In this paper,a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve ...In this paper,a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve the same conservation as that for the exact solution.The stability and convergence of the proposed scheme are proved.Numerical results demonstrate the efficiency of this approach.We also establish some basic results on the generalized Laguerre-spherical harmonic orthogonal approximation,which play an important role in spectral methods for various problems defined on the whole space and unbounded domains with spherical geometry.展开更多
When wind appears over the free surface, water waves and turbulence are generated by an interfacial shear stress. In particular, turbulent diffusion promotes significantly mass and momentum transport beneath the inter...When wind appears over the free surface, water waves and turbulence are generated by an interfacial shear stress. In particular, turbulent diffusion promotes significantly mass and momentum transport beneath the interface between the water and air significantly in ocean and lakes, and thus it is very important for global environment problems to reveal such turbulence property and coherent structure. Simultaneous measurements of velocities and free-surface elevation allow us to conduct reasonably the phase analysis of the coherent structure in interfacial shear layer. Furthermore, multi-point measurements such as PIV are very powerful to detect the space-time structure of coherent motions. Therefore, in the present study, we developed a specially designed PIV system which can measure the velocity components and surface-elevation fluctuation simultaneously by using two sets of high-speed cameras to reveal the coherent structure in the interfacial shear layer.展开更多
This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green＇s functions of relevant boundary-value problems s...This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green＇s functions of relevant boundary-value problems stated in multiply-connected regions for Laplace equation written in geographical coordinates. Those are efficiently computed by a modification of the method of functional equations, with closed analytical forms preliminary obtained for Green＇s functions for the corresponding simply-connected regions.展开更多
We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameteri...We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.展开更多
Discontinuous deformation analysis （DDA） method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration （OCI） m...Discontinuous deformation analysis （DDA） method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration （OCI） method to deal with contact prob- lem, its computational efficiency is relatively low. However, spherical element based discontinuous deformation analysis （SDDA）, which uses very simple contact type like point-to-point contact, has higher calculation speed. In the framework of SDDA, this paper presents a very simple contact calculation approach by removing the OCI scheme and by adopting the maximal displacement increment （MDI）. Through some verification examples, it is proved that the proposed method is correct and effective, and a higher computational efficiency is obtained.展开更多
基金supported in part by NSF of China N.10871131The Science and Technology Commission of Shanghai Municipality,Grant N.075105118+1 种基金Shanghai Leading Academic Discipline Project N.T0401Fund for E-institute of Shanghai Universities N.E03004.
文摘In this paper,a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve the same conservation as that for the exact solution.The stability and convergence of the proposed scheme are proved.Numerical results demonstrate the efficiency of this approach.We also establish some basic results on the generalized Laguerre-spherical harmonic orthogonal approximation,which play an important role in spectral methods for various problems defined on the whole space and unbounded domains with spherical geometry.
文摘When wind appears over the free surface, water waves and turbulence are generated by an interfacial shear stress. In particular, turbulent diffusion promotes significantly mass and momentum transport beneath the interface between the water and air significantly in ocean and lakes, and thus it is very important for global environment problems to reveal such turbulence property and coherent structure. Simultaneous measurements of velocities and free-surface elevation allow us to conduct reasonably the phase analysis of the coherent structure in interfacial shear layer. Furthermore, multi-point measurements such as PIV are very powerful to detect the space-time structure of coherent motions. Therefore, in the present study, we developed a specially designed PIV system which can measure the velocity components and surface-elevation fluctuation simultaneously by using two sets of high-speed cameras to reveal the coherent structure in the interfacial shear layer.
文摘This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green＇s functions of relevant boundary-value problems stated in multiply-connected regions for Laplace equation written in geographical coordinates. Those are efficiently computed by a modification of the method of functional equations, with closed analytical forms preliminary obtained for Green＇s functions for the corresponding simply-connected regions.
基金Project supported by the National Natural Science Foundation of China (Nos. 60673006 and 60533060)the Program for New Century Excellent Talents in University (No. NCET-05-0275), Chinathe IDeA Network of Biomedical Research Excellence Grant (No. 5P20RR01647206) from National Institutes of Health (NIH), USA
文摘We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
基金supported by the National Basic Research Program of China("973" Project)(Grant Nos.2014CB046904&2014CB047101)the National Natural Science Foundation of China(Grant Nos.51479191&51509242)
文摘Discontinuous deformation analysis （DDA） method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration （OCI） method to deal with contact prob- lem, its computational efficiency is relatively low. However, spherical element based discontinuous deformation analysis （SDDA）, which uses very simple contact type like point-to-point contact, has higher calculation speed. In the framework of SDDA, this paper presents a very simple contact calculation approach by removing the OCI scheme and by adopting the maximal displacement increment （MDI）. Through some verification examples, it is proved that the proposed method is correct and effective, and a higher computational efficiency is obtained.
