The convergent iterative procedure for solving the groundstate Schrodinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-di...The convergent iterative procedure for solving the groundstate Schrodinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.展开更多
The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and m...The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples.展开更多
In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain exist...In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .展开更多
Linear Least Squares(LLS) problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares(LLS) problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm(SAIA) is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in...In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.展开更多
This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the mo...This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the monotone iterative technique.Furthermore,the uniqueness of the C3 positive solution,and the iterative sequence of the C3 positive solution are also obtained.展开更多
Train–track–substructure dynamic interaction is an extension of the vehicle–track coupled dynamics.It contributes to evaluate dynamic interaction and performance between train–track system and its substructures.Fo...Train–track–substructure dynamic interaction is an extension of the vehicle–track coupled dynamics.It contributes to evaluate dynamic interaction and performance between train–track system and its substructures.For the first time,this work devotes to presenting engineering practical methods for modeling and solving such large-scale train–track–substructure interaction systems from a unified viewpoint.In this study,a train consists of several multi-rigid-body vehicles,and the track is modeled by various finite elements.The track length needs only satisfy the length of a train plus boundary length at two sides,despite how long the train moves on the track.The substructures and their interaction matrices to the upper track are established as independent modules,with no need for additionally building the track structures above substructures,and accordingly saving computational cost.Track–substructure local coordinates are defined to assist the confirming of the overlapped portions between the train–track system and the substructural system to effectively combine the cyclic calculation and iterative solution procedures.The advancement of this model lies in its convenience,efficiency and accuracy in continuously considering the vibration participation of multi-types of substructures against the moving of a train on the track.Numerical examples have shown the effectiveness of this method;besides,influence of substructures on train–track dynamic behaviors is illustrated accompanied by clarifying excitation difference of different track irregularity spectrums.展开更多
The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed ...The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes<em> one </em>primordial field and analyzes the evolution of this field. The key assumption is that <em>only</em> the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the <em>Principle</em> <em>of </em><em>Self-interaction</em> and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.展开更多
Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. Howev...Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. However, the penalty has tobe chosen properly. If it is too large, the matrix equation may become ill-conditioned. Onthe other hand, the matrix equation may give incorrect answer if the penalty is too small.In non-linear regime, the difficulty is more serious because the magnitude order of the matrix varies considerably in the entire loading history. The paper suggests an iteration solution and applies it to non-linear FEM of rubber-like hyper-elasticity. This type of analysisis highly non-linear both in physics and in geometry as well as the strong constraint of incompressibility. The iteration solution is demonstrated to possess super precision and excellent convergence characteristics.展开更多
This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kut...This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.展开更多
By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f(t,u) is non-increasing respect to u.
In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green's function is established. In o...In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green's function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.展开更多
Consider the inverse scattering problem in terms of Helmholtz equation.We study a simply connected domain with oblique derivative boundary condition.In the case of constant l,given a finite number of incident wave,the...Consider the inverse scattering problem in terms of Helmholtz equation.We study a simply connected domain with oblique derivative boundary condition.In the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field data.We propose a Newton method which is based on the nonlinear boundary integral equation.After computing the Fr´echet derivatives with respect to the unknown boundary,the nonlinear equation is transformed to its linear form,then we show the iteration scheme for the inverse problem.We conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.展开更多
基金This research was supported in part by the U.S. Department of Energy (Grant No DE-FG02-92ER-40699) and the National Natural Science Foundation of China (Grant No 10547001).
文摘The convergent iterative procedure for solving the groundstate Schrodinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.
文摘The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples.
文摘In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares(LLS) problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm(SAIA) is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
基金This work has been carried out as of a research project which has been supported by the National Structural Strength & Vibration Laboratory of Xi'an Jiaotong University with National Fund
文摘In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.
文摘This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the monotone iterative technique.Furthermore,the uniqueness of the C3 positive solution,and the iterative sequence of the C3 positive solution are also obtained.
基金This work was supported by the National Natural Science Foundation of China(Grant No.52008404)the National Natural Science Foundation of Hunan Province(Grant No.2021JJ30850).
文摘Train–track–substructure dynamic interaction is an extension of the vehicle–track coupled dynamics.It contributes to evaluate dynamic interaction and performance between train–track system and its substructures.For the first time,this work devotes to presenting engineering practical methods for modeling and solving such large-scale train–track–substructure interaction systems from a unified viewpoint.In this study,a train consists of several multi-rigid-body vehicles,and the track is modeled by various finite elements.The track length needs only satisfy the length of a train plus boundary length at two sides,despite how long the train moves on the track.The substructures and their interaction matrices to the upper track are established as independent modules,with no need for additionally building the track structures above substructures,and accordingly saving computational cost.Track–substructure local coordinates are defined to assist the confirming of the overlapped portions between the train–track system and the substructural system to effectively combine the cyclic calculation and iterative solution procedures.The advancement of this model lies in its convenience,efficiency and accuracy in continuously considering the vibration participation of multi-types of substructures against the moving of a train on the track.Numerical examples have shown the effectiveness of this method;besides,influence of substructures on train–track dynamic behaviors is illustrated accompanied by clarifying excitation difference of different track irregularity spectrums.
文摘The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes<em> one </em>primordial field and analyzes the evolution of this field. The key assumption is that <em>only</em> the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the <em>Principle</em> <em>of </em><em>Self-interaction</em> and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.
文摘Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. However, the penalty has tobe chosen properly. If it is too large, the matrix equation may become ill-conditioned. Onthe other hand, the matrix equation may give incorrect answer if the penalty is too small.In non-linear regime, the difficulty is more serious because the magnitude order of the matrix varies considerably in the entire loading history. The paper suggests an iteration solution and applies it to non-linear FEM of rubber-like hyper-elasticity. This type of analysisis highly non-linear both in physics and in geometry as well as the strong constraint of incompressibility. The iteration solution is demonstrated to possess super precision and excellent convergence characteristics.
文摘This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.
基金supported by Program for Scientific research innovation team in Colleges and universities of Shandong Provincethe Doctoral Program Foundation of Education Ministry of China(20133705110003)+1 种基金the Natural Science Foundation of Shandong Province of China(ZR2014AM007)the National Natural Science Foundation of China(11571197)
文摘By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f(t,u) is non-increasing respect to u.
基金Supported by NNSF of China(11201213,11371183)NSF of Shandong Province(ZR2010AM022,ZR2013AM004)+2 种基金the Project of Shandong Provincial Higher Educational Science and Technology(J15LI07)the Project of Ludong University High-Quality Curriculum(20130345)the Teaching Reform Project of Ludong University in 2014(20140405)
文摘In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green's function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.
基金foundation of Jinling Institute of Technology(No.jit-b-201524)the Science Foundation of Jinling Institute of Technology(No.Jit-fhxm-201809).
文摘Consider the inverse scattering problem in terms of Helmholtz equation.We study a simply connected domain with oblique derivative boundary condition.In the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field data.We propose a Newton method which is based on the nonlinear boundary integral equation.After computing the Fr´echet derivatives with respect to the unknown boundary,the nonlinear equation is transformed to its linear form,then we show the iteration scheme for the inverse problem.We conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.