Ultrasound is a low-cost,non-invasive and real-time imaging modality that has proved popular for many medical applications.Unfortunately,the acquired ultrasound images are often corrupted by speckle noise from scatter...Ultrasound is a low-cost,non-invasive and real-time imaging modality that has proved popular for many medical applications.Unfortunately,the acquired ultrasound images are often corrupted by speckle noise from scatterers smaller than ultrasound beam wavelength.The signal-dependent speckle noise makes visual observation difficult.In this paper,we propose a patch-based low-rank approach for reducing the speckle noise in ultrasound images.After constructing the patch group of the ultrasound images by the block-matching scheme,we establish a variational model using the weighted nuclear norm as a regularizer for the patch group.The alternating direction method of multipliers(ADMM)is applied for solving the established nonconvex model.We return all the approximate patches to their original locations and get the final restored ultrasound images.Experimental results are given to demonstrate that the proposed method outperforms some existing state-of-the-art methods in terms of visual quality and quantitative measures.展开更多
Consider the inverse scattering problem in terms of Helmholtz equation.We study a simply connected domain with oblique derivative boundary condition.In the case of constant l,given a finite number of incident wave,the...Consider the inverse scattering problem in terms of Helmholtz equation.We study a simply connected domain with oblique derivative boundary condition.In the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field data.We propose a Newton method which is based on the nonlinear boundary integral equation.After computing the Fr´echet derivatives with respect to the unknown boundary,the nonlinear equation is transformed to its linear form,then we show the iteration scheme for the inverse problem.We conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.展开更多
This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usua...This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usually used in formulating the Navier-Stokes(N-S)equations,and there are two major concerns in constructing the corresponding BGK model.One is the change of the convective velocities in the N-S equations,which can be reflected through modification of the gas streaming velocity.The other one is the necessity to account for the effect of the additional Coriolis and centrifugal forces.Here,a specifically-designed acceleration term is added into the modified Boltzmann equation so that the source effects can be naturally included into the gas evolution process and the resulted fluxes.Under the finitevolume framework,the constructed BGK model is locally solved at each cell interface and then the numerical fluxes can be evaluated.When employing the BGK scheme,it is sometimes found that the calculated spatial derivatives of the initial and equilibrium distribution functions are sensitive to the mesh quality especially in complex rotating flow applications,which may significantly influence flux evaluation.Therefore,an improved approach for computing these slopes is adopted,through which the modeling capability for viscous flows is enhanced.For validation,several numerical examples are presented.The computed results show that the present method can be well applied to a wide range of flows in rotating machinery with favorable accuracy.展开更多
We propose two variants of tailored finite point(TFP)methods for discretizing two dimensional singular perturbed eigenvalue(SPE)problems.A continuation method and an iterative method are exploited for solving discreti...We propose two variants of tailored finite point(TFP)methods for discretizing two dimensional singular perturbed eigenvalue(SPE)problems.A continuation method and an iterative method are exploited for solving discretized systems of equations to obtain the eigen-pairs of the SPE.We study the analytical solutions of two special cases of the SPE,and provide an asymptotic analysis for the solutions.The theoretical results are verified in the numerical experiments.The numerical results demonstrate that the proposed schemes effectively resolve the delta function like of the eigenfunctions on relatively coarse grid.展开更多
Taking vibration converter of intelligent damper for drill strings as the study object,this paper analyzes the influential factors of motion state of the ball and conducts an explicit dynamics simulation by establishi...Taking vibration converter of intelligent damper for drill strings as the study object,this paper analyzes the influential factors of motion state of the ball and conducts an explicit dynamics simulation by establishing a mechanics model of vibration converter.The study basis is Newton’s laws of motion,d’alembert’s principle and hertz contact theory.And we use world coordinate system,rotating coordinate system and Frenet coordinate system to deduce kinematics equations of vibration converter.The ultimate result demonstrates that the axial velocity and maximum contact stress change with the increment of ball diameter and helix angle.It also proves the validity of our derived kinematics and mechanical models and provides a good consultant value for the design and theoretical arithmetic of vibration converter for intelligent damper of drill strings.展开更多
