Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofpropertie...Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofproperties allows MEE materials to respond to mechanical,electric,and magnetic stimuli,making them versatile forvarious applications.This paper investigates the static and time-harmonic field solutions induced by the surface loadin a three-dimensional(3D)multilayered transversally isotropic(TI)linear MEE layered solid.Green’s functionscorresponding to the applied uniform load(in both horizontal and vertical directions)are derived using the Fourier-Bessel series(FBS)system of vector functions.By virtue of this FBS method,two sets of first-order ordinarydifferential equations(i.e.,N-type and LM-type)are obtained,with the expansion coefficients being Love numbers.It is noted that the LM-type system corresponds to the MEE-coupled P-,SV-,and Rayleigh waves,while the N-typecorresponds to the purely elastic SH-and Love waves.By applying the continuity conditions across interfaces,the solutions for each layer of the structure(from the bottom to the top)are derived using the dual-variable andposition(DVP)method.This method(i.e.,DVP)is unconditionally stable when propagating solutions throughdifferent layers.Numerical examples illustrate the impact of load types,layering,and frequency on the response ofthe structure,as well as the accuracy and convergence of the proposed approach.The numerical results are usefulin designing smart devices made of MEE solids,which are applicable to engineering fields like renewable energy.展开更多
We develop a uniaxial optimal perfectly matched layer (opt PML) method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. W...We develop a uniaxial optimal perfectly matched layer (opt PML) method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. With this choice, the solution of the optimal PML problem not only converges exponentially to the solution of the original scatting problem, but also is insensitive to the thickness of the PML layer for sufficiently small parameter ε0. Numerical experiments are included to illustrate the competitive behavior of the proposed optimal method.展开更多
This paper introduces a novel method for fast calculating the electromagnetic forces in interior permanent magnet synchronous machines(IPMSMs)under pulse width modulation(PWM)voltage source inverter(VSI)supply based o...This paper introduces a novel method for fast calculating the electromagnetic forces in interior permanent magnet synchronous machines(IPMSMs)under pulse width modulation(PWM)voltage source inverter(VSI)supply based on the small-signal time-harmonic finite element analysis(THFEA),which has been successfully utilized for fast calculating the PWMinduced losses in silicon steel sheets and permanent magnets.Based on the small-signal THFEA,the functional relationships between high-frequency harmonic voltages(HFHVs)and corresponding airgap flux densities are established,which are used for calculating the flux density spectra caused by each HFHV in the PWM voltage spectra.Then,the superposition principle is applied for calculating the flux density spectra caused by fundamental currents and all HFHVs,which are converted to the electromagnetic force spectra at last.The relative errors between the force density spectra calculated with the proposed method and those obtained from traditional time-stepping finite element analysis(TSFEA)using PWM voltages as input are within 3.1%,while the proposed method is 24 times faster than the traditional TSFEA.展开更多
The uniqueness theorem of time-harmonic electromagnetic fields, which is the theoretical basis of boundary value problem (BVP) of electromagnetic fields, is reviewed. So far there are many versions of the statements a...The uniqueness theorem of time-harmonic electromagnetic fields, which is the theoretical basis of boundary value problem (BVP) of electromagnetic fields, is reviewed. So far there are many versions of the statements and proofs on the theorem. However, there exist some limitations and lack of strictness in these versions, for instance, the discussion of the uniqueness of solution without considering the existence of solution and the lack of strictness in the case of loss-less medium. In contrast with the traditional statements and proofs, this paper introduces some important conclusions on operator equation from modern theory of partial differential equation (PDE) and attempts to solve the problems on the existence and uniqueness of the solution to operator equation which is derived from Maxwell’s equations of time-harmonic electromagnetic fields. This method provides a novel and rigorous approach to discuss and solve the existence and uniqueness of the solution to time- harmonic fields in the new mathematical framework. Some important conclusions are presented.展开更多
A time-harmonic equivalent current dipole model is proposed to simulate EEG source which deals with the problem concerning the capacitance effect. The expressions of potentials in both homogeneous infinite dielectric ...A time-harmonic equivalent current dipole model is proposed to simulate EEG source which deals with the problem concerning the capacitance effect. The expressions of potentials in both homogeneous infinite dielectric medium and dielectric sphere on the electroquasistatic condition are presented. The potential in a 3-layer inhomogeneous spherical head is computed by using this model. The influences on potential produced by time-harmonic character and permittivity are discussed. The results show that potentials in dielectric sphere are affected by frequency and permittivity.展开更多
