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Multiplicity Results for Second Order Impulsive Differential Equations via Variational Methods 认领 引用 被引量：3
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作者 Huanhuan Wang Dan Lu Huiqin Lu 《Engineering（科研）》 2021年第2期82-93,共12页
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of and prove that the norm which is deduced by the inner product is equ... In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result. 展开更多
关键词 Impulsive Differential Equation Sign-Changing Solution Critical Point Theory Variational Method
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Variational approximation methods for long-range force transmission in biopolymer gels 认领 引用
2
作者 Haiqin Wang Xinpeng Xu 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第10期429-435,共7页
The variational principle of minimum free energy(MFEVP)has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary ... The variational principle of minimum free energy(MFEVP)has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary conditions),but also to develop direct variational methods(such as Ritz method)to find approximate solutions to these equilibrium equations.We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels.It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in threedimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels. 展开更多
关键词 biopolymer gels cell-cell communications force transmission variational methods
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Projecting the pan-Arctic three-dimensional ocean thermohaline structure using satellite sea surface data and a variational approach 认领 引用
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作者 Zikang He Xidong Wang +4 位作者 Yuan Cao Jinlong Li Yixuan Li Xuezhu Wang Jian Chen 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2025年第5期1-15,共15页
Satellite altimetry missions at high latitude have opened new avenues for understanding the changes occurring over the ice-covered region.By incorporating Arctic satellite remote sensing data-including sea surface tem... Satellite altimetry missions at high latitude have opened new avenues for understanding the changes occurring over the ice-covered region.By incorporating Arctic satellite remote sensing data-including sea surface temperature(SST),sea surface height anomaly(SSHA),and sea surface salinity(SSS).This study employs a variational method to reconstruct the three-dimensional thermohaline structure of the Arctic Ocean.Compared to the Regional Arctic Reanalysis(RARE),the reconstruction well captures both the horizontal and vertical temperature and salinity structures in the Arctic.It demonstrates superior skill over RARE,when compared with Argo profiles and Ice-Tethered Profiler(ITP)observations.The reconstruction is particularly effective in ice-covered regions,where it more accurately captures the transition from Pacific water to Atlantic water compared to RARE.These findings underscore the potential of applying Arctic satellite data to reconstruct vertical thermohaline structures in the Arctic,particularly in areas due to lack of the subsurface observation reanalysis data exhibit significant biases.As Arctic satellite observations continue to advance,the applications of this method are becoming increasingly promising,which is useful for monitoring the ice-covered region environment and can be applied to oceanographic research. 展开更多
关键词 thermohaline structure Arctic variational method Arctic satellite observation reconstruction
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A variational differential quadrature formulation for buckling analysis of anisogrid composite lattice conical shells 认领 引用 被引量：1
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作者 Yongqi LIU Jianwei WANG +1 位作者 Dong DU Guohua NIE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2025年第11期2155-2176,共22页
Anisogrid composite lattice conical shells, which exhibit varying stiffness along their cone generators, are widely used as interstage structures in aerospace applications. Buckling under axial compression represents ... Anisogrid composite lattice conical shells, which exhibit varying stiffness along their cone generators, are widely used as interstage structures in aerospace applications. Buckling under axial compression represents one of the most hazardous failure modes for such structures. In this paper, the smeared stiffness method, which incorporates the effect of component torsion, is used to obtain the equivalent stiffness coefficients for composite lattice conical shells with triangular and hexagonal patterns. A unified framework based on the variational differential quadrature (VDQ) method is established, leveraging its suitability for asymptotic expansion to determine the critical buckling loads and the b-imperfection sensitivity parameter of lattice conical shells with axially varying stiffness due to rib layout. The influence of pre-buckling deformation is taken into account to enhance the accuracy of predictions on the linear buckling loads. The feasibility of the present equivalent continuum model is verified, and the differences in buckling behaviors for composite lattice conical shells with both triangular and hexagonal unit cells are numerically evaluated through the finite element (FE) simulations and the VDQ method. 展开更多
关键词 lattice conical shell smeared stiffness method variational differential quadrature(VDQ)method parametric finite element(FE)model buckling
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EXISTENCE AND MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE PLANAR SCHRODINGER-POISSON SYSTEM WITH EXPONENTIAL CRITICAL GROWTH 认领 引用
