The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectra...The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.展开更多
We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H（div） conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy e...We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H（div） conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy equations and a stabilized H（div） finite element method for the Stokes equations. Optimal error estimates for the fluid velocity and pressure are derived. The finite element solutions from the new scheme not only feature a full satisfaction of the continuity equation, which is highly demanded in scientific computing, but also satisfy the mass conservation.展开更多
We present a systematic investigation of calculating quantum dots （QDs） energy levels using finite element method in the frame of eight-band k · p method. Numerical results including piezoelectricity, electron ...We present a systematic investigation of calculating quantum dots （QDs） energy levels using finite element method in the frame of eight-band k · p method. Numerical results including piezoelectricity, electron and hole levels, as well as wave functions are achieved. In the calculation of energy levels, we do observe spurious solutions （SSs） no matter Burt Foreman or symmetrized Hamiltonians are used. Different theories are used to analyse the SSs, we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs. The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs, different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.展开更多
In the design of the fatigue strength of dynamically loaded bearing in the equipmentssuch as internal combustion engines and roimg mun, the solution to the stress distribution on thebushing alloy layer is an important...In the design of the fatigue strength of dynamically loaded bearing in the equipmentssuch as internal combustion engines and roimg mun, the solution to the stress distribution on thebushing alloy layer is an important and difficult problem. In this paper, a new method has beenproposed by coupling BEM with etheticity method, The algorithm and its implementation were deseribed in details The calculation results verify that this up-dated method can provide us a moresimple and effective tool for solvingthe fatigue stress of the bushing alloy with tangible benefit oftime-saving and high computation accuraey. It may open a new vista in bearing fatigue strength design.展开更多
The rule of levitation force variation with different structure and electromagnetic parameters provides a basis for electromagnet design of electromagnetic suspension （EMS） medium and low speed maglev vehicles. In o...The rule of levitation force variation with different structure and electromagnetic parameters provides a basis for electromagnet design of electromagnetic suspension （EMS） medium and low speed maglev vehicles. In order to acquire accurate calculation results of levitation force, different calculation methods, including analytical method, 2D FEM （finite element method）, and 3D FEM, are applied to investigate the impact of various structural parameters, such as excitation current, air gap, lateral offset, and pole width, on levitation force. The analytical analysis is based on the classic mathematical model of levitation force between electromagnet and rail and performed with MATLAB. In the 2D and 3D FEMs, the numerical calculation of the levitation force is conducted with Ansoft by taking the magnetic saturation into account. In addition, the longitudinal end effect on the levitation force calculation is considered in the 3D FEM. The results show that the 3D FEM is the most accurate among the above three methods for calculating the levitation force, and the analytical method can only work for small current and/or large air gap conditions. A lateral- offset between vehicle and rail will reduce the levitation force; the levitation force descends sharply once the lateral offset exceeds the threshold, i.e., 8% of the pole width for U-shaped electromagnets. The maximum lift-to-weight ratio emerges when the pole width ratio of F type rail to electromagnet is 6：7. This may offer a reference for EMS maglev vehicle design and application.展开更多
In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solut...In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.展开更多
This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilin...This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.展开更多
在导弹类金属-介质复合目标电磁散射特性求解过程中,采用常规迭代求解方法存在难以收敛以及内迭代边界积分区域重复求解的问题。针对该问题,在传统有限元边界积分区域分解法(finite element boundary integral domain decomposition met...在导弹类金属-介质复合目标电磁散射特性求解过程中,采用常规迭代求解方法存在难以收敛以及内迭代边界积分区域重复求解的问题。针对该问题,在传统有限元边界积分区域分解法(finite element boundary integral domain decomposition method,FE-BI-DDM)的基础上,采用了更为灵活的多区多求解器的方法(multi domain multi solver method,MDMSM)。该方法对导弹类金属-介质复合目标中难以收敛的金属区域,使用快速直接求逆的方法求解,由于可以使用独立的网格模型进行电磁建模,避免了内迭代部分的模型重复建立过程,从而大幅减少了整体模型求解时间。实验结果表明:所提方法可以在相同计算精度的条件下,以不过多增加内存空间为前提,大幅缩短了导弹类目标的金属-介质复合模型的电磁求解时间。该方法为开展导弹类目标特性分析提供了一条可行的技术途径。展开更多
基金Research was supported in part by NSF grant DMS-0800612Research was supported by Applied Mathematics program of the US DOE Office of Advanced Scientific Computing ResearchThe Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830
文摘The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.
