In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated por...In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.展开更多
A multiple monopole （or multipole） method based on the generalized mul- tipole technique （GMT） is proposed to calculate the band structures of scalar waves in two-dimensional phononic crystals which are composed o...A multiple monopole （or multipole） method based on the generalized mul- tipole technique （GMT） is proposed to calculate the band structures of scalar waves in two-dimensional phononic crystals which are composed of arbitrarily shaped cylinders embedded in a host medium. In order to find the eigenvalues of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure is obtained. Some numerical examples are presented to validate the proposed method.展开更多
A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is pr...A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems.展开更多
The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm（PMLFMA）.Considering the main complements of multilevel fast multipole algorithm（M...The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm（PMLFMA）.Considering the main complements of multilevel fast multipole algorithm（MLFMA） memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects.展开更多
In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced...In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.展开更多
In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on ...In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element （RVE） for short fiberreinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.展开更多
It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current mult...It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current multipole model expanded to the first order terms. This magnetic imaging is realized in a reconstruction plane in the centre of human heart, where the current dipole array is employed to represent realistic cardiac current distribution. The current multipole as testing source generates magnetic fields in the measuring plane, serving as inputs of cardiac magnetic inverse problem. In the heart-torso model constructed by boundary element method, the current multipole magnetic field distribution is compared with that in the homogeneous infinite space, and also with the single current dipole magnetic field distribution. Then the minimum-norm least-squares （MNLS） method, the optimal weighted pseudoinverse method （OWPIM）, and the optimal constrained linear inverse method （OCLIM） are selected as the algorithms for inverse computation based on current multipole model innovatively, and the imaging effects of these three inverse methods are compared. Besides, two reconstructing parameters, residual and mean residual, are also discussed, and their trends under MNLS, OWPIM and OCLIM each as a function of SNR are obtained and compared.展开更多
A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to...A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.展开更多
A 16-pole superconducting multipole wiggler with a large gap of 68 mm was designed and fabricated to serve as a multipole wiggler for HEPS-TF.The wiggler consists of 16 pairs of NbTi superconducting coils with a perio...A 16-pole superconducting multipole wiggler with a large gap of 68 mm was designed and fabricated to serve as a multipole wiggler for HEPS-TF.The wiggler consists of 16 pairs of NbTi superconducting coils with a period length of 170 mm,and its maximum peak field is 2.6 Tesla.In magnet design,magnet poles were optimized.Furthermore,the Lorentz force on the coils and electromagnetic force between the upper and lower halves were computed and analyzed along with the stored energy and inductance at different currents.To enhance the critical current of the magnet coil,all the pole coils selected for the magnet exhibited excellent performance,and appropriate prestress derived from the coil force analysis was applied to the pole coils during magnet assembly.The entire magnet structure was immersed in 4.2-K liquid helium in the cryostat cooled solely by four two-stage cryocoolers,and the performance test of the superconducting wiggler was appropriately completed.Based on the measured results,the first and second field integrals on the axis of the superconducting wiggler were significantly improved at different field levels after the compensation of the corrector coils.Subsequently,the wiggler was successfully installed in the storage ring of BEPCII operation with beams.展开更多
A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu...A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu（PMCHW） approach for homogeneous dielectric objects and the electric field integral equation for conducting objects. The integral equations are discretized by the method of moment （MoM）, in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions. The resultant matrix equation is then solved by the multilevel fast multipole algorithm （MLFMA） and fast far-field approximation （FAFFA） is used to further accelerate the computation. The radiation patterns of dipole arrays in the presence of radomes are presented. The numerical results demonstrate the accuracy and versatility of this method.展开更多
A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-M...A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.展开更多
The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced ...The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O (N2), we present an OeNT Dipole Panel Fast Multipole Method(DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P.Two methods(the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments(with three harmonics),DPFMM is approximately two times faster for N2 [103,106]. The simulation time of a multirotor(N~104) is reduced from 100 min(with unaccelerated direct solver) to 2 min(with DPFMM).展开更多