The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic,thermodiffusive,elastic plate have been investigated in the context of linear theory of generalized thermodiffusion.After ...The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic,thermodiffusive,elastic plate have been investigated in the context of linear theory of generalized thermodiffusion.After developing the formal solution of the mathematical model consisting of partial differential equations,the secular equations have been derived by using relevant boundary conditions prevailing at the surfaces of the plate for symmetric and asymmetric wave modes in completely separate terms.The secular equations for long wavelength and short wavelength waves have also been deduced and discussed.The amplitudes of displacement components,temperature change and mass concentration under the Lamb wave propagation conditions have also been obtained.The complex transcendental secular equations have been solved by using a hybrid numerical technique consisting of irreducible Cardano method along with function iteration technique after splitting these in a system of real transcendental equations.The numerically simulated results in respect of phase velocity,attenuation coefficient,specific loss factor and relative frequency shift of thermoelastic diffusive waves have been presented graphically in the case of brass material.展开更多
Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is a...Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is an infinitedimensional Hermitian eigenvalue optimization problem with non-convex and low regularity.Usually,such a continuous optimization problem can be transformed into a large-scale discrete optimization problem by using the finite element methods.We use a subspace technique to reduce the scale of discrete problem,which is really effective to deal with the large-scale problem.To overcome the difficulties caused by the low regularity and non-convexity,we creatively introduce several new artificial variables to transform the non-convex problem into a convex linear semidefinite programming.By introducing linear approximation vectors,this linear semidefinite programming can be approximated by a very simple linear relaxation problem.Moreover,we theoretically prove this approximation.Our proposed algorithm is used to optimize the photonic band gaps of two-dimensional Gallium Arsenide-based photonic crystals as an application.The results of numerical examples show the effectiveness of our proposed algorithm,while they also provide several optimized photonic crystal structures with a desired wide-band-gap.In addition,our proposed algorithm provides a technical way for solving a kind of PDE constrained fractional optimization problems with a generalized eigenvalue constraint.展开更多
A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further c...A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical experiments.Especially, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.展开更多
In this paper,we propose a finite element time-domain(FETD)method for the Maxwell’s equations in chiral metamaterials(CMMs).The time-domain model equations are constructed by the auxiliary differential equations(ADEs...In this paper,we propose a finite element time-domain(FETD)method for the Maxwell’s equations in chiral metamaterials(CMMs).The time-domain model equations are constructed by the auxiliary differential equations(ADEs)method.The source excitation method entitled total-field and scattered-field(TF/SF)decomposition technique is applied to FETD method for the first time in simulating the propagation of electromagnetic wave in CMMs,based on which a unified ADE-FETD-UPMLTF/SF scheme is proposed to simulate the wave in CMMs.The following properties of CMMs can be observed successfully from the numerical experiments based on our method,i.e.,the ability of the polarization rotation,and the negative phase velocity.The amplitude of reflected wave can effectively be controlled by the physical parameters of CMMs.展开更多
This paper investigates two methods of coupling fluids across an interface,motivated by air-sea interaction in application codes.One method is for sequential configurations,where the air code module in invoked over so...This paper investigates two methods of coupling fluids across an interface,motivated by air-sea interaction in application codes.One method is for sequential configurations,where the air code module in invoked over some time interval prior to the sea module.The other method is for concurrent setups,in which the air and sea modules run in parallel.The focus is the temporal representation of air-sea fluxes.The methods we study conserve moments of the fluxes,with an arbitrary order of accuracy possible in time.Different step sizes are allowed for the two fluid codes.An a posteriori stability indicator is defined,which can be computed efficiently on-the-fly over each coupling interval.For a model of two coupled fluids with natural heat convection,using finite elements in space,we prove the sufficiency of our stability indicator.Under certain conditions,we also prove that stability can be enforced by iteration when the coupling interval is small enough.In particular,for solutions in a certain class,we show that the step size scaling is no worse than O(h)in three dimensions of space,where Oh is a mesh parameter.This is a sharper result than what has been shown previously for related algorithms with finite element methods.Computational examples illustrate the behavior of the algorithms under a wide variety of configurations.展开更多