基金The Key Technologies R&D Program ofSichuan Province (No.05GG006-0062)
文摘We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H（div） conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy equations and a stabilized H（div） finite element method for the Stokes equations. Optimal error estimates for the fluid velocity and pressure are derived. The finite element solutions from the new scheme not only feature a full satisfaction of the continuity equation, which is highly demanded in scientific computing, but also satisfy the mass conservation.
基金Project supported by the National High Technology Research and Development Program of China(Grant No.2006AA03Z401)'One-Hundred Talents Program' of the Chinese Academy of Sciences,and the National Natural Science Foundation of China (Grant No.60876033)
文摘We present a systematic investigation of calculating quantum dots （QDs） energy levels using finite element method in the frame of eight-band k · p method. Numerical results including piezoelectricity, electron and hole levels, as well as wave functions are achieved. In the calculation of energy levels, we do observe spurious solutions （SSs） no matter Burt Foreman or symmetrized Hamiltonians are used. Different theories are used to analyse the SSs, we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs. The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs, different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.
文摘In the design of the fatigue strength of dynamically loaded bearing in the equipmentssuch as internal combustion engines and roimg mun, the solution to the stress distribution on thebushing alloy layer is an important and difficult problem. In this paper, a new method has beenproposed by coupling BEM with etheticity method, The algorithm and its implementation were deseribed in details The calculation results verify that this up-dated method can provide us a moresimple and effective tool for solvingthe fatigue stress of the bushing alloy with tangible benefit oftime-saving and high computation accuraey. It may open a new vista in bearing fatigue strength design.
文摘The rule of levitation force variation with different structure and electromagnetic parameters provides a basis for electromagnet design of electromagnetic suspension （EMS） medium and low speed maglev vehicles. In order to acquire accurate calculation results of levitation force, different calculation methods, including analytical method, 2D FEM （finite element method）, and 3D FEM, are applied to investigate the impact of various structural parameters, such as excitation current, air gap, lateral offset, and pole width, on levitation force. The analytical analysis is based on the classic mathematical model of levitation force between electromagnet and rail and performed with MATLAB. In the 2D and 3D FEMs, the numerical calculation of the levitation force is conducted with Ansoft by taking the magnetic saturation into account. In addition, the longitudinal end effect on the levitation force calculation is considered in the 3D FEM. The results show that the 3D FEM is the most accurate among the above three methods for calculating the levitation force, and the analytical method can only work for small current and/or large air gap conditions. A lateral- offset between vehicle and rail will reduce the levitation force; the levitation force descends sharply once the lateral offset exceeds the threshold, i.e., 8% of the pole width for U-shaped electromagnets. The maximum lift-to-weight ratio emerges when the pole width ratio of F type rail to electromagnet is 6：7. This may offer a reference for EMS maglev vehicle design and application.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10732010,10972010,and 11332002)
文摘In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.
基金This research was supported by the National Natural Science Foundation of China (10571053)Scientific Research Fund of Hunan Provincial Education Department (0513039)the Special Funds of State Major Basic Research Projects (G1999032804)
文摘This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.
文摘在导弹类金属-介质复合目标电磁散射特性求解过程中,采用常规迭代求解方法存在难以收敛以及内迭代边界积分区域重复求解的问题。针对该问题,在传统有限元边界积分区域分解法(finite element boundary integral domain decomposition method,FE-BI-DDM)的基础上,采用了更为灵活的多区多求解器的方法(multi domain multi solver method,MDMSM)。该方法对导弹类金属-介质复合目标中难以收敛的金属区域,使用快速直接求逆的方法求解,由于可以使用独立的网格模型进行电磁建模,避免了内迭代部分的模型重复建立过程,从而大幅减少了整体模型求解时间。实验结果表明:所提方法可以在相同计算精度的条件下,以不过多增加内存空间为前提,大幅缩短了导弹类目标的金属-介质复合模型的电磁求解时间。该方法为开展导弹类目标特性分析提供了一条可行的技术途径。