In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecule...In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecules have not been clearly elucidated.In this work,based on the molecular point group,the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered.Based on the summarized selection rules,the electron energy loss spectra of H2O,CO_(2),and N_(2)O are identified,and the momentum transfer dependence behaviors of their valence-shell excitations are explained.展开更多
This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the...This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.展开更多
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations s...This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.展开更多
There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle th...There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.展开更多
Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calc...Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical andexperimental ones.展开更多
The effect of multipole resonance in the interaction between a spherical metallic nanoparticle （MNP） and an emitting dipole is studied with the Mie theory. The results show that the absorption peak of the MNP with r...The effect of multipole resonance in the interaction between a spherical metallic nanoparticle （MNP） and an emitting dipole is studied with the Mie theory. The results show that the absorption peak of the MNP with respect to the field of the emitting dipole is blue-shifted with the decrease of the spacing between MNP and emitting dipole due to the enhanced multipole resonance. At a short distance, the enhanced multipole terms of scattering are not obvious compared with the dipole term. For the decay rate of the emitting dipole, multipole resonance brings about the enhancement of it largely at short spacing. For the radiative decay rate, the behavior is quite different. The dipole term is dominant at a short spacing, and the multipole term is dominant at a larger spacing.展开更多
The interaction between a solute atom and an extended dislocation was investigated using a continuum approximation method with force multipoles.The dislocation core structure of extended dislocation was modeled with t...The interaction between a solute atom and an extended dislocation was investigated using a continuum approximation method with force multipoles.The dislocation core structure of extended dislocation was modeled with the Peierls-Nabarro model discretized with a number of infinitesimal Volterra dislocations.The interaction energy and force between a nickel solute atom and perfect and extended dislocation in copper were successfully calculated using the force multipoles.The results clearly show that the core structure of extended dislocation weakens the interaction with solute atoms.The interaction energy and force for extended dislocations are almost the half of those for perfect dislocations.展开更多
The Buckingham expansion is important for understanding molecular multipoles and(hyper)polarizabilities.In this study,we give a complete derivation of the Buckingham expansion in the traced form using successive Taylo...The Buckingham expansion is important for understanding molecular multipoles and(hyper)polarizabilities.In this study,we give a complete derivation of the Buckingham expansion in the traced form using successive Taylor series.Based on the derivation results,a general Buckingham expansion in the traced form is proposed,from which highly accurate numerical calculations using the finite field method can be achieved.The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient.The applications of thefinite field method in this study show good agreements with previous theoretical calculations and experimental measurements.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.42074139)the Natural Science Foundation of Jilin Province,China (Grant No.20210101140JC)。
文摘In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.
基金supported by the National Natural Science Foundation of China(Nos.51178037 and10632020)the German Research Foundation(DFG)(Nos.ZH 15/11-1 and ZH 15/16-1)+1 种基金the International Bureau of the German Federal Ministry of Education and Research(BMBF)(No.CHN11/045)the National Basic Research Program of China(No.2010CB732104)
文摘A multiple monopole （or multipole） method based on the generalized mul- tipole technique （GMT） is proposed to calculate the band structures of scalar waves in two-dimensional phononic crystals which are composed of arbitrarily shaped cylinders embedded in a host medium. In order to find the eigenvalues of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure is obtained. Some numerical examples are presented to validate the proposed method.
基金The project supported by the National Nature Science Foundation of China(10172053)the Ministry of Education
文摘A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems.
基金supported by the National Basic Research Program of China (973 Program) (61320)
文摘The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm（PMLFMA）.Considering the main complements of multilevel fast multipole algorithm（MLFMA） memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects.
基金the National Natural Science Foundation of China (No. 11074170)the Independent Research Program of State Key Laboratory of Machinery System and Vibration (SKLMSV) (No. MSV-MS-2008-05)the Visiting Scholar Program of SKLMSV (No. MSV-2009-06)
文摘In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.
基金The project supported by the National Natural Science Foundation of China (10472051)
文摘In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element （RVE） for short fiberreinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.
