In this paper,several new energy identities of metamaterial Maxwell’s equations with the perfectly electric conducting(PEC)boundary condition are proposed and proved.These new energy identities are different from the...In this paper,several new energy identities of metamaterial Maxwell’s equations with the perfectly electric conducting(PEC)boundary condition are proposed and proved.These new energy identities are different from the Poynting theorem.By using these new energy identities,it is proved that the Yee scheme on non-uniform rectangular meshes is stable in the discrete L2 and H1 norms when the Courant-Friedrichs-Lewy(CFL)condition is satisfied.Numerical experiments in twodimension(2D)and 3D are carried out and confirm our analysis,and the superconvergence in the discrete H1 norm is found.展开更多
In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional...In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional relation for electromagnetic field components. Lots of characteristics are obtained for different mesh sizes and frequencies. Then the reflection coefficient caused by the non-uniform mesh can be calculated according to the theory of equivalent transmission line. By comparing it with that calculated by MWI in the uniform mesh, it is found that the evaluating error can be largely reduced and is in good agreement with that directly computed by FDTD method. And this extension of MWI can be used in the error analysis of complex mesh.展开更多
Currently, the flow field of annular seals disturbed by the circular whirl motion of rotors is usually solved using computational fluid dynamics(CFD) to evaluate the five rotordynamic coefficients. The simulations are...Currently, the flow field of annular seals disturbed by the circular whirl motion of rotors is usually solved using computational fluid dynamics(CFD) to evaluate the five rotordynamic coefficients. The simulations are based on the traditional quasi-steady method. In this work, an improved quasi-steady method along with the transient method was presented to compute the rotordynamic coefficients of a long seal. By comparisons with experimental data, the shortcomings of quasi-steady methods have been identified. Then, the effects of non-uniform incoming flow on seal dynamic coefficients were studied by transient simulations. Results indicate that the long seal has large cross stiffness k and direct mass M which are not good for rotor stability, while the transient method is more suitable for the long seal for its excellent performance in predicting M. When the incoming flow is non-uniform, the stiffness coefficients vary with the eccentric directions. Based on the rotordynamic coefficients under uniform incoming flow, the linearized fluid force formulas, which can consider the effects of non-uniform incoming flow, have been presented and can well explain the varying-stiffness phenomenon.展开更多
Non-uniformity of light sources is one of the inevitable error factors causing poor shape recoveryaccuracy of photometric stereo methods under close-range lighting with quasi point lights. Semi-calibrated photometrics...Non-uniformity of light sources is one of the inevitable error factors causing poor shape recoveryaccuracy of photometric stereo methods under close-range lighting with quasi point lights. Semi-calibrated photometricstereo methods are required to avoid repeated, tedious and impractical photometric calibration. In thispaper, two simple, concise but effective mesh-based semi-calibrated photometric stereo methods are proposed.The proposed methods extend the traditional mesh-based photometric stereo methods and further allow joint andaccurate estimation of normals and non-uniform light intensities by alternatively updating normals, depth mapsand intensities. Extensive experiments are conducted to validate the effectiveness and robustness of the proposedalgorithms. Even under extremely severe non-uniform lighting, the proposed methods can still suppress the errorand improve the shape recovery accuracy by up to 65.6% in real-world experiments.展开更多
A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direct...A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direction finite elements.The displacement is approximated by C^(1)-Q_(k+1,k+1).The method is locking-free without using any projection/reduction operator.Theoretical proof and numerical confirmation are presented.展开更多
A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution tw...A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution two orders above the continuous finite element counterpart.Superconvergence of order two for the CDG finite element solution is proved in an energy norm and the L^(2)norm.A local post-process is defined which lifts a P_(k)CDG solution to a discontinuous P_(k+2)solution.It is proved that the lifted P_(k+2)solution converges at the optimal order.The numerical tests illustrate the theoretic findings.展开更多
基金supported by the National Natural Science Foundation of China Grant No.11671233 and the Shandong Provincial Science and Technology Development Program Grant No.2018GGX101036.
文摘In this paper,several new energy identities of metamaterial Maxwell’s equations with the perfectly electric conducting(PEC)boundary condition are proposed and proved.These new energy identities are different from the Poynting theorem.By using these new energy identities,it is proved that the Yee scheme on non-uniform rectangular meshes is stable in the discrete L2 and H1 norms when the Courant-Friedrichs-Lewy(CFL)condition is satisfied.Numerical experiments in twodimension(2D)and 3D are carried out and confirm our analysis,and the superconvergence in the discrete H1 norm is found.
文摘In order to increase the evaluating precision of mesh reflection wave, the mesh wave impedance (MWI) is extended to the non-uniform mesh in 1-D and 2-D cases for the first time on the basis of the Yee's positional relation for electromagnetic field components. Lots of characteristics are obtained for different mesh sizes and frequencies. Then the reflection coefficient caused by the non-uniform mesh can be calculated according to the theory of equivalent transmission line. By comparing it with that calculated by MWI in the uniform mesh, it is found that the evaluating error can be largely reduced and is in good agreement with that directly computed by FDTD method. And this extension of MWI can be used in the error analysis of complex mesh.
基金Project(51276213)supported by the National Natural Science Foundation of ChinaProject(2013BAF01B00)supported by the National Science and Technology Support Program of China
文摘Currently, the flow field of annular seals disturbed by the circular whirl motion of rotors is usually solved using computational fluid dynamics(CFD) to evaluate the five rotordynamic coefficients. The simulations are based on the traditional quasi-steady method. In this work, an improved quasi-steady method along with the transient method was presented to compute the rotordynamic coefficients of a long seal. By comparisons with experimental data, the shortcomings of quasi-steady methods have been identified. Then, the effects of non-uniform incoming flow on seal dynamic coefficients were studied by transient simulations. Results indicate that the long seal has large cross stiffness k and direct mass M which are not good for rotor stability, while the transient method is more suitable for the long seal for its excellent performance in predicting M. When the incoming flow is non-uniform, the stiffness coefficients vary with the eccentric directions. Based on the rotordynamic coefficients under uniform incoming flow, the linearized fluid force formulas, which can consider the effects of non-uniform incoming flow, have been presented and can well explain the varying-stiffness phenomenon.
基金the National Natural Science Foundation of China(No.61927822)。
文摘Non-uniformity of light sources is one of the inevitable error factors causing poor shape recoveryaccuracy of photometric stereo methods under close-range lighting with quasi point lights. Semi-calibrated photometricstereo methods are required to avoid repeated, tedious and impractical photometric calibration. In thispaper, two simple, concise but effective mesh-based semi-calibrated photometric stereo methods are proposed.The proposed methods extend the traditional mesh-based photometric stereo methods and further allow joint andaccurate estimation of normals and non-uniform light intensities by alternatively updating normals, depth mapsand intensities. Extensive experiments are conducted to validate the effectiveness and robustness of the proposedalgorithms. Even under extremely severe non-uniform lighting, the proposed methods can still suppress the errorand improve the shape recovery accuracy by up to 65.6% in real-world experiments.
文摘A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direction finite elements.The displacement is approximated by C^(1)-Q_(k+1,k+1).The method is locking-free without using any projection/reduction operator.Theoretical proof and numerical confirmation are presented.
文摘A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution two orders above the continuous finite element counterpart.Superconvergence of order two for the CDG finite element solution is proved in an energy norm and the L^(2)norm.A local post-process is defined which lifts a P_(k)CDG solution to a discontinuous P_(k+2)solution.It is proved that the lifted P_(k+2)solution converges at the optimal order.The numerical tests illustrate the theoretic findings.
