A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to...A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.展开更多
Heating or cooling one-dimensional inviscid compressible flow can be modeled by the Euler equations with energy sources.A tricky situation is the sudden appearance of a single-point energy source term.This source is d...Heating or cooling one-dimensional inviscid compressible flow can be modeled by the Euler equations with energy sources.A tricky situation is the sudden appearance of a single-point energy source term.This source is discontinuous in both the time and space directions,and results in multiple discontinuous waves in the solution.We establish a mathematical model of the generalized Riemann problem of the Euler equations with source term.Based on the double CRPs coupling method proposed by the authors,we determine the wave patterns of the solution.Theoretically,we prove the existence and uniqueness of solutions to both"heat removal"problem and"heat addition"problem.Our results provide a theoretical explanation for the effect of instantaneous addition or removal of heat on the fluid.展开更多
The inverse scattering problems are to detect the property of obstacles from the measurements outside the obstacles. One of important research areas in this topic is the recovery of boundary property for impenetrable ...The inverse scattering problems are to detect the property of obstacles from the measurements outside the obstacles. One of important research areas in this topic is the recovery of boundary property for impenetrable obstacles. In this paper, we would like to give a brief review about the recently developed singular source methods. There are three different methods in this category, namely, linear sampling method, pointsource method and probe method. We also present some recent new results about the probe method.展开更多
In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving...In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.展开更多
An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid,consisting of a set of structured rectangular component grids with hanging nodes on the gr...An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid,consisting of a set of structured rectangular component grids with hanging nodes on the grid refinement interface.Previously developed summation-by-parts properties are generalized to devise a stable second order accurate coupling of the solution across mesh refinement interfaces.The discretization of singular source terms of point force and point moment tensor type are also studied.Based on enforcing discrete moment conditions that mimic properties of the Dirac distribution and its gradient,previous single grid formulas are generalized to work in the vicinity of grid refinement interfaces.These source discretization formulas are shown to give second order accuracy in the solution,with the error being essentially independent of the distance between the source and the grid refinement boundary.Several numerical examples are given to illustrate the properties of the proposed method.展开更多
柔性直流输电(voltagesourceconverterbasedhigh voltage direct current transmission,VSC-HVDC)已成为海上风电远距离、大容量送出必然的发展方向。然而,海上风电场汇集升压接入VSC-HVDC换流站的交流线路两端均体现电力电子受控源特征...柔性直流输电(voltagesourceconverterbasedhigh voltage direct current transmission,VSC-HVDC)已成为海上风电远距离、大容量送出必然的发展方向。然而,海上风电场汇集升压接入VSC-HVDC换流站的交流线路两端均体现电力电子受控源特征,系统的故障特征发生了根本性变化。近端严重的交流故障可能引起VSC-HVDC换流设备闭锁,此时系统中故障电流持续时间短暂,失去故障特征后传统交流线路保护面临严重的不正确动作风险。针对该问题,提出基于奇异值分解的交流线路保护新原理。对交流线路两侧短路电流分别构造Hankel矩阵,综合利用Hankel矩阵能够快速反映信号及信号的导数奇异性的特点,以及奇异值分解法可以使用短窗提取波形特征的优点以实现故障的快速识别,所提原理可以利用VSC-HVDC换流器闭锁前故障特征可靠实现故障区段、类型的识别,从而解决传统保护因故障特征消失引发的不正确动作问题。在PSCAD中搭建了海上永磁风电场VSC-HVDC并网的精细化电磁暂态模型,通过仿真验证了所提保护原理的有效性。仿真结果表明,所提方法能够快速、可靠地识别区内、外各种类型故障,故障识别时间小于5ms,解决了传统保护在该场景下的不正确动作问题。展开更多
This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
There is a large surface-groundwater exchange downstream ofwastewater treatment plants(WWTPs),and antibiotics upstream may influence sites downstream of rivers.Thus,samples from 9 effluent-receiving urban rivers(ERURs...There is a large surface-groundwater exchange downstream ofwastewater treatment plants(WWTPs),and antibiotics upstream may influence sites downstream of rivers.Thus,samples from 9 effluent-receiving urban rivers(ERURs)and 12 groundwater sites were collected in Shijiazhuang City in December 2020 and April 2021.For ERURs,8 out of 13 target quinolone antibiotics(QNs)were detected,and the total concentration of QNs in December and April were 100.6-4,398 ng/L and 8.02–2,476 ng/L,respectively.For groundwater,all target QNs were detected,and the total QNs concentration was 1.09–23.03 ng/L for December and 4.54–170.3 ng/L for April.The distribution of QNs was dissimilar between ERURs and groundwater.Most QN concentrations were weakly correlated with land use types in the system.The results of a positive matrix factorization model(PMF)indicated four potential sources of QNs in both ERURs and groundwater,and WWTP effluents were the main source of QNs.From December to April,the contribution of WWTP effluents and agricultural emissions increased,while livestock activities decreased.Singular value decomposition(SVD)results showed that the spatial variation of most QNs was mainly contributed by sites downstream(7.09%-88.86%)of ERURs.Then,a new method that combined the results of SVD and PMF was developed for a specific-source-site risk quotient(SRQ),and the SRQ for QNs was at high level,especially for the sites downstream of WWTPs.Regarding temporal variation,the SRQ for WWTP effluents,aquaculture,and agricultural emissions increased.Therefore,in order to control the antibiotic pollution,more attention should be paid to WWTP effluents,aquaculture,and agricultural emission sources for the benefit of sites downstream of WWTPs.展开更多
The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition exp...The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing anal an integral inequality. Examples of part of these singular sources such as Kelvin's point force, Point-Ring-Couple (PRC) etc. are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.展开更多
文摘A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.