The Ellipsoidal Statistical model(ES-model)and the Shakhov model(S-model)were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heatflux.With the introduction of ...The Ellipsoidal Statistical model(ES-model)and the Shakhov model(S-model)were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heatflux.With the introduction of a new pa-rameter to combine the ES-model and S-model,a generalized kinetic model can be developed.This new model can give the correct Navier-Stokes equations in the con-tinuumflow regime.Through the adjustment of the new parameter,it provides abun-dant dynamic effect beyond the ES-model and S-model.Changing the free parameter,the physical performance of the new model has been tested numerically.The unified gas kinetic scheme(UGKS)is employed for the study of the new model.In transitionflow regime,many physical problems,i.e.,the shock structure and micro-flows,have been studied using the generalized model.With a careful choice of the free parameter,good results can be achieved for most test cases.Due to the property of the Boltz-mann collision integral,the new parameter in the generalized kinetic model cannot be fully determined.It depends on the specific problem.Generally speaking,the S-model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model,while ES-model performs better in the cases where theflow is mostly driven by temperature gradient,such as a channelflow with large boundary temperature variation at high Knudsen number.展开更多
An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro ge-netic algorithm.For this purpose,the general equilibrium equ...An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro ge-netic algorithm.For this purpose,the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into ac-count,respectively,are formulated.The compatibility equations in terms of forces are explicitly presented using the singular value decomposition(SVD)technique.Then governing equations with unknown reaction forces and initial elongations are derived.Next,the micro genetic algorithm(MGA)is used to properly identify the site and ex-tent of multiple damage cases in truss structures.In order to verify the accuracy and the superiority of the proposed damage detection technique,the numerical solutions are presented for the planar and space truss models.The numerical results indicate that the combination of the force method and the MGA can provide a reliable tool to accurately and efficiently identify the multiple damages of the truss structures.展开更多
Phase change in ice-water systems in the geometry of horizontal cylindrical annulus with constant inner wall temperature and adiabatic outer wall is modeled with an enthalpy-based mixture model.Solidification and melt...Phase change in ice-water systems in the geometry of horizontal cylindrical annulus with constant inner wall temperature and adiabatic outer wall is modeled with an enthalpy-based mixture model.Solidification and melting phenomena under different temperature conditions are analyzed through a sequence of numerical calculations.In the case of freezing of water,the importance of convection and conduction as well as the influence of cold pipe temperature on time for the complete solidification are examined.As for the case of melting of ice,the influence of the inner pipe wall temperature on the shape of the ice-water interface,the flow and temperature fields in the liquid,the heat transfer coefficients and the rate of melting are analyzed.The results of numerical calculations point to good qualitative agreement with the available experimental and other numerical results.展开更多
In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)...In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.展开更多
In this paper,a novel unconditionally energy stable Smoothed Particle Hydrodynamics(SPH)method is proposed and implemented for incompressible fluid flows.In this method,we apply operator splitting to break the momentu...In this paper,a novel unconditionally energy stable Smoothed Particle Hydrodynamics(SPH)method is proposed and implemented for incompressible fluid flows.In this method,we apply operator splitting to break the momentum equation into equations involving the non-pressure term and pressure term separately.The idea behind the splitting is to simplify the calculation while still maintaining energy stability,and the resulted algorithm,a type of improved pressure correction scheme,is both efficient and energy stable.We show in detail that energy stability is preserved at each full-time step,ensuring unconditionally numerical stability.Numerical examples are presented and compared to the analytical solutions,suggesting that the proposed method has better accuracy and stability.Moreover,we observe that if we are interested in steady-state solutions only,our method has good performance as it can achieve the steady-state solutions rapidly and accurately.展开更多