In this paper, we obtain optimal error estimates in both L^2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretize...In this paper, we obtain optimal error estimates in both L^2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L^2 error estimates into the L^2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.展开更多
We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R...We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.展开更多
In this paper,we consider a modified alternating positive semidefinite splitting preconditioner for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the tim...In this paper,we consider a modified alternating positive semidefinite splitting preconditioner for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current model.The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are studied for both simple and general topology.Numerical results demonstrate the effectiveness of the proposed preconditioner when it is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.展开更多
The aim of this work is to analyze the role of the impressed sources in determining the well or ill-posedness of time harmonic electromagnetic boundary value problems involving isotropic effective media.It is shown,in...The aim of this work is to analyze the role of the impressed sources in determining the well or ill-posedness of time harmonic electromagnetic boundary value problems involving isotropic effective media.It is shown,in particular,that,even if all interfaces are regular,the class of ill-posed problems can be very large in the presence of general square-integrable impressed sources.However,when a simple and realistic constraint is enforced on these sources,requiring that the support of the sources does not include any interface between a traditional medium and a metamaterial,among the problems here considered just those involving an interface between complementary materials remain ill-posed.These considerations have a very significant impact also on the approximability of the solution of well-posed problems since the numerical noise can introduce small fictitious sources even where the sources to be simulated are not present.These effects on finite element simulators are fully analyzed.Finally,we propose an algorithm that allows to obtain much better approximations of the solutions of the most critical wellposed problems.展开更多
Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting (APSS) iteration method for the saddle point problem arising from the fin...Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting (APSS) iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.展开更多
The scope of this paper is to show how a two-scale asymptotic analysis,based on a superposition principle,allows us to derive high order approximate boundary conditions for a scattering problem of a time-harmonic wave...The scope of this paper is to show how a two-scale asymptotic analysis,based on a superposition principle,allows us to derive high order approximate boundary conditions for a scattering problem of a time-harmonic wave by a thin and tangentially periodic multi-layered domain.The periods are assumed of the same order of the thickness.New terms like memory effect and variance-covariance ones are observed contrarily to the laminar case.As a result,optimal error estimates are obtained.展开更多
The dynamic behavior of a rectangular crack in a three-dimensional (3D) orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional (2D) Fourier trans...The dynamic behavior of a rectangular crack in a three-dimensional (3D) orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional (2D) Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.展开更多
Modifying the equivalent rotor resistivity with rotor end factor in 2-dimension(2-D)finite element analysis(FEA)is an effective way to analyze the 3-dimension(3-D)solid rotor problems.For the smooth solid rotor,five d...Modifying the equivalent rotor resistivity with rotor end factor in 2-dimension(2-D)finite element analysis(FEA)is an effective way to analyze the 3-dimension(3-D)solid rotor problems.For the smooth solid rotor,five different rotor end factors are discussed and compared with each other.It is theoretically clarified that the resistivity of rotor in 2-D FEA should be multiplied by the square of rotor end factors to take the 3-D end effect of solid rotor into account.For the slitted solid rotor,an improved rotor end factor is proposed based on the equivalent area algorithm of eddy currents in rotor,since the end factors of smooth solid rotor are not applicable.Finally,the time-harmonic finite element method(FEM)combined with the rotor end factor is applied to analyze the performance of solid rotor induction motor.The tested and computed results are in good agreement,which proves the effectiveness of rotor end factor for the simplication of 3-D solid rotor problems.展开更多