基金supports of the NSFC-NSAF joint fund,No.U1730118 and Science Challenge Project,No.JCKY2016212A502 are gratefully acknowledged.
文摘Heating or cooling one-dimensional inviscid compressible flow can be modeled by the Euler equations with energy sources.A tricky situation is the sudden appearance of a single-point energy source term.This source is discontinuous in both the time and space directions,and results in multiple discontinuous waves in the solution.We establish a mathematical model of the generalized Riemann problem of the Euler equations with source term.Based on the double CRPs coupling method proposed by the authors,we determine the wave patterns of the solution.Theoretically,we prove the existence and uniqueness of solutions to both"heat removal"problem and"heat addition"problem.Our results provide a theoretical explanation for the effect of instantaneous addition or removal of heat on the fluid.
文摘The inverse scattering problems are to detect the property of obstacles from the measurements outside the obstacles. One of important research areas in this topic is the recovery of boundary property for impenetrable obstacles. In this paper, we would like to give a brief review about the recently developed singular source methods. There are three different methods in this category, namely, linear sampling method, pointsource method and probe method. We also present some recent new results about the probe method.
基金the Council of Scientific and Industrial Research,New Delhi,India for its financial support.
文摘In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.
基金the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344contribution LLNL-JRNL-419382.
文摘An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid,consisting of a set of structured rectangular component grids with hanging nodes on the grid refinement interface.Previously developed summation-by-parts properties are generalized to devise a stable second order accurate coupling of the solution across mesh refinement interfaces.The discretization of singular source terms of point force and point moment tensor type are also studied.Based on enforcing discrete moment conditions that mimic properties of the Dirac distribution and its gradient,previous single grid formulas are generalized to work in the vicinity of grid refinement interfaces.These source discretization formulas are shown to give second order accuracy in the solution,with the error being essentially independent of the distance between the source and the grid refinement boundary.Several numerical examples are given to illustrate the properties of the proposed method.
文摘柔性直流输电(voltagesourceconverterbasedhigh voltage direct current transmission,VSC-HVDC)已成为海上风电远距离、大容量送出必然的发展方向。然而,海上风电场汇集升压接入VSC-HVDC换流站的交流线路两端均体现电力电子受控源特征,系统的故障特征发生了根本性变化。近端严重的交流故障可能引起VSC-HVDC换流设备闭锁,此时系统中故障电流持续时间短暂,失去故障特征后传统交流线路保护面临严重的不正确动作风险。针对该问题,提出基于奇异值分解的交流线路保护新原理。对交流线路两侧短路电流分别构造Hankel矩阵,综合利用Hankel矩阵能够快速反映信号及信号的导数奇异性的特点,以及奇异值分解法可以使用短窗提取波形特征的优点以实现故障的快速识别,所提原理可以利用VSC-HVDC换流器闭锁前故障特征可靠实现故障区段、类型的识别,从而解决传统保护因故障特征消失引发的不正确动作问题。在PSCAD中搭建了海上永磁风电场VSC-HVDC并网的精细化电磁暂态模型,通过仿真验证了所提保护原理的有效性。仿真结果表明,所提方法能够快速、可靠地识别区内、外各种类型故障,故障识别时间小于5ms,解决了传统保护在该场景下的不正确动作问题。
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
基金This work was supported by the Natural Science Foundation of Hebei Province(No.D2019208152)the Natural Science Foundation of Higher Education Institutions of Hebei Province(No.ZD2021046).
文摘There is a large surface-groundwater exchange downstream ofwastewater treatment plants(WWTPs),and antibiotics upstream may influence sites downstream of rivers.Thus,samples from 9 effluent-receiving urban rivers(ERURs)and 12 groundwater sites were collected in Shijiazhuang City in December 2020 and April 2021.For ERURs,8 out of 13 target quinolone antibiotics(QNs)were detected,and the total concentration of QNs in December and April were 100.6-4,398 ng/L and 8.02–2,476 ng/L,respectively.For groundwater,all target QNs were detected,and the total QNs concentration was 1.09–23.03 ng/L for December and 4.54–170.3 ng/L for April.The distribution of QNs was dissimilar between ERURs and groundwater.Most QN concentrations were weakly correlated with land use types in the system.The results of a positive matrix factorization model(PMF)indicated four potential sources of QNs in both ERURs and groundwater,and WWTP effluents were the main source of QNs.From December to April,the contribution of WWTP effluents and agricultural emissions increased,while livestock activities decreased.Singular value decomposition(SVD)results showed that the spatial variation of most QNs was mainly contributed by sites downstream(7.09%-88.86%)of ERURs.Then,a new method that combined the results of SVD and PMF was developed for a specific-source-site risk quotient(SRQ),and the SRQ for QNs was at high level,especially for the sites downstream of WWTPs.Regarding temporal variation,the SRQ for WWTP effluents,aquaculture,and agricultural emissions increased.Therefore,in order to control the antibiotic pollution,more attention should be paid to WWTP effluents,aquaculture,and agricultural emission sources for the benefit of sites downstream of WWTPs.
文摘The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing anal an integral inequality. Examples of part of these singular sources such as Kelvin's point force, Point-Ring-Couple (PRC) etc. are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.