A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high comput...A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.展开更多
We propose a robust approximate solver for the hydro-elastoplastic solid material,a general constitutive law extensively applied in explosion and high speed impact dynamics,and provide a natural transformation between...We propose a robust approximate solver for the hydro-elastoplastic solid material,a general constitutive law extensively applied in explosion and high speed impact dynamics,and provide a natural transformation between the fluid and solid in the case of phase transitions.The hydrostatic components of the solid is described by a family of general Mie-Gruneisen equation of state(EOS),while the deviatoric component includes the elastic phase,linearly hardened plastic phase and fluid phase.The approximate solver provides the interface stress and normal velocity by an iterative method.The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state.The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds.Several numerical examples,including Riemann problems,shock-bubble interactions,implosions and high speed impact applications,are presented to validate the approximate solver.展开更多
In this research,motion and deformation of a red blood cell(RBC)in a microchannel with stenosis is investigated by combined Lattice Boltzmann-Immersed Boundary method.The fluid flow occurs due to the pressure differen...In this research,motion and deformation of a red blood cell(RBC)in a microchannel with stenosis is investigated by combined Lattice Boltzmann-Immersed Boundary method.The fluid flow occurs due to the pressure difference between the inlet and the outlet of the microchannel.The immersed boundary algorithm guaranteed that there is no relative velocity between the RBC and fluid.Therefore,mass transfer along the immersed border does not occur.It can be seen that the healthy RBC has more deformation and passes the stenosis easier while the sick one passes the stenosis with less deformation and returns to its initial state faster.Increasing the pressure gradient(i.e.,increasing Reynolds number)would cause more deformation of the RBC.It is found that a healthy RBC moves faster than a sick one along the microchannel.Blood pressure increases due to the presence of stenosis and low deformable RBCs.It is the reason of many serious diseases including cardiovascular diseases.The results of this paper were compared to the previous valid results and good agreements were observed.展开更多
In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundatio...In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading.The normal mode analysis is used to obtain the analytical expressions for the displacements,stresses and temperature distributions.The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags.Effect of phase-lags,reinforcement and initial stress on the field quantities is shown graphically.The results due to the coupled thermoelasticity theory,Lord and Shulman’s theory,and Green and Naghdi’s theory have been derived as limiting cases.The graphs illustrated that the initial stress,the reinforcement and phase-lags have great effects on the distributions of the field quantities.展开更多
In this paper,we consider the numerical stability of gravity-capillary waves generated by a localized pressure in water of finite depth based on the forced Korteweg-de Vries(FKdV)framework and the polynomial chaos.The...In this paper,we consider the numerical stability of gravity-capillary waves generated by a localized pressure in water of finite depth based on the forced Korteweg-de Vries(FKdV)framework and the polynomial chaos.The stability studies are focused on the symmetric solitary wave for the subcritical flow with the Bond number greater than one third.When its steady symmetric solitarywave-like solutions are randomly perturbed,the evolutions of some waves show stability in time regardless of the randomness while other waves produce unstable fluctuations.By representing the perturbation with a random variable,the governing FKdV equation is interpreted as a stochastic equation.The polynomial chaos expansion of the random solution has been used for the study of stability in two ways.First it allows us to identify the stable solution of the stochastic governing equation.Secondly it is used to construct upper and lower bounding surfaces for unstable solutions,which encompass the fluctuations of waves.展开更多
基金supported by NSF of Jiangsu Province(No.BK20181483),NSFC(Nos.11671002,11701079,61731009)the Fundamental Research Funds for the Central Universities,and Science and Technology Commission of Shanghai Municipality(Nos.19JC1420102,18dz2271000)Hai Yan project,Lianyungang 521 project and NSF of HHIT(No.Z2017004).
