In this paper,strategies are provided for a powerful numerical manifold method(NMM)with h and p refinement in analyses of elasticity and elasto-plasticity.The new NMM is based on the concept of the independent cover,w...In this paper,strategies are provided for a powerful numerical manifold method(NMM)with h and p refinement in analyses of elasticity and elasto-plasticity.The new NMM is based on the concept of the independent cover,which gets rid of NMM's important defect of rank deficiency when using higher-order local approximation functions.Several techniques are presented.In terms of mesh generation,a relationship between the quadtree structure and the mathematical mesh is established to allow a robust h-refinement.As to the condition number,a scaling based on the physical patch is much better than the classical scaling based on the mathematical patch;an overlapping width of 1%–10%can ensure a good condition number for 2nd,3rd,and 4th order local approximation functions;the small element issue can be overcome after the local approximation on small patch is replaced by that on a regular patch.On numerical accuracy,local approximation using complete polynomials is necessary for the optimal convergence rate.Two issues that may damage the convergence rate should be prevented.The first is to approximate the curved boundary of a higher-order element by overly few straight lines,and the second is excessive overlapping width.Finally,several refinement strategies are verified by numerical examples.展开更多
In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element method...In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods.The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k≥0).A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained.Finally,we present some numerical examples which confirm our theoretical results.展开更多
In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a...In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.展开更多
As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO...As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO techniques are subjected to the limited number of EOs,and they cannot reflect the non-linearity of the machinery dynamic systems and affect the noise reduction.As a result,the fault-related transients strengthened by these improved EO techniques are still subject to contamination of strong noises.To address these issues,this paper presents a novel EO fusion strategy for enhancing the bearing fault feature nonlinearly and effectively.Specifically,the proposed strategy is conducted through the following three steps.First,a multi-dimensional information matrix(MDIM)is constructed by performing the higher order energy operator(HOEO)on the analysis signal iteratively.MDIM is regarded as the fusion source of the proposed strategy with the properties of improving the signal-to-interference ratio and suppressing the noise in the low-frequency region.Second,an enhanced manifold learning algorithm is performed on the normalized MDIM to extract the intrinsic manifolds correlated with the fault-related impulses.Third,the intrinsic manifolds are weighted to recover the fault-related transients.Simulation studies and experimental verifications confirm that the proposed strategy is more effective for enhancing the bearing fault feature than the existing methods,including HOEOs,the weighting HOEO fusion,the fast Kurtogram,and the empirical mode decomposition.展开更多
A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity poten...A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.展开更多
To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed...To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.展开更多
A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been...A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.展开更多
In this paper,we discuss an algebraic multigrid(AMG)method for nearly incompressible elasticity problems in two-dimensions.First,a two-level method is proposed by analyzing the relationship between the linear finite e...In this paper,we discuss an algebraic multigrid(AMG)method for nearly incompressible elasticity problems in two-dimensions.First,a two-level method is proposed by analyzing the relationship between the linear finite element space and the quartic finite element space.By choosing different smoothers,we obtain two types of two-level methods,namely TL-GS and TL-BGS.The theoretical analysis and numerical results show that the convergence rates of TL-GS and TL-BGS are independent of the mesh size and the Young’s modulus,and the convergence of the latter is greatly improved on the order p.However the convergence of both methods still depends on the Poisson’s ratio.To fix this,we obtain a coarse level matrix with less rigidity based on selective reduced integration(SRI)method and get some types of two-level methods by combining different smoothers.With the existing AMG method used as a solver on the first coarse level,an AMG method can be finally obtained.Numerical results show that the resulting AMG method has better efficiency for nearly incompressible elasticity problems.展开更多
A novel,highly efficient and accurate adaptive higher-order finite element method(hp-FEM)is used to simulate a multi-frequency resistivity loggingwhile-drilling(LWD)tool response in a borehole environment.Presented in...A novel,highly efficient and accurate adaptive higher-order finite element method(hp-FEM)is used to simulate a multi-frequency resistivity loggingwhile-drilling(LWD)tool response in a borehole environment.Presented in this study are the vector expression of Maxwell’s equations,three kinds of boundary conditions,stability weak formulation of Maxwell’s equations,and automatic hpadaptivity strategy.The new hp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation.Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom,which provides more accurate results than those obtained using the adaptive h-FEM.The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models,which further confirm the accuracy of the results using the Hermes library(http://hpfem.org/hermes)with a multi-frequency resistivity LWD tool response in a borehole environment.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52130905 and 52079002)。
文摘In this paper,strategies are provided for a powerful numerical manifold method(NMM)with h and p refinement in analyses of elasticity and elasto-plasticity.The new NMM is based on the concept of the independent cover,which gets rid of NMM's important defect of rank deficiency when using higher-order local approximation functions.Several techniques are presented.In terms of mesh generation,a relationship between the quadtree structure and the mathematical mesh is established to allow a robust h-refinement.As to the condition number,a scaling based on the physical patch is much better than the classical scaling based on the mathematical patch;an overlapping width of 1%–10%can ensure a good condition number for 2nd,3rd,and 4th order local approximation functions;the small element issue can be overcome after the local approximation on small patch is replaced by that on a regular patch.On numerical accuracy,local approximation using complete polynomials is necessary for the optimal convergence rate.Two issues that may damage the convergence rate should be prevented.The first is to approximate the curved boundary of a higher-order element by overly few straight lines,and the second is excessive overlapping width.Finally,several refinement strategies are verified by numerical examples.
