The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear probl...The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.展开更多
Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted ...Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.展开更多
Quantum dynamics for the D＋OD＋ reaction at the collision energy range of 0.0-1.0 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction （D＋OD＋-→O＋＋D2） and thermo...Quantum dynamics for the D＋OD＋ reaction at the collision energy range of 0.0-1.0 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction （D＋OD＋-→O＋＋D2） and thermoneutral exchange （D＋OD＋--＊D＋OD＋） channels were investigated from the same set of time-dependent quantum wave packets method under cen- trifugal sudden approximation. The reaction probability dependence with collision energy, the integral cross sections, and the thermal rate constant of the both channels are calculated. It is found that there is a convex structure in the reaction path of the exchange reaction. The calculated time evolution of the wave packet distribution at J=0 clearly indicates that the convex structure significantly influences the dynamics of the exchange and abstraction channels of title reaction.展开更多
We introduced a decision tree method called Random Forests for multiwavelength data classification. The data were adopted from different databases, including the Sloan Digital Sky Survey （SDSS） Data Release five, US...We introduced a decision tree method called Random Forests for multiwavelength data classification. The data were adopted from different databases, including the Sloan Digital Sky Survey （SDSS） Data Release five, USNO, FIRST and ROSAT. We then studied the discrimination of quasars from stars and the classification of quasars, stars and galaxies with the sample from optical and radio bands and with that from optical and X-ray bands. Moreover, feature selection and feature weighting based on Random Forests were investigated. The performances based on different input patterns were compared. The experimental results show that the random forest method is an effective method for astronomical object classification and can be applied to other classification problems faced in astronomy. In addition, Random Forests will show its superiorities due to its own merits, e.g. classification, feature selection, feature weighting as well as outlier detection.展开更多
基金supported by the National Natural Science Foundation of China(Nos.51378293,51078199,50678093,and 50278046)the Program for Changjiang Scholars and the Innovative Research Team in University of China(No.IRT00736)
文摘The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
基金Project supported by the National Natural Science Foundation of China (No.50278046)
文摘Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
文摘Quantum dynamics for the D＋OD＋ reaction at the collision energy range of 0.0-1.0 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction （D＋OD＋-→O＋＋D2） and thermoneutral exchange （D＋OD＋--＊D＋OD＋） channels were investigated from the same set of time-dependent quantum wave packets method under cen- trifugal sudden approximation. The reaction probability dependence with collision energy, the integral cross sections, and the thermal rate constant of the both channels are calculated. It is found that there is a convex structure in the reaction path of the exchange reaction. The calculated time evolution of the wave packet distribution at J=0 clearly indicates that the convex structure significantly influences the dynamics of the exchange and abstraction channels of title reaction.
基金Supported by the National Natural Science Foundation of ChinaThis paper is funded by the National Natural Science Foundation of China under grant under GrantNos. 10473013, 90412016 and 10778724 by the 863 project under Grant No. 2006AA01A120
文摘We introduced a decision tree method called Random Forests for multiwavelength data classification. The data were adopted from different databases, including the Sloan Digital Sky Survey （SDSS） Data Release five, USNO, FIRST and ROSAT. We then studied the discrimination of quasars from stars and the classification of quasars, stars and galaxies with the sample from optical and radio bands and with that from optical and X-ray bands. Moreover, feature selection and feature weighting based on Random Forests were investigated. The performances based on different input patterns were compared. The experimental results show that the random forest method is an effective method for astronomical object classification and can be applied to other classification problems faced in astronomy. In addition, Random Forests will show its superiorities due to its own merits, e.g. classification, feature selection, feature weighting as well as outlier detection.
