The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.However,its convergence was not guaranteed without extra requ...The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.However,its convergence was not guaranteed without extra requirements.He et al.(SIAM J.Optim.24:1011-1040,2014)proved the convergence of a strictly contractive Peaceman-Rachford splitting method by employing a suitable underdetermined relaxation factor.In this paper,we further extend the so-called strictly contractive Peaceman-Rachford splitting method by using two different relaxation factors.Besides,motivated by the recent advances on the ADMM type method with indefinite proximal terms,we employ the indefinite proximal term in the strictly contractive Peaceman-Rachford splitting method.We show that the proposed indefinite-proximal strictly contractive Peaceman-Rachford splitting method is convergent and also prove the o(1/t)convergence rate in the nonergodic sense.The numerical tests on the l 1 regularized least square problem demonstrate the efficiency of the proposed method.展开更多
The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its imp...The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its important variants. It is known that the convergence of the inertial proximal Peaceman- Rachford splitting method can be ensured if the relaxation factor in Lagrangian multiplier updates is underdetermined, which means that the steps for the Lagrangian multiplier updates are shrunk conservatively. Although small steps play an important role in ensuring convergence, they should be strongly avoided in practice. In this article, we propose a relaxed inertial proximal Peaceman- Rachford splitting method, which has a larger feasible set for the relaxation factor. Thus, our method provides the possibility to admit larger steps in the Lagrangian multiplier updates. We establish the global convergence of the proposed algorithm under the same conditions as the inertial proximal Peaceman-Rachford splitting method. Numerical experimental results on a sparse signal recovery problem in compressive sensing and a total variation based image denoising problem demonstrate the effectiveness of our method.展开更多
Noble metal-loaded layered hydroxides exhibit high efficiency in electrocatalyzing water splitting.However,their widespread use as bifunctional electrocatalysts is hindered by low metal loading,inefficient yield,and c...Noble metal-loaded layered hydroxides exhibit high efficiency in electrocatalyzing water splitting.However,their widespread use as bifunctional electrocatalysts is hindered by low metal loading,inefficient yield,and complex synthesis processes.In this work,platinum atoms were anchored onto nickel-iron layered double hydroxide/carbon nanotube(LDH/CNT)hybrid electrocatalysts by using a straightforward milling technique with K_(2)Pt Cl_(6)·6H_(2)O as the Pt source.By adjusting the Pt-to-Fe ratio to 1/2 and 1/10,excellent electrocatalysts—Pt_(1/6)-Ni_(2/3)Fe_(1/3)-LDH/CNT and Pt_(1/30)-Ni_(2/3)Fe_(1/3)-LDH/CNT—were achieved with superior performance in hydrogen evolution reaction(HER)and oxygen evolution reaction(OER),outperforming the corresponding commercial Pt/C(20 wt%)and Ru O_(2)electrocatalysts.The enhanced electrochemical performance is attributed to the modification of Pt's electronic structure,which exhibits electron-rich states for HER and electrondeficient states for OER,significantly boosting Pt's electrochemical activity.Furthermore,the simple milling technology for controlling Pt loading offers a promising approach for scaling up the production of electrocatalysts.展开更多
In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.1...In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.134:108344,2022).The convergence analysis of the proposed method is established,which can improve the existing results.Numerical examples show that the proposed method is efficient with the two-step technique.展开更多
The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation wit...The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.展开更多
In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the...In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.展开更多
In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and ...In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.展开更多
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this pap...Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.展开更多
Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is...Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.展开更多
The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation dur...The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.展开更多
In order to make a more effective use of the data from regional digital seismograph networks and to promote the study on shear wave splitting and its application to earthquake stress-forecasting, SAM software system, ...In order to make a more effective use of the data from regional digital seismograph networks and to promote the study on shear wave splitting and its application to earthquake stress-forecasting, SAM software system, i.e., the software on systematic analysis method of shear wave splitting has been developed. This paper introduces the design aims, system structure, function and characteristics about the SAM software system and shows some graphical interfaces of data input and result output. Lastly, it discusses preliminarily the study of shear wave splitting and its application to earthquake forecasting.展开更多
By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose...By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.展开更多
This paper briefly discusses the new methods that the authors have put forward to distinguish splitting shear-waves.By combining these new methods with other methods,the authors have processed the recorded data of an ...This paper briefly discusses the new methods that the authors have put forward to distinguish splitting shear-waves.By combining these new methods with other methods,the authors have processed the recorded data of an earthquake.The study results are consistent with each other.展开更多
Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The ...Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.展开更多
During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the fi...During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the finite element method in splitting rolling. The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes, and a finite element mesh is unnecessary, and there is no explicit limitation of mesh when the metal is split. To ensure stability in the large deformation elastoplastic analysis, the Lagrange material shape function was introduced. The transformation method was utilized to impose the essential boundary conditions. The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature.展开更多
We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can...We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.展开更多
In this work, a new numerical technique is proposed for the resolution of a fluid model based on three Boltzmann moments. The main purpose of this technique is to calculate electric and physical properties in the non-...In this work, a new numerical technique is proposed for the resolution of a fluid model based on three Boltzmann moments. The main purpose of this technique is to calculate electric and physical properties in the non-equilibrium electric discharge at low pressure. The transport and Poisson＇s equations form a self-consistent model. This equation system is written in cylindrical coordinates following the geometric shape of a plasma reactor. Our transport equation system is discretized using the finite volume approach and resolved by the N-BEE explicit scheme coupled to the time splitting method. This programming structure reduces computation time considerably. The 2D code is carried out and tested by comparing our results with those found in literature.展开更多
In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split i...In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.展开更多
This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method fo...This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.展开更多
Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical exp...Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.展开更多
基金supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20210267)supported by the National Natural Science Foundation of China (Grant No.11971239)+1 种基金the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.21KJA110002)supported by the National Natural Science Foundation of China (Grant Nos.12131004,11625105).
文摘The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.However,its convergence was not guaranteed without extra requirements.He et al.(SIAM J.Optim.24:1011-1040,2014)proved the convergence of a strictly contractive Peaceman-Rachford splitting method by employing a suitable underdetermined relaxation factor.In this paper,we further extend the so-called strictly contractive Peaceman-Rachford splitting method by using two different relaxation factors.Besides,motivated by the recent advances on the ADMM type method with indefinite proximal terms,we employ the indefinite proximal term in the strictly contractive Peaceman-Rachford splitting method.We show that the proposed indefinite-proximal strictly contractive Peaceman-Rachford splitting method is convergent and also prove the o(1/t)convergence rate in the nonergodic sense.The numerical tests on the l 1 regularized least square problem demonstrate the efficiency of the proposed method.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11671116, 11271107, 91630202） and the Natural Science Foundation of Hebei Province of China （No. A2015202365）.
文摘The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its important variants. It is known that the convergence of the inertial proximal Peaceman- Rachford splitting method can be ensured if the relaxation factor in Lagrangian multiplier updates is underdetermined, which means that the steps for the Lagrangian multiplier updates are shrunk conservatively. Although small steps play an important role in ensuring convergence, they should be strongly avoided in practice. In this article, we propose a relaxed inertial proximal Peaceman- Rachford splitting method, which has a larger feasible set for the relaxation factor. Thus, our method provides the possibility to admit larger steps in the Lagrangian multiplier updates. We establish the global convergence of the proposed algorithm under the same conditions as the inertial proximal Peaceman-Rachford splitting method. Numerical experimental results on a sparse signal recovery problem in compressive sensing and a total variation based image denoising problem demonstrate the effectiveness of our method.
基金supported by the Natural Science Foundation of Henan(242300421230)the Young Teacher Fundamental Research Cultivation Program of Zhengzhou University(JC23557030)the National Natural Science Foundation of China(U21A20281 and 22208322)。
文摘Noble metal-loaded layered hydroxides exhibit high efficiency in electrocatalyzing water splitting.However,their widespread use as bifunctional electrocatalysts is hindered by low metal loading,inefficient yield,and complex synthesis processes.In this work,platinum atoms were anchored onto nickel-iron layered double hydroxide/carbon nanotube(LDH/CNT)hybrid electrocatalysts by using a straightforward milling technique with K_(2)Pt Cl_(6)·6H_(2)O as the Pt source.By adjusting the Pt-to-Fe ratio to 1/2 and 1/10,excellent electrocatalysts—Pt_(1/6)-Ni_(2/3)Fe_(1/3)-LDH/CNT and Pt_(1/30)-Ni_(2/3)Fe_(1/3)-LDH/CNT—were achieved with superior performance in hydrogen evolution reaction(HER)and oxygen evolution reaction(OER),outperforming the corresponding commercial Pt/C(20 wt%)and Ru O_(2)electrocatalysts.The enhanced electrochemical performance is attributed to the modification of Pt's electronic structure,which exhibits electron-rich states for HER and electrondeficient states for OER,significantly boosting Pt's electrochemical activity.Furthermore,the simple milling technology for controlling Pt loading offers a promising approach for scaling up the production of electrocatalysts.