文摘Ultrasound is a low-cost,non-invasive and real-time imaging modality that has proved popular for many medical applications.Unfortunately,the acquired ultrasound images are often corrupted by speckle noise from scatterers smaller than ultrasound beam wavelength.The signal-dependent speckle noise makes visual observation difficult.In this paper,we propose a patch-based low-rank approach for reducing the speckle noise in ultrasound images.After constructing the patch group of the ultrasound images by the block-matching scheme,we establish a variational model using the weighted nuclear norm as a regularizer for the patch group.The alternating direction method of multipliers(ADMM)is applied for solving the established nonconvex model.We return all the approximate patches to their original locations and get the final restored ultrasound images.Experimental results are given to demonstrate that the proposed method outperforms some existing state-of-the-art methods in terms of visual quality and quantitative measures.
基金foundation of Jinling Institute of Technology(No.jit-b-201524)the Science Foundation of Jinling Institute of Technology(No.Jit-fhxm-201809).
文摘Consider the inverse scattering problem in terms of Helmholtz equation.We study a simply connected domain with oblique derivative boundary condition.In the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field data.We propose a Newton method which is based on the nonlinear boundary integral equation.After computing the Fr´echet derivatives with respect to the unknown boundary,the nonlinear equation is transformed to its linear form,then we show the iteration scheme for the inverse problem.We conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.
基金This work has been supported by the National Natural Science Foundation of China(Grant No.11372135)the National Basic Research Program of China(“973”Project)(Grant No.2014CB046200).
文摘This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usually used in formulating the Navier-Stokes(N-S)equations,and there are two major concerns in constructing the corresponding BGK model.One is the change of the convective velocities in the N-S equations,which can be reflected through modification of the gas streaming velocity.The other one is the necessity to account for the effect of the additional Coriolis and centrifugal forces.Here,a specifically-designed acceleration term is added into the modified Boltzmann equation so that the source effects can be naturally included into the gas evolution process and the resulted fluxes.Under the finitevolume framework,the constructed BGK model is locally solved at each cell interface and then the numerical fluxes can be evaluated.When employing the BGK scheme,it is sometimes found that the calculated spatial derivatives of the initial and equilibrium distribution functions are sensitive to the mesh quality especially in complex rotating flow applications,which may significantly influence flux evaluation.Therefore,an improved approach for computing these slopes is adopted,through which the modeling capability for viscous flows is enhanced.For validation,several numerical examples are presented.The computed results show that the present method can be well applied to a wide range of flows in rotating machinery with favorable accuracy.
基金the National Natural Science Foundation of China through NSFC No.11371218 and No.91330203the second author was supported by the National Science Council of Taiwan through NSC 102-2115-M005-005.
文摘We propose two variants of tailored finite point(TFP)methods for discretizing two dimensional singular perturbed eigenvalue(SPE)problems.A continuation method and an iterative method are exploited for solving discretized systems of equations to obtain the eigen-pairs of the SPE.We study the analytical solutions of two special cases of the SPE,and provide an asymptotic analysis for the solutions.The theoretical results are verified in the numerical experiments.The numerical results demonstrate that the proposed schemes effectively resolve the delta function like of the eigenfunctions on relatively coarse grid.
基金This work was supported by National Natural Science Fund of China(51222406,51004082)New Century Excellent Talents in University of China(NCET-12-1061)+1 种基金Scientific Research Innovation Team Project of Sichuan Colleges and Universities(12TD007),Sichuan Youth Sci-tech Fund(2011JQ0020)the 7th graduate innovation funds of Southwest Petroleum University(GIFSS0720),and Special thanks to PhD C.S.Shi.
文摘Taking vibration converter of intelligent damper for drill strings as the study object,this paper analyzes the influential factors of motion state of the ball and conducts an explicit dynamics simulation by establishing a mechanics model of vibration converter.The study basis is Newton’s laws of motion,d’alembert’s principle and hertz contact theory.And we use world coordinate system,rotating coordinate system and Frenet coordinate system to deduce kinematics equations of vibration converter.The ultimate result demonstrates that the axial velocity and maximum contact stress change with the increment of ball diameter and helix angle.It also proves the validity of our derived kinematics and mechanical models and provides a good consultant value for the design and theoretical arithmetic of vibration converter for intelligent damper of drill strings.