Dynamic stresses around three parallel cracks in an infinite elastic plate that is subjected to incident time-harmonic stress waves normal to the cracks have been solved. Using the Fourier transform technique, the bou...Dynamic stresses around three parallel cracks in an infinite elastic plate that is subjected to incident time-harmonic stress waves normal to the cracks have been solved. Using the Fourier transform technique, the boundary conditions are reduced to six simultaneous integral equations. To solve these equations, the differences of displacements inside the cracks are expanded in a series. The unknown coefficients in those series are solved using the Schmidt method such that the conditions inside the cracks are satisfied. Numerical calculations are carried out for some crack configurations.展开更多
We propose an adaptive strategy for solving high frequency Helmholtz scattering problems.The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into ...We propose an adaptive strategy for solving high frequency Helmholtz scattering problems.The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into the bounded domain.The parameters in the uniaxial PML method are determined by sharp a posteriori error estimates developed by Chen and Wu[8].An hp-adaptive finite element strategy is proposed to solve the uniaxial PML equation.Numerical experiments are included which indicate the desirable exponential decay property of the error.展开更多
In this paper,we consider the scattering problem of time-harmonic electromagnetic waves from an infinite cylinder having an open arc Γ and a bounded domain D in R^2 as cross section.We focus on the inverse scattering...In this paper,we consider the scattering problem of time-harmonic electromagnetic waves from an infinite cylinder having an open arc Γ and a bounded domain D in R^2 as cross section.We focus on the inverse scattering problem,that is,to reconstruct the shape of Γ and D from the far-field pattern by using the factorization method.Through establishing a mixed reciprocity relation,we prove that the scatters Γ and D can be uniquely determined by the far-field pattern.Furthermore,the mathematical basis is given to explain that the factorization method is feasible to our problem.At the end of this paper,we give some numerical examples to show the efficaciousness of the algorithms.展开更多
We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer.These models appear as first order approximations of the electromagnetic field.Th...We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer.These models appear as first order approximations of the electromagnetic field.They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer,that makes possible to replace the thin layer by approximate conditions.We present the advantages and the drawbacks of several approximations together with numerical validations and simulations.The main motivation of this work concerns the computation of electromagnetic field in biological cells.The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane,which provides a specific behavior of the electromagnetic field at low frequencies.展开更多
基金The National Science and Technology Council of Taiwan(Grant No.NSTC 111-2811-E-516 A49-534)provided financial support for this study。
文摘Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofproperties allows MEE materials to respond to mechanical,electric,and magnetic stimuli,making them versatile forvarious applications.This paper investigates the static and time-harmonic field solutions induced by the surface loadin a three-dimensional(3D)multilayered transversally isotropic(TI)linear MEE layered solid.Green’s functionscorresponding to the applied uniform load(in both horizontal and vertical directions)are derived using the Fourier-Bessel series(FBS)system of vector functions.By virtue of this FBS method,two sets of first-order ordinarydifferential equations(i.e.,N-type and LM-type)are obtained,with the expansion coefficients being Love numbers.It is noted that the LM-type system corresponds to the MEE-coupled P-,SV-,and Rayleigh waves,while the N-typecorresponds to the purely elastic SH-and Love waves.By applying the continuity conditions across interfaces,the solutions for each layer of the structure(from the bottom to the top)are derived using the dual-variable andposition(DVP)method.This method(i.e.,DVP)is unconditionally stable when propagating solutions throughdifferent layers.Numerical examples illustrate the impact of load types,layering,and frequency on the response ofthe structure,as well as the accuracy and convergence of the proposed approach.The numerical results are usefulin designing smart devices made of MEE solids,which are applicable to engineering fields like renewable energy.
基金The Major State Research Development Program (2005CB321701) of Chinathe NSF(10801063) of China
文摘We develop a uniaxial optimal perfectly matched layer (opt PML) method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. With this choice, the solution of the optimal PML problem not only converges exponentially to the solution of the original scatting problem, but also is insensitive to the thickness of the PML layer for sufficiently small parameter ε0. Numerical experiments are included to illustrate the competitive behavior of the proposed optimal method.