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作者 Xueqin PENG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第2期529-548,共20页
The paper deals with the following planar Schrödinger-Poisson system{-Δu+λu+φu=f(u), in ℝ2,-Δuφ=u2,in ℝ2,fR2u2dx=a2,u∈H1(ℝ2),where a∈(0,1),λ∈ℝis an undetermined parameter which... The paper deals with the following planar Schrödinger-Poisson system{-Δu+λu+φu=f(u), in ℝ2,-Δuφ=u2,in ℝ2,fR2u2dx=a2,u∈H1(ℝ2),where a∈(0,1),λ∈ℝis an undetermined parameter which appears as a Lagrange multiplier and f satisfies the exponential critical growth.Under suitable conditions on f,we manage to establish such critical points which emerge as a local minimizer or correspond to a mountain pass.Furthermore,by using genus theory,we obtain infinitely many solutions.The proofs are based upon the reduction method by working on a natural constraint,which is introduced by Bartsch and Soave[J Funct Anal,2017,272:4998–5037].Our results complement the results made by Cingolani and Jeanjean[SIAM J Math Anal,2019,51:3533–3568]where handle the Sobolev subcritical case. 展开更多
关键词 Schrödinger-Poisson system normalized solution exponential critical growth variational methods
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Casting computational fluid mechanics into a convex quadratic optimization framework 认领 引用
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作者 Hussam Sababha Haithem Taha Mohammed Daqaq 《Theoretical & Applied Mechanics Letters》 EI CAS CSCD 2026年第3期127-131,共5页
We employ the principle of a minimum pressure gradient to transform problems in unsteady computational fluid dynamics(CFD)into a convex optimization framework subject to linear constraints.This formulation permits sol... We employ the principle of a minimum pressure gradient to transform problems in unsteady computational fluid dynamics(CFD)into a convex optimization framework subject to linear constraints.This formulation permits solving,for the first time,CFD problems efficiently via well-established quadratic programming tools.The proposed approach is demonstrated via three benchmark examples.In particular,through comparison with traditional CFD tools,the proposed framework is capable of predicting the flow field in a lid-driven cavity,in a uniform pipe(Poiseuille flow),and that past a backward facing step.The results highlight the potential of the method as a simple,robust,and potentially transformative alternative to traditional CFD approaches. 展开更多
关键词 Computational methods Convex optimization Variational methods Principle of minimum pressure gradient
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Existence of Ground State Solutions to Nonlinear Schrödinger-Poisson System with Doping Profile and Coercive Potential 认领 引用
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作者 HAO Xiaodong HUANG Shuibo ZHANG Huanhuan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2026年第3期281-290,共10页
This paper investigates the existence of ground state solutions to the following nonlinear Schrödinger-Poisson system by variational methods{-Δu+ωu+V(x)u+eФu=|u|p-2u,x∈R3,-ΔФ=e/2(u2-ρ(x)),x∈R3... This paper investigates the existence of ground state solutions to the following nonlinear Schrödinger-Poisson system by variational methods{-Δu+ωu+V(x)u+eФu=|u|p-2u,x∈R3,-ΔФ=e/2(u2-ρ(x)),x∈R3,provided that ρ(x)≥0 and e2‖ρ‖6/5≤ρ0with ρ0>0 small enough,where 40 denotes a coupling constant,ω>0 is a Lagrange multiplier,the potential V(x)is coercive and the doping profile ρ(x)satisfies appropriate decay conditions.The introduction of ρ(x)compromises the coercivity of the energy functional.Therefore,we establish the existence of ground state solutions by considering the minimization problem on Nehari manifold. 展开更多
关键词 doping profile ground state solution Nehari manifold variational methods
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Research on the discrete variational method for a Birkhoffian system 认领 引用 被引量：2
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作者 刘世兴 花巍 郭永新 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第6期328-332,共5页
In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structure... In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system. 展开更多
关键词 Birkhoff＇s equations discrete variational methods general symplectic structure discrete Birkhoff＇s equations
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Ground State Normalized Solution for Nonhomogeneous Schrödinger-Poisson-Slater Equations with Potential 认领 引用
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作者 QIU Shuang-shuang XU Li-ping 《Chinese Quarterly Journal of Mathematics》 2026年第2期147-161,共15页
In this paper,we primarily investigate the existence of ground state normalized solutions to the following nonhomogeneous Schrödinger-Poisson-Slater equation:−Δu+λu+V(∣x∣)u+(∣x∣−1∗∣u∣2)u=g(u)+h(∣x... In this paper,we primarily investigate the existence of ground state normalized solutions to the following nonhomogeneous Schrödinger-Poisson-Slater equation:−Δu+λu+V(∣x∣)u+(∣x∣−1∗∣u∣2)u=g(u)+h(∣x∣)in R3,∫R3∣u∣2dx=m,00 is prescribed.Under suitable assumptions on V(|x|)and h(|x|),and assuming that the nonlinear term g is mass subcritical,we establish the existence of a ground state normalized solution through variational methods,thereby extending previous results in the literature. 展开更多
关键词 Nonlinear Schrödinger-Poisson-Slater equations Ground state normalized solutions Variational methods Potential Perturbation
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Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model 认领 引用 被引量：15
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作者 MO Jiaqi WANG Hui +1 位作者 LIN Wantao LIN Yihua 《Acta Oceanologica Sinica》 SCIE CAS 2005年第5期35-38,共4页