文摘The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic,thermodiffusive,elastic plate have been investigated in the context of linear theory of generalized thermodiffusion.After developing the formal solution of the mathematical model consisting of partial differential equations,the secular equations have been derived by using relevant boundary conditions prevailing at the surfaces of the plate for symmetric and asymmetric wave modes in completely separate terms.The secular equations for long wavelength and short wavelength waves have also been deduced and discussed.The amplitudes of displacement components,temperature change and mass concentration under the Lamb wave propagation conditions have also been obtained.The complex transcendental secular equations have been solved by using a hybrid numerical technique consisting of irreducible Cardano method along with function iteration technique after splitting these in a system of real transcendental equations.The numerically simulated results in respect of phase velocity,attenuation coefficient,specific loss factor and relative frequency shift of thermoelastic diffusive waves have been presented graphically in the case of brass material.
基金supported by National Natural Science Foundation of China(Grant Nos.12171052 and 11871115)BUPT Excellent Ph.D.Students Foundation(Grant No.CX2021320).
文摘Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is an infinitedimensional Hermitian eigenvalue optimization problem with non-convex and low regularity.Usually,such a continuous optimization problem can be transformed into a large-scale discrete optimization problem by using the finite element methods.We use a subspace technique to reduce the scale of discrete problem,which is really effective to deal with the large-scale problem.To overcome the difficulties caused by the low regularity and non-convexity,we creatively introduce several new artificial variables to transform the non-convex problem into a convex linear semidefinite programming.By introducing linear approximation vectors,this linear semidefinite programming can be approximated by a very simple linear relaxation problem.Moreover,we theoretically prove this approximation.Our proposed algorithm is used to optimize the photonic band gaps of two-dimensional Gallium Arsenide-based photonic crystals as an application.The results of numerical examples show the effectiveness of our proposed algorithm,while they also provide several optimized photonic crystal structures with a desired wide-band-gap.In addition,our proposed algorithm provides a technical way for solving a kind of PDE constrained fractional optimization problems with a generalized eigenvalue constraint.
基金National Natural Science Foundation of China(Grant No.11971412)Key Project of Education Department of Hunan Province(Grant No.20A484)Project of Hunan National Center for Applied Mathematics(Grant No.2020ZYT003).
文摘A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical experiments.Especially, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.
基金supported partially by the Science and Technology Development Fund,Macao SAR(0070/2019/A2)and National Natural Science Foundation of China,Grant No.11701598,Scientific Research Fund of Hunan Provincial Science and Technology Department(No.2018WK4006)NSFC Projects No.11771371,and Key Project of Hunan Education Department No.18A056.
文摘In this paper,we propose a finite element time-domain(FETD)method for the Maxwell’s equations in chiral metamaterials(CMMs).The time-domain model equations are constructed by the auxiliary differential equations(ADEs)method.The source excitation method entitled total-field and scattered-field(TF/SF)decomposition technique is applied to FETD method for the first time in simulating the propagation of electromagnetic wave in CMMs,based on which a unified ADE-FETD-UPMLTF/SF scheme is proposed to simulate the wave in CMMs.The following properties of CMMs can be observed successfully from the numerical experiments based on our method,i.e.,the ability of the polarization rotation,and the negative phase velocity.The amplitude of reflected wave can effectively be controlled by the physical parameters of CMMs.