基金supported in part by the National Natural Science Foundation of China under projects 51907053by Natural Science Foundation of Jiangsu Province of China under Project BK20190489+1 种基金by the Fundamental Research Funds for the Central Universities under grant B200202167by the China Postdoctoral Science Foundation under grant no.2019M661708。
文摘This paper introduces a novel method for fast calculating the electromagnetic forces in interior permanent magnet synchronous machines(IPMSMs)under pulse width modulation(PWM)voltage source inverter(VSI)supply based on the small-signal time-harmonic finite element analysis(THFEA),which has been successfully utilized for fast calculating the PWMinduced losses in silicon steel sheets and permanent magnets.Based on the small-signal THFEA,the functional relationships between high-frequency harmonic voltages(HFHVs)and corresponding airgap flux densities are established,which are used for calculating the flux density spectra caused by each HFHV in the PWM voltage spectra.Then,the superposition principle is applied for calculating the flux density spectra caused by fundamental currents and all HFHVs,which are converted to the electromagnetic force spectra at last.The relative errors between the force density spectra calculated with the proposed method and those obtained from traditional time-stepping finite element analysis(TSFEA)using PWM voltages as input are within 3.1%,while the proposed method is 24 times faster than the traditional TSFEA.
文摘The uniqueness theorem of time-harmonic electromagnetic fields, which is the theoretical basis of boundary value problem (BVP) of electromagnetic fields, is reviewed. So far there are many versions of the statements and proofs on the theorem. However, there exist some limitations and lack of strictness in these versions, for instance, the discussion of the uniqueness of solution without considering the existence of solution and the lack of strictness in the case of loss-less medium. In contrast with the traditional statements and proofs, this paper introduces some important conclusions on operator equation from modern theory of partial differential equation (PDE) and attempts to solve the problems on the existence and uniqueness of the solution to operator equation which is derived from Maxwell’s equations of time-harmonic electromagnetic fields. This method provides a novel and rigorous approach to discuss and solve the existence and uniqueness of the solution to time- harmonic fields in the new mathematical framework. Some important conclusions are presented.
基金This work was supported by the Science and Technology Foundation of Guizhou Province under Grant No.20052005.
文摘A time-harmonic equivalent current dipole model is proposed to simulate EEG source which deals with the problem concerning the capacitance effect. The expressions of potentials in both homogeneous infinite dielectric medium and dielectric sphere on the electroquasistatic condition are presented. The potential in a 3-layer inhomogeneous spherical head is computed by using this model. The influences on potential produced by time-harmonic character and permittivity are discussed. The results show that potentials in dielectric sphere are affected by frequency and permittivity.
基金supported in part by National Natural Science Foundation of China(Grant Nos.10771178 and 10676031)National Key Basic Research Program of China(973 Program)(Grant No.2005CB321702)+3 种基金the Key Proiect of Chinese Ministry of Education and Scientific Research Fund of Hunan Provincial Education Department(Grant Nos.208093 and 07A068)Especially,the first author was also supported in part by Hunan Provincial Innovation Foundation for Postgraduatesupported by Alexander von Humboldt Research Award for Senior US Scientists,NSF DMS-0609727,NSFC-10528102Furong Professor Scholar Program of Hunan Province of China through Xiangtan University
文摘In this paper, we obtain optimal error estimates in both L^2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L^2 error estimates into the L^2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.
基金supported by the National Science Centre of Poland (Grant No. 2013/09/B/ST1/01963)
文摘We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.
基金This research is supported by the National Key Research and Development Program of China(Nos.2019YFC0312003 and 2018YFC1504200)the National Natural Science Foundation of China(Nos.11901098 and U1839207).
文摘In this paper,we consider a modified alternating positive semidefinite splitting preconditioner for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current model.The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are studied for both simple and general topology.Numerical results demonstrate the effectiveness of the proposed preconditioner when it is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.
文摘The aim of this work is to analyze the role of the impressed sources in determining the well or ill-posedness of time harmonic electromagnetic boundary value problems involving isotropic effective media.It is shown,in particular,that,even if all interfaces are regular,the class of ill-posed problems can be very large in the presence of general square-integrable impressed sources.However,when a simple and realistic constraint is enforced on these sources,requiring that the support of the sources does not include any interface between a traditional medium and a metamaterial,among the problems here considered just those involving an interface between complementary materials remain ill-posed.These considerations have a very significant impact also on the approximability of the solution of well-posed problems since the numerical noise can introduce small fictitious sources even where the sources to be simulated are not present.These effects on finite element simulators are fully analyzed.Finally,we propose an algorithm that allows to obtain much better approximations of the solutions of the most critical wellposed problems.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 11301521, 11771467, 11071041), the Natural Science Foundation of Fujian Province (Nos. 2016J01005, 2015J01578), and the National Post- doctoral Program for Innovative Talents (No. BX201700234).
