Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid...Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery...Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
A two-level discretization method for eigenvalue problems is studied.Compared to the standard Galerkin finite element discretization technique performed on a fine gridthis method discretizes the eigenvalue problem on ...A two-level discretization method for eigenvalue problems is studied.Compared to the standard Galerkin finite element discretization technique performed on a fine gridthis method discretizes the eigenvalue problem on a coarse grid and obtains an improved eigenvector(eigenvalue) approximation by solving only a linear problem on the fine grid (or two linear problemsfor the case of eigenvalue approximation of nonsymmetric problems). The improved solution has theasymptotic accuracy of the Galerkin discretization solution. The link between the method and theiterated Galerkin method is established. Error estimates for the general nonsymmetric case arederived.展开更多
In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique ...In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.展开更多
Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derive...Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.展开更多
A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh si...A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.展开更多
A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inne...A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations...Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.展开更多
Based on the recently developed data-driven time-frequency analysis(Hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we...Based on the recently developed data-driven time-frequency analysis(Hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we first run a local algorithm to get a good approximation of the instantaneous frequency. We then pass this instantaneous frequency to the global algorithm to get an accurate global intrinsic mode function(IMF)and instantaneous frequency. The two-level method alleviates the difficulty of the mode mixing to some extent.We also present a method to reduce the end effects.展开更多
In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p <...In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.展开更多
In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue problem.This new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem itself.The co...In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue problem.This new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem itself.The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained.Moreover,we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem.Furthermore,we have proved a priori error estimates for this new two-level stabilized method.Finally,numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.展开更多
In view of two-level multiobjective decision making problem, and employing satisfactoriness of objective function and trade-off rate between objective functions, an interactive two-level multiobjective decision making...In view of two-level multiobjective decision making problem, and employing satisfactoriness of objective function and trade-off rate between objective functions, an interactive two-level multiobjective decision making method is proposed in this paper. By using the method, the obtained solution can be acceptable to both the follower and the requirement of the leader. It's an efficient method to solve two-level multiobjective decision making problems.展开更多
A two-level additive Schwarz preconditioner based on the overlapping domain decomposition approach is proposed for the local C0 discontinuous Galerkin (LCDG) method of Kirchhoff plates.Then with the help of an intergr...A two-level additive Schwarz preconditioner based on the overlapping domain decomposition approach is proposed for the local C0 discontinuous Galerkin (LCDG) method of Kirchhoff plates.Then with the help of an intergrid transfer operator and its error estimates,it is proved that the condition number is bounded by O(1 + (H4/δ4)),where H is the diameter of the subdomains and δ measures the overlap among subdomains.And for some special cases of small overlap,the estimate can be improved as O(1 + (H3/δ3)).At last,some numerical results are reported to demonstrate the high efficiency of the two-level additive Schwarz preconditioner.展开更多
In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the...In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters accordi...Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.展开更多
To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fract...To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.展开更多
In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this ...In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this paper is to present the formulation of a two-level decomposition scheme for decoupling the linear system obtained from the discretization into independent subsystems. This scheme takes advantage of the homogeneity property of the physical problem along one direction to reduce a 2D problem to several 1D problems via a block diagonalization approach and the reflexivity property along the second direction to decompose each of the 1D problems to two independent subproblems using a reflexive decomposition, effectively doubling the number of subproblems. Based on the special structure of the coefficient matrix of the linear system derived from the discretization and a reflexivity property of the second-order Chebyshev differentiation matrix, we show that the decomposed submatrices exhibits a similar property, enabling the system to be decomposed using reflexive decompositions. Explicit forms of the decomposed submatrices are derived. The decomposition not only yields more efficient algorithm but introduces coarse-grain parallelism. Furthermore, it preserves all eigenvalues of the original matrix.展开更多
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate init...In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.展开更多
文摘Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
文摘A two-level discretization method for eigenvalue problems is studied.Compared to the standard Galerkin finite element discretization technique performed on a fine gridthis method discretizes the eigenvalue problem on a coarse grid and obtains an improved eigenvector(eigenvalue) approximation by solving only a linear problem on the fine grid (or two linear problemsfor the case of eigenvalue approximation of nonsymmetric problems). The improved solution has theasymptotic accuracy of the Galerkin discretization solution. The link between the method and theiterated Galerkin method is established. Error estimates for the general nonsymmetric case arederived.
文摘In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.
基金The research is SUpported by the NatlOllal Science Foundation of China(No.10371096)
文摘Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.
基金Project supported by the National Natural Science Foundation of China(Nos.10901131,10971166, and 10961024)the National High Technology Research and Development Program of China (No.2009AA01A135)the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No.2010211B04)
文摘A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.