文摘This paper investigates two methods of coupling fluids across an interface,motivated by air-sea interaction in application codes.One method is for sequential configurations,where the air code module in invoked over some time interval prior to the sea module.The other method is for concurrent setups,in which the air and sea modules run in parallel.The focus is the temporal representation of air-sea fluxes.The methods we study conserve moments of the fluxes,with an arbitrary order of accuracy possible in time.Different step sizes are allowed for the two fluid codes.An a posteriori stability indicator is defined,which can be computed efficiently on-the-fly over each coupling interval.For a model of two coupled fluids with natural heat convection,using finite elements in space,we prove the sufficiency of our stability indicator.Under certain conditions,we also prove that stability can be enforced by iteration when the coupling interval is small enough.In particular,for solutions in a certain class,we show that the step size scaling is no worse than O(h)in three dimensions of space,where Oh is a mesh parameter.This is a sharper result than what has been shown previously for related algorithms with finite element methods.Computational examples illustrate the behavior of the algorithms under a wide variety of configurations.
基金This work was supported by Hong Kong Research Grant Council(621011,620813)SRFI11SC05 at HKUST and the National Natural Science Funds for Distin-guished Young Scholar group under Grant No.11221061.
文摘The Ellipsoidal Statistical model(ES-model)and the Shakhov model(S-model)were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heatflux.With the introduction of a new pa-rameter to combine the ES-model and S-model,a generalized kinetic model can be developed.This new model can give the correct Navier-Stokes equations in the con-tinuumflow regime.Through the adjustment of the new parameter,it provides abun-dant dynamic effect beyond the ES-model and S-model.Changing the free parameter,the physical performance of the new model has been tested numerically.The unified gas kinetic scheme(UGKS)is employed for the study of the new model.In transitionflow regime,many physical problems,i.e.,the shock structure and micro-flows,have been studied using the generalized model.With a careful choice of the free parameter,good results can be achieved for most test cases.Due to the property of the Boltz-mann collision integral,the new parameter in the generalized kinetic model cannot be fully determined.It depends on the specific problem.Generally speaking,the S-model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model,while ES-model performs better in the cases where theflow is mostly driven by temperature gradient,such as a channelflow with large boundary temperature variation at high Knudsen number.
基金This researchwas supported by a grant(14CTAP-C077285-01-000000)from Infrastructure and transportation technology promotion research Program funded by MOLIT(Min-istry of Land,Infrastructure and Transport)of Korean government and a grant(2013-R1A12058208)from NRF(National Research Foundation of Korea)funded by MEST(Ministry of Education and Science Technology)of Korean government.
文摘An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro ge-netic algorithm.For this purpose,the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into ac-count,respectively,are formulated.The compatibility equations in terms of forces are explicitly presented using the singular value decomposition(SVD)technique.Then governing equations with unknown reaction forces and initial elongations are derived.Next,the micro genetic algorithm(MGA)is used to properly identify the site and ex-tent of multiple damage cases in truss structures.In order to verify the accuracy and the superiority of the proposed damage detection technique,the numerical solutions are presented for the planar and space truss models.The numerical results indicate that the combination of the force method and the MGA can provide a reliable tool to accurately and efficiently identify the multiple damages of the truss structures.
文摘Phase change in ice-water systems in the geometry of horizontal cylindrical annulus with constant inner wall temperature and adiabatic outer wall is modeled with an enthalpy-based mixture model.Solidification and melting phenomena under different temperature conditions are analyzed through a sequence of numerical calculations.In the case of freezing of water,the importance of convection and conduction as well as the influence of cold pipe temperature on time for the complete solidification are examined.As for the case of melting of ice,the influence of the inner pipe wall temperature on the shape of the ice-water interface,the flow and temperature fields in the liquid,the heat transfer coefficients and the rate of melting are analyzed.The results of numerical calculations point to good qualitative agreement with the available experimental and other numerical results.
基金The work is supported by the National Natural Science Foundation of China(No.11871441)Beijing Natural Science Foundation(No.1192003).
文摘In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.
基金This work is partially supported by King Abdullah University of Science and Technology(KAUST)through the grants BAS/1/1351-01,URF/1/4074-01,and URF/1/3769-01.