A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conce... A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method. 展开更多
关键词 nonlinear variational iteration method E1 Niйo phenomenon
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Variational method based robust adaptive control for a guided spinning rocket 认领 引用 被引量：9
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作者 Zhongjiao Shi Liangyu Zhao Zhijie Liu 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2021年第3期164-175,共12页
In this paper,a robust adaptive controller is designed for a guided spinning rocket,whose dynamics presents the characteristics of pitch-yaw cross coupling,fast time-varying aerodynamics parameters and wide flight env... In this paper,a robust adaptive controller is designed for a guided spinning rocket,whose dynamics presents the characteristics of pitch-yaw cross coupling,fast time-varying aerodynamics parameters and wide flight envelop.First,a coupled nonlinear six-degree-of-freedom equation of motion for a guided spinning rocket is developed,and the lateral acceleration motion is modeled as a control plant with time-varying matched uncertainties and unmodeled dynamics.Then,a robust adaptive control method is proposed by combining Bregman divergence and variational method to achieve fast adaption and maintain bounded tracking.The stability of the resulting closed-loop system is proved,and the ultimate bound and convergence rate are also analyzed.Finally,numerical simulations are performed for a single operating point and the whole flight trajectory to show the robustness and adaptability of the proposed method with respect to timevarying uncertainties and unmodeled dynamics. 展开更多
关键词 Autopilot design Guided spinning rockets Robust adaptive control Second-order adaptive law Variational method
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Three-Dimensional Wind Field Retrieved from Dual-Doppler Radar Based on a Variational Method:Refinement of Vertical Velocity Estimates 认领 引用 被引量：3
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作者 Chenbin XUE Zhiying DING +1 位作者 Xinyong SHEN Xian CHEN 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2022年第1期145-160,共16页
In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through min... In this paper,a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps.First,the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method,avoiding a weighting parameter specification step.Compared with conventional dual-Doppler wind synthesis approaches,this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process,which is one of the main sources of errors.Then,through the accelerated Liebmann method,the vertical velocity is further reestimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause.The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation.Compared with the method proposed by O’Brien,this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability.Furthermore,the method proposed in this paper is applied to Doppler radar observation of a squall line process.It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display(VAD)method,and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations.There is a good correspondence between the divergence field of the derived wind field and the vertical velocity.And,the horizontal and vertical circulations within and around the squall line,as well as strong updrafts,the associated downdrafts,and associated rear inflow of the bow echo,are analyzed well.It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations. 展开更多
关键词 dual-Doppler radar three-dimensional wind a variational method vertical velocity wind synthesis
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Variational iteration method for solving compressible Euler equations 认领 引用 被引量：4
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作者 赵国忠 蔚喜军 +1 位作者 徐云 朱江 《Chinese Physics B》 SCIE EI CAS 2010年第7期28-34,共7页
This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification o... This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient. 展开更多
关键词 variational iteration method compressible Euler equations approximate analytic solu-tions Lagrange multiplier
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General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off 认领 引用 被引量：4
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作者 Shiguo XIAO Yuan QI Pan XIA 《Journal of Zhejiang University-SCIENCE A》 SCIE EI CAS CSCD 2023年第5期432-449,共18页
According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach,a general closed-form solution to seismic and static active earth pressure on the walls,which considers shear and ten... According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach,a general closed-form solution to seismic and static active earth pressure on the walls,which considers shear and tension failure of the retained soil,is put forward using a variational calculus method.The application point of the active resultant force specified in the proposed method is explained with a clear physical meaning related to possible movement modes of the walls.In respect of the derived nine dependent equations reflecting the functional characteristics of the earth pressure,the proposed method can be performed easily via an implicit strategy.There are 13 basic factors related to the retained soils,walls,and external loads to be involved in the proposed method.The tension crack segment of the slip surface is obviously influenced by these parameters,apart from vertical seismic coefficient and geometric bounds of the surcharge,but the shear slip segment maintains an approximately planar shape almost uninfluenced by these parameters.Noticeably,the proposed method quantitatively reflects that the resultant of the active earth pressure is always within a limited range under different possible movements of the same wall. 展开更多