基金supported by the Scientific Computing Research Innovation Team of Guangdong Province(no.2021KCXTD052)the Science and Technology Development Fund,Macao SAR(no.0096/2022/A,0151/2022/A)+3 种基金University of Macao(no.MYRG2020-00035-FST,MYRG2022-00076-FST)the Guangdong Key Construction Discipline Research Capacity Enhancement Project(no.2022ZDJS049)Technology Planning Project of Shaoguan(no.210716094530390)the ScienceFoundation of Shaoguan University(no.SZ2020KJ01).
文摘In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.134:108344,2022).The convergence analysis of the proposed method is established,which can improve the existing results.Numerical examples show that the proposed method is efficient with the two-step technique.
基金This work was supported by China State Major Key Project for Basic Researches.
文摘The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.
基金Partly supported by the State Major Key Project for Basic Researches
文摘In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.
基金Partly supported by the State Major Key Project for Researches and Project 85-906-04.
文摘In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.
基金Supported by the Natural Science Foundation of China under Grant No.0971226the 973 Project of China under Grant No.2009CB723802+1 种基金the Research Innovation Fund of Hunan Province under Grant No.CX2011B011the Innovation Fund of NUDT under Grant No.B110205
文摘Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
文摘Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.
基金This study was supported financially by the National Key Research and Development Program of China(Grant no.2018YFA0605902)the National Natural Science Foundation of China(Grant no.52101300)+1 种基金the Fundamental Research Funds for the Central Universities(Grant no.DUT21LK03)Joint Scientific Research Fund Project of DBJI(Grant no.ICR2102).
文摘The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.
文摘In order to make a more effective use of the data from regional digital seismograph networks and to promote the study on shear wave splitting and its application to earthquake stress-forecasting, SAM software system, i.e., the software on systematic analysis method of shear wave splitting has been developed. This paper introduces the design aims, system structure, function and characteristics about the SAM software system and shows some graphical interfaces of data input and result output. Lastly, it discusses preliminarily the study of shear wave splitting and its application to earthquake forecasting.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY20A010021,LY19A010002,LY20G030025)the Natural Science Founda-tion of Ningbo City,China(Grant Nos.2021J147,2021J235).
文摘By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.
文摘This paper briefly discusses the new methods that the authors have put forward to distinguish splitting shear-waves.By combining these new methods with other methods,the authors have processed the recorded data of an earthquake.The study results are consistent with each other.
文摘Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.
基金Item Sponsored by National Natural Science Foundation of China(50474016)
文摘During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the finite element method in splitting rolling. The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes, and a finite element mesh is unnecessary, and there is no explicit limitation of mesh when the metal is split. To ensure stability in the large deformation elastoplastic analysis, the Lagrange material shape function was introduced. The transformation method was utilized to impose the essential boundary conditions. The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10971226,91130013,and 11001270)the National Basic Research Program of China(Grant No.2009CB723802)+1 种基金the Research Innovation Fund of Hunan Province,China (Grant No.CX2011B011)the Innovation Fund of National University of Defense Technology,China(Grant No.B120205)
文摘We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.
文摘In this work, a new numerical technique is proposed for the resolution of a fluid model based on three Boltzmann moments. The main purpose of this technique is to calculate electric and physical properties in the non-equilibrium electric discharge at low pressure. The transport and Poisson＇s equations form a self-consistent model. This equation system is written in cylindrical coordinates following the geometric shape of a plasma reactor. Our transport equation system is discretized using the finite volume approach and resolved by the N-BEE explicit scheme coupled to the time splitting method. This programming structure reduces computation time considerably. The 2D code is carried out and tested by comparing our results with those found in literature.
基金financially supported by the National Natural Science Foundation of China(Grant No.51349011)the Foundation of Si’chuan Educational Committee(Grant No.17ZB0452)+1 种基金the Innovation Team Project of Si’chuan Educational Committee(Grant No.18TD0019)the Longshan Academic Talent Research Support Program of the Southwest of Science and Technology(Grant Nos.18LZX715 and 18LZX410)
文摘In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.
基金supported by the National Natural Science Foundation of China(12171106)the Natural Science Foundation of Guangxi Province(2020GXNSFDA238017 and 2018GXNSFFA281007)the Shanghai Sailing Program(21YF1430300)。
文摘This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.
基金support provided by the Deutsche Forschun-gsgemeinschaft(DFG,German Research Foundation)through the project GRK 2160/1“Droplet Interaction Technologies”and through the project no.457811052
文摘Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.