文摘Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting (APSS) iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.
文摘The scope of this paper is to show how a two-scale asymptotic analysis,based on a superposition principle,allows us to derive high order approximate boundary conditions for a scattering problem of a time-harmonic wave by a thin and tangentially periodic multi-layered domain.The periods are assumed of the same order of the thickness.New terms like memory effect and variance-covariance ones are observed contrarily to the laminar case.As a result,optimal error estimates are obtained.
基金Project supported by the National Natural Science Foundation of China(Nos.11272105 and 11572101)
文摘The dynamic behavior of a rectangular crack in a three-dimensional (3D) orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional (2D) Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.
基金This work was supported by the National Natural Science Foundation of China under Grant No.51177077.
文摘Modifying the equivalent rotor resistivity with rotor end factor in 2-dimension(2-D)finite element analysis(FEA)is an effective way to analyze the 3-dimension(3-D)solid rotor problems.For the smooth solid rotor,five different rotor end factors are discussed and compared with each other.It is theoretically clarified that the resistivity of rotor in 2-D FEA should be multiplied by the square of rotor end factors to take the 3-D end effect of solid rotor into account.For the slitted solid rotor,an improved rotor end factor is proposed based on the equivalent area algorithm of eddy currents in rotor,since the end factors of smooth solid rotor are not applicable.Finally,the time-harmonic finite element method(FEM)combined with the rotor end factor is applied to analyze the performance of solid rotor induction motor.The tested and computed results are in good agreement,which proves the effectiveness of rotor end factor for the simplication of 3-D solid rotor problems.
文摘Dynamic stresses around three parallel cracks in an infinite elastic plate that is subjected to incident time-harmonic stress waves normal to the cracks have been solved. Using the Fourier transform technique, the boundary conditions are reduced to six simultaneous integral equations. To solve these equations, the differences of displacements inside the cracks are expanded in a series. The unknown coefficients in those series are solved using the Schmidt method such that the conditions inside the cracks are satisfied. Numerical calculations are carried out for some crack configurations.
文摘We propose an adaptive strategy for solving high frequency Helmholtz scattering problems.The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into the bounded domain.The parameters in the uniaxial PML method are determined by sharp a posteriori error estimates developed by Chen and Wu[8].An hp-adaptive finite element strategy is proposed to solve the uniaxial PML equation.Numerical experiments are included which indicate the desirable exponential decay property of the error.
基金the National Naturel Science Foundation(NNSF)of China grant 11601138NNSF of China grant 11571132.
文摘In this paper,we consider the scattering problem of time-harmonic electromagnetic waves from an infinite cylinder having an open arc Γ and a bounded domain D in R^2 as cross section.We focus on the inverse scattering problem,that is,to reconstruct the shape of Γ and D from the far-field pattern by using the factorization method.Through establishing a mixed reciprocity relation,we prove that the scatters Γ and D can be uniquely determined by the far-field pattern.Furthermore,the mathematical basis is given to explain that the factorization method is feasible to our problem.At the end of this paper,we give some numerical examples to show the efficaciousness of the algorithms.
基金the Investments for the Future Programme IdEx Bordeaux CPU(ANR-10-IDEX-03-02).C.P.is partly funded by ANR projects INTCELL(ANR 2010-BLAN-916)MEMOVE(ANR 2011 BS0100601)。
文摘We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer.These models appear as first order approximations of the electromagnetic field.They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer,that makes possible to replace the thin layer by approximate conditions.We present the advantages and the drawbacks of several approximations together with numerical validations and simulations.The main motivation of this work concerns the computation of electromagnetic field in biological cells.The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane,which provides a specific behavior of the electromagnetic field at low frequencies.