基金Project supported by the State Key Development Program for Basic Research of China(Grant No.2006CB601007)the National Natural Science Foundation of China(Grant No.10674006)the National High Technology Research and Development Program of China(Grant No.2007AA03Z238)
文摘It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current multipole model expanded to the first order terms. This magnetic imaging is realized in a reconstruction plane in the centre of human heart, where the current dipole array is employed to represent realistic cardiac current distribution. The current multipole as testing source generates magnetic fields in the measuring plane, serving as inputs of cardiac magnetic inverse problem. In the heart-torso model constructed by boundary element method, the current multipole magnetic field distribution is compared with that in the homogeneous infinite space, and also with the single current dipole magnetic field distribution. Then the minimum-norm least-squares （MNLS） method, the optimal weighted pseudoinverse method （OWPIM）, and the optimal constrained linear inverse method （OCLIM） are selected as the algorithms for inverse computation based on current multipole model innovatively, and the imaging effects of these three inverse methods are compared. Besides, two reconstructing parameters, residual and mean residual, are also discussed, and their trends under MNLS, OWPIM and OCLIM each as a function of SNR are obtained and compared.
文摘A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.
文摘A 16-pole superconducting multipole wiggler with a large gap of 68 mm was designed and fabricated to serve as a multipole wiggler for HEPS-TF.The wiggler consists of 16 pairs of NbTi superconducting coils with a period length of 170 mm,and its maximum peak field is 2.6 Tesla.In magnet design,magnet poles were optimized.Furthermore,the Lorentz force on the coils and electromagnetic force between the upper and lower halves were computed and analyzed along with the stored energy and inductance at different currents.To enhance the critical current of the magnet coil,all the pole coils selected for the magnet exhibited excellent performance,and appropriate prestress derived from the coil force analysis was applied to the pole coils during magnet assembly.The entire magnet structure was immersed in 4.2-K liquid helium in the cryostat cooled solely by four two-stage cryocoolers,and the performance test of the superconducting wiggler was appropriately completed.Based on the measured results,the first and second field integrals on the axis of the superconducting wiggler were significantly improved at different field levels after the compensation of the corrector coils.Subsequently,the wiggler was successfully installed in the storage ring of BEPCII operation with beams.
基金the National Natural Science Foundation of China (60431010)
文摘A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu（PMCHW） approach for homogeneous dielectric objects and the electric field integral equation for conducting objects. The integral equations are discretized by the method of moment （MoM）, in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions. The resultant matrix equation is then solved by the multilevel fast multipole algorithm （MLFMA） and fast far-field approximation （FAFFA） is used to further accelerate the computation. The radiation patterns of dipole arrays in the presence of radomes are presented. The numerical results demonstrate the accuracy and versatility of this method.
文摘A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.
文摘The Unsteady Vortex Lattice Method(UVLM) is a medium-fidelity aerodynamic tool that has been widely used in aeroelasticity and flight dynamics simulations. The most timeconsuming step is the evaluation of the induced velocity. Supposing that the number of bound and wake lattices is N and the computational cost is O (N2), we present an OeNT Dipole Panel Fast Multipole Method(DPFMM) for the rapid evaluation of the induced velocity in UVLM. The multipole expansion coefficients of a quadrilateral dipole panel have been derived in spherical coordinates, whose accuracy is the same as that of the Biot-Savart kernel at the same truncation degree P.Two methods(the loosening method and the shrinking method) are proposed and tested for space partitioning volumetric panels. Compared with FMM for vortex filaments(with three harmonics),DPFMM is approximately two times faster for N2 [103,106]. The simulation time of a multirotor(N~104) is reduced from 100 min(with unaccelerated direct solver) to 2 min(with DPFMM).
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0402300)the National Natural Science Foundation of China(Grant No.U1732133)the Science Fund from Chinese Academy of Sciences(Grant No.11320101003)
文摘In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecules have not been clearly elucidated.In this work,based on the molecular point group,the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered.Based on the summarized selection rules,the electron energy loss spectra of H2O,CO_(2),and N_(2)O are identified,and the momentum transfer dependence behaviors of their valence-shell excitations are explained.
基金Project supported by the National Natural Science Foundation of China(No.11074170)the State Key Laboratory Foundation of Shanghai Jiao Tong University(No.MSVMS201105)
文摘This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.
基金supported by the National Natural Science Foundation of China (11172291)the National Science Foundation for Post-doctoral Scientists of China (2012M510162)the Fundamental Research Funds for the Central Universities (KB2090050024)
文摘This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.
文摘There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.
文摘Higher electric multipole moments for the ground-state electronic configuration of some polyatomicