In this paper,a set of closed-form formulas for vector Finite Element Method(FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme.By analyzing ...In this paper,a set of closed-form formulas for vector Finite Element Method(FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme.By analyzing the open region problems,the first-order Absorbing Boundary Condition(ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form.Based on the formulas,the hybrid Expanded Cholesky Method(ECM) and MultiFrontal algorithm(MF) is applied to solve finite element equations.Using the closed-form solution,the elec-tromagnetic field of three dimensional targets can be studied sententiously and accurately.Simulation results show that the presented formulas are successfully and concise,which can be easily used to analyze three dimensional electromagnetic problems.展开更多
The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of pl...The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of plate was constrained by lots of factors. And because the speed was a flexible control parameter,the calculation method of optimal speed profile was developed based on the measured start cooling temperature and its matrix equation was solved by the Cholesky decomposition method. The optimal speed profile was used in online control system. As a result,the temperature distribution along the plate length direction was relatively uniform,and 95% of measured final cooling temperature difference from the target temperature 700 ℃ was controlled within ±20 ℃.展开更多
Taking the element specific-heat interpolation function into account, a one-dimensional （l-D） finite ele- ment temperature field model for the on-line control of the ultra fast cooling process was developed based on...Taking the element specific-heat interpolation function into account, a one-dimensional （l-D） finite ele- ment temperature field model for the on-line control of the ultra fast cooling process was developed based on the heat transfer theory. This 1-D model was successfully implemented in one 4 300 mm plate production line. To improve the calculation accuracy of this model, the temperature-dependent material properties inside an element were considered during the modeling process. Furthermore, in order to satisfy the real-time requirements of the on-line model, the variable bandwidth storage method and the Cholesky decomposition method were used in the programming to storage the data and carry out the numerical solution. The on-line application of the proposed model indicated that the devia- tion between the calculated cooling stop temperature and the measured one was less than ± 15 ℃.展开更多
基金Supported by the National Science Foundation of China(No. 60801039)
文摘In this paper,a set of closed-form formulas for vector Finite Element Method(FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme.By analyzing the open region problems,the first-order Absorbing Boundary Condition(ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form.Based on the formulas,the hybrid Expanded Cholesky Method(ECM) and MultiFrontal algorithm(MF) is applied to solve finite element equations.Using the closed-form solution,the elec-tromagnetic field of three dimensional targets can be studied sententiously and accurately.Simulation results show that the presented formulas are successfully and concise,which can be easily used to analyze three dimensional electromagnetic problems.
文摘The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of plate was constrained by lots of factors. And because the speed was a flexible control parameter,the calculation method of optimal speed profile was developed based on the measured start cooling temperature and its matrix equation was solved by the Cholesky decomposition method. The optimal speed profile was used in online control system. As a result,the temperature distribution along the plate length direction was relatively uniform,and 95% of measured final cooling temperature difference from the target temperature 700 ℃ was controlled within ±20 ℃.
基金Item Sponsored by National Key Technologies Research and Development Program of China(2012BAF04B01)
文摘Taking the element specific-heat interpolation function into account, a one-dimensional （l-D） finite ele- ment temperature field model for the on-line control of the ultra fast cooling process was developed based on the heat transfer theory. This 1-D model was successfully implemented in one 4 300 mm plate production line. To improve the calculation accuracy of this model, the temperature-dependent material properties inside an element were considered during the modeling process. Furthermore, in order to satisfy the real-time requirements of the on-line model, the variable bandwidth storage method and the Cholesky decomposition method were used in the programming to storage the data and carry out the numerical solution. The on-line application of the proposed model indicated that the devia- tion between the calculated cooling stop temperature and the measured one was less than ± 15 ℃.