基金The National Natural Science Foundation of China (No.61362001,61102043,61262084,20132BAB211030,20122BAB211015)the Basic Research Program of Shenzhen(No.JC201104220219A)
文摘A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
基金Project supported by the National Natural Science Foundation of China(No.11001061)the Science and Technology Foundation of Guizhou Province of China(No.[2008]2123)
文摘Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.
基金supported by National Science Foundation of USA (Grants Nos. DMS1318377 and DMS-1613861)National Natural Science Foundation of China (Grant Nos. 11371220, 11671005, 11371173, 11301222 and 11526096)
文摘Based on the recently developed data-driven time-frequency analysis(Hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we first run a local algorithm to get a good approximation of the instantaneous frequency. We then pass this instantaneous frequency to the global algorithm to get an accurate global intrinsic mode function(IMF)and instantaneous frequency. The two-level method alleviates the difficulty of the mode mixing to some extent.We also present a method to reduce the end effects.
基金the National Natural Science Foundation of China(Nos.6136200161365013 and 51165033)+3 种基金the Natural Science Foundation of Jiangxi Province(Nos.20132BAB211030 and 20122BAB211015)the Technology Foundation of Department of Education in Jiangxi Province(Nos.GJJ 13061 and GJJ14196)the National Postdoctoral Research Funds(No.2014M551867)the Jiangxi Advanced Projects for Postdoctoral Research Funds(No.2014KY02)
文摘In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.
基金supported by the National Key R&D Program of China(2018YFB1501001)the NSF of China(11771348)China Postdoctoral Science Foundation(2019M653579)。
文摘In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue problem.This new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem itself.The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained.Moreover,we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem.Furthermore,we have proved a priori error estimates for this new two-level stabilized method.Finally,numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.
文摘In view of two-level multiobjective decision making problem, and employing satisfactoriness of objective function and trade-off rate between objective functions, an interactive two-level multiobjective decision making method is proposed in this paper. By using the method, the obtained solution can be acceptable to both the follower and the requirement of the leader. It's an efficient method to solve two-level multiobjective decision making problems.
文摘A two-level additive Schwarz preconditioner based on the overlapping domain decomposition approach is proposed for the local C0 discontinuous Galerkin (LCDG) method of Kirchhoff plates.Then with the help of an intergrid transfer operator and its error estimates,it is proved that the condition number is bounded by O(1 + (H4/δ4)),where H is the diameter of the subdomains and δ measures the overlap among subdomains.And for some special cases of small overlap,the estimate can be improved as O(1 + (H3/δ3)).At last,some numerical results are reported to demonstrate the high efficiency of the two-level additive Schwarz preconditioner.
基金Supported by the National Natural Science Foundation of China(No.61261010No.61362001+7 种基金No.61365013No.61262084No.51165033)Technology Foundation of Department of Education in Jiangxi Province(GJJ13061GJJ14196)Young Scientists Training Plan of Jiangxi Province(No.20133ACB21007No.20142BCB23001)National Post-Doctoral Research Fund(No.2014M551867)and Jiangxi Advanced Project for Post-Doctoral Research Fund(No.2014KY02)
文摘In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
基金supported by the Innovation Foundation of Provincial Education Department of Gansu(2024B-005)the Gansu Province National Science Foundation(22YF7GA182)the Fundamental Research Funds for the Central Universities(No.lzujbky2022-kb01)。
文摘Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.
基金funded by the project of the Major Scientific and Technological Projects of CNOOC in the 14th Five-Year Plan(No.KJGG2022-0701)the CNOOC Research Institute(No.2020PFS-03).
文摘To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.
文摘In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this paper is to present the formulation of a two-level decomposition scheme for decoupling the linear system obtained from the discretization into independent subsystems. This scheme takes advantage of the homogeneity property of the physical problem along one direction to reduce a 2D problem to several 1D problems via a block diagonalization approach and the reflexivity property along the second direction to decompose each of the 1D problems to two independent subproblems using a reflexive decomposition, effectively doubling the number of subproblems. Based on the special structure of the coefficient matrix of the linear system derived from the discretization and a reflexivity property of the second-order Chebyshev differentiation matrix, we show that the decomposed submatrices exhibits a similar property, enabling the system to be decomposed using reflexive decompositions. Explicit forms of the decomposed submatrices are derived. The decomposition not only yields more efficient algorithm but introduces coarse-grain parallelism. Furthermore, it preserves all eigenvalues of the original matrix.
文摘In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.