文摘In this paper,a novel unconditionally energy stable Smoothed Particle Hydrodynamics(SPH)method is proposed and implemented for incompressible fluid flows.In this method,we apply operator splitting to break the momentum equation into equations involving the non-pressure term and pressure term separately.The idea behind the splitting is to simplify the calculation while still maintaining energy stability,and the resulted algorithm,a type of improved pressure correction scheme,is both efficient and energy stable.We show in detail that energy stability is preserved at each full-time step,ensuring unconditionally numerical stability.Numerical examples are presented and compared to the analytical solutions,suggesting that the proposed method has better accuracy and stability.Moreover,we observe that if we are interested in steady-state solutions only,our method has good performance as it can achieve the steady-state solutions rapidly and accurately.
基金supported by the National Natural Science Foundation of China(Nos.11872220,11772119)the Natural Science Foundation of Shandong Province of China(Nos.ZR2017JL004,2019KJI009)。
文摘A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.
基金supports provided by the National Natural Science Foundation of China(Grant Nos.91630310,11421110001,and 11421101)and Science Challenge Project(No.TZ 2016002).
文摘We propose a robust approximate solver for the hydro-elastoplastic solid material,a general constitutive law extensively applied in explosion and high speed impact dynamics,and provide a natural transformation between the fluid and solid in the case of phase transitions.The hydrostatic components of the solid is described by a family of general Mie-Gruneisen equation of state(EOS),while the deviatoric component includes the elastic phase,linearly hardened plastic phase and fluid phase.The approximate solver provides the interface stress and normal velocity by an iterative method.The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state.The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds.Several numerical examples,including Riemann problems,shock-bubble interactions,implosions and high speed impact applications,are presented to validate the approximate solver.
文摘In this research,motion and deformation of a red blood cell(RBC)in a microchannel with stenosis is investigated by combined Lattice Boltzmann-Immersed Boundary method.The fluid flow occurs due to the pressure difference between the inlet and the outlet of the microchannel.The immersed boundary algorithm guaranteed that there is no relative velocity between the RBC and fluid.Therefore,mass transfer along the immersed border does not occur.It can be seen that the healthy RBC has more deformation and passes the stenosis easier while the sick one passes the stenosis with less deformation and returns to its initial state faster.Increasing the pressure gradient(i.e.,increasing Reynolds number)would cause more deformation of the RBC.It is found that a healthy RBC moves faster than a sick one along the microchannel.Blood pressure increases due to the presence of stenosis and low deformable RBCs.It is the reason of many serious diseases including cardiovascular diseases.The results of this paper were compared to the previous valid results and good agreements were observed.
文摘In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading.The normal mode analysis is used to obtain the analytical expressions for the displacements,stresses and temperature distributions.The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags.Effect of phase-lags,reinforcement and initial stress on the field quantities is shown graphically.The results due to the coupled thermoelasticity theory,Lord and Shulman’s theory,and Green and Naghdi’s theory have been derived as limiting cases.The graphs illustrated that the initial stress,the reinforcement and phase-lags have great effects on the distributions of the field quantities.
基金The authors are grateful to the anonymous referees for their valuable comments and suggestions.This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(20110005272).
文摘In this paper,we consider the numerical stability of gravity-capillary waves generated by a localized pressure in water of finite depth based on the forced Korteweg-de Vries(FKdV)framework and the polynomial chaos.The stability studies are focused on the symmetric solitary wave for the subcritical flow with the Bond number greater than one third.When its steady symmetric solitarywave-like solutions are randomly perturbed,the evolutions of some waves show stability in time regardless of the randomness while other waves produce unstable fluctuations.By representing the perturbation with a random variable,the governing FKdV equation is interpreted as a stochastic equation.The polynomial chaos expansion of the random solution has been used for the study of stability in two ways.First it allows us to identify the stable solution of the stochastic governing equation.Secondly it is used to construct upper and lower bounding surfaces for unstable solutions,which encompass the fluctuations of waves.