基金supported by the Foundation for Talent Introduction of Guangdong Provincial Universities and CollegesPearl River Scholar Funded Scheme(2008)National Science Foundation of China(10971074).
文摘In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods.The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k≥0).A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained.Finally,we present some numerical examples which confirm our theoretical results.
基金supported by the National Natural Science Foundation of China (10701083 and 10425105)the National Basic Research Program of China (2005CB321704).
文摘In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
基金supported by the National Natural Science Foundation of China (Grant Nos.52172406 and 51875376)the China Postdoctoral Science Foundation (Grant Nos.2022T150552 and 2021M702752)the Suzhou Prospective Research Program,China (Grant No.SYG202111)。
文摘As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO techniques are subjected to the limited number of EOs,and they cannot reflect the non-linearity of the machinery dynamic systems and affect the noise reduction.As a result,the fault-related transients strengthened by these improved EO techniques are still subject to contamination of strong noises.To address these issues,this paper presents a novel EO fusion strategy for enhancing the bearing fault feature nonlinearly and effectively.Specifically,the proposed strategy is conducted through the following three steps.First,a multi-dimensional information matrix(MDIM)is constructed by performing the higher order energy operator(HOEO)on the analysis signal iteratively.MDIM is regarded as the fusion source of the proposed strategy with the properties of improving the signal-to-interference ratio and suppressing the noise in the low-frequency region.Second,an enhanced manifold learning algorithm is performed on the normalized MDIM to extract the intrinsic manifolds correlated with the fault-related impulses.Third,the intrinsic manifolds are weighted to recover the fault-related transients.Simulation studies and experimental verifications confirm that the proposed strategy is more effective for enhancing the bearing fault feature than the existing methods,including HOEOs,the weighting HOEO fusion,the fast Kurtogram,and the empirical mode decomposition.
基金financially supported by the National Natural Science Foundation of China (Grant Nos.52271276,52271319,and 52201364)the Natural Science Foundation of Jiangsu Province (Grant No.BK20201006)。
文摘A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.
基金Supported by the National Natural Science Foundation of China under (Grant No.107 72040,50709005 and 50921001)the Major National Science and Technology Projects of China under (Grant No.2008ZX05026-02)the Open Fund of State Key Laboratory of Ocean Engineering
文摘To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.
文摘A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.
基金supported in part by NSF-10771178 and NSF-10672138 in Chinathe Basic Research Program of China under the grant 2005CB321702+1 种基金the Key Project of Chinese Ministry of Education and the Scientific Research Fund of Hunan Provincial Education Department(208093,07A068)the Provincial Natural Science Foundation of Hunan(07JJ6004)。
文摘In this paper,we discuss an algebraic multigrid(AMG)method for nearly incompressible elasticity problems in two-dimensions.First,a two-level method is proposed by analyzing the relationship between the linear finite element space and the quartic finite element space.By choosing different smoothers,we obtain two types of two-level methods,namely TL-GS and TL-BGS.The theoretical analysis and numerical results show that the convergence rates of TL-GS and TL-BGS are independent of the mesh size and the Young’s modulus,and the convergence of the latter is greatly improved on the order p.However the convergence of both methods still depends on the Poisson’s ratio.To fix this,we obtain a coarse level matrix with less rigidity based on selective reduced integration(SRI)method and get some types of two-level methods by combining different smoothers.With the existing AMG method used as a solver on the first coarse level,an AMG method can be finally obtained.Numerical results show that the resulting AMG method has better efficiency for nearly incompressible elasticity problems.
基金The work for this paper was supported by the National Natural Science Foundation of China under Projects No.41074099。
文摘A novel,highly efficient and accurate adaptive higher-order finite element method(hp-FEM)is used to simulate a multi-frequency resistivity loggingwhile-drilling(LWD)tool response in a borehole environment.Presented in this study are the vector expression of Maxwell’s equations,three kinds of boundary conditions,stability weak formulation of Maxwell’s equations,and automatic hpadaptivity strategy.The new hp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation.Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom,which provides more accurate results than those obtained using the adaptive h-FEM.The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models,which further confirm the accuracy of the results using the Hermes library(http://hpfem.org/hermes)with a multi-frequency resistivity LWD tool response in a borehole environment.
