subproblems and solving these subproblems optimally. The opt...This paper presents an optimal solver for the Morley element problem for the boundaryvalue problem of the biharmonic equation by decomposing it into several subproblems and solving these subproblems optimally. The optimality of the proposed method is mathematically proved for general shape-regular grids.展开更多
The main aim of this paper is to study tile convergence of a nonconforming triangular plate element-Morley element under anisotropic meshes. By a novel approach, an explicit bound for the interpolation error is derive...The main aim of this paper is to study tile convergence of a nonconforming triangular plate element-Morley element under anisotropic meshes. By a novel approach, an explicit bound for the interpolation error is derived for arbitrary triangular meshes （which even need not satisfy the maximal angle condition and the coordinate system condition ）, the optimal consistency error is obtained for a family of anisotropically graded finite element meshes.展开更多
文摘This paper formulates the light timing calculations for each interferometer arm;one that is parallel to the direction of motion of the interferometer through space and the other that is perpendicular. The calculations are done for a vacuum-mode interferometer and then for a gas-mode interferometer. The calculations show that no light timing difference is detectable in a vacuum-mode interferometer, but once an optical medium is present in the light path down the arms of the interferometer, this is no longer the case and a timing difference is detectable. Further to this, the timing equations obtained from the analysis are used to model the historical experiments of Michelson-Morley and Miller (Mt Wilson) and predictions are made by the model that accurately match the actual recorded results from those experiments. Thus, this timing analysis confirms that there is a light speed anisotropy in a reference frame that is moving through space, indicating the presence of a preferred Aether reference frame through which the Earth is moving.
文摘In this paper, we develop a two-level additive Schwarz preconditioner for Morley element using nonnested meshes. We define an intergrid transfer operator that satisfies certain stable approximation properties by using a conforming interpolation operator and construct a uniformly bounded decomposition for the finite element space. Both coarse and fine grid spaces are nonconforming. We get optimal convergence properties of the additive Schwarz algorithm that is constructed on nonnested meshes and with a not necessarily shape regular subdomain partitioning. Our analysis is based on the theory of Dryja and Widlund.It is interesting to mention that when coarse and fine spaces are all nonconforming, a natural intergrid operator seems to be one defined by taking averages of the nodal parameters. In this way, we obtain the stable factor (H/h)3/2, and show that this factor can not be improved. However, to get an optimal preconditioner,we need in general the stability with a factor C independent of mesh parameters.Therefore. the latter can not be used in this case.
基金The work of the first author was supported by the National Natural Science Foundation of China （10571006）. The work of the second author was supported by National Science Foundation DMS-0209479 and DMS-0215392 and the Changjiang Professorship through Peking University.
文摘This paper proposes a modified Morley element method for a fourth order elliptic singular perturbation problem. The method also uses Morley element or rectangle Morley element, but linear or bilinear approximation of finite element functions is used in the lower part of the bilinear form. It is shown that the modified method converges uniformly in the perturbation parameter.
基金Acknowledgments. The authors would like to thank Professor Jinchao Xu for his valuable suggestions and comments. The author C. Feng is partially supported by the NSFC Grants NO. 11571293 and 11201398, the Project of Scientific Research Fund of Hunan Provincial Education Department （14B044）, Specialized research Fund for the Doctoral Program of Higher Education of China Grant 20124301110003 and Hunan Provincial Natural Science Foundation of China （14JJ2063） S. Zhang is partially supported by the NSFC Grants NO. 11101415 and 11471026, and the SRF for ROCS, SEM.
文摘This paper presents an optimal solver for the Morley element problem for the boundaryvalue problem of the biharmonic equation by decomposing it into several subproblems and solving these subproblems optimally. The optimality of the proposed method is mathematically proved for general shape-regular grids.
文摘The main aim of this paper is to study tile convergence of a nonconforming triangular plate element-Morley element under anisotropic meshes. By a novel approach, an explicit bound for the interpolation error is derived for arbitrary triangular meshes （which even need not satisfy the maximal angle condition and the coordinate system condition ）, the optimal consistency error is obtained for a family of anisotropically graded finite element meshes.