关键词 Active earth pressure Tensile strength cut-off Variational calculus method Pseudo-static method Strip surcharge
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An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems 认领 引用 被引量：3
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作者 Han Yin Xiao-Jing Liu Teng-Fei Zhang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2024年第4期29-45,共17页
The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-... The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs.This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard.The algorithm evenly distributes the response matrix sets among processors during the matrix formation process,thus enabling independent construction without communication.Once the formation tasks are completed,a collective operation merges and shares the matrix sets among the processors.For the solution process,the problem domain is decomposed into subdomains assigned to specific processors,and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation.Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries.The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases.Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations.The parallelization of HVNM results in eigenvalue errors of 31 pcm/-90 pcm and fission rate RMS errors of 1.22%/0.66%,respectively,for the 3D KAIST problem and the 3D JRR-3 problem.In addition,the parallel algorithm significantly reduces computation time,with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem. 展开更多
关键词 Neutron transport Variational nodal method Parallelization KAIST JRR-3
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GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS 认领 引用 被引量：2
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作者 盛东发 程昌钧 扶名福 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第4期381-389,共9页
From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given.... From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids. 展开更多
关键词 viscoelastic solid with void variational integral method generalized variational principle generalized potential energy principle Timoshenko beam
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VARIATIONAL PRINCIPLES OF FLUID FULLFILLED ELASTIC SOLIDS 认领 引用 被引量：1
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作者 石志飞 黄淑萍 章梓茂 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第3期262-268,共7页
The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational pr... The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up. 展开更多
关键词 fluid full-filled elastic solids variational integral method variational principles generalized variational principles
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Variational iteration method for solving time-fractional diffusion equations in porous the medium 认领 引用 被引量：6
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作者 吴国成 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期118-122,共5页
The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models... The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order. 展开更多
关键词 time-fractional diffusion equation Captuo derivative Riemann-Liouville derivative,variational iteration method Laplace transform
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Robust SLAM localization method based on improved variational Bayesian filtering 认领 引用 被引量：1
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作者 Zhai Hongqi Wang Lihui +1 位作者 Cai Tijing Meng Qian 《Journal of Southeast University(English Edition)》 EI CAS 2022年第4期340-349,共10页
Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outli... Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outliers,or unknown and time-varying noise statistical characteristics,a robust SLAM method based on the improved variational Bayesian adaptive Kalman filtering(IVBAKF)is proposed.First,the measurement noise covariance is estimated using the variable Bayesian adaptive filtering algorithm.Then,the estimated covariance matrix is robustly processed through the weight function constructed in the form of a reweighted average.Finally,the system updates are iterated multiple times to further gradually correct the state estimation error.Furthermore,to observe features at different depths,a feature measurement model containing depth parameters is constructed.Experimental results show that when the measurement noise does not obey the Gaussian distribution and there are outliers in the measurement information,compared with the variational Bayesian adaptive SLAM method,the positioning accuracy of the proposed method is improved by 17.23%,20.46%,and 17.76%,which has better applicability and robustness to environmental disturbance. 展开更多
关键词 underwater navigation and positioning non-Gaussian distribution time-varying noise variational Bayesian method simultaneous localization and mapping(SLAM)
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A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems 认领 引用 被引量：3
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作者 Jufeng Wang Yong Wu +1 位作者 Ying Xu Fengxin Sun 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第4期341-356,共16页
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
关键词 Dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method interpolating variational multiscale element-free Galerkin(VMIEFG)method dimension splitting method singularly perturbed convection-diffusion problems
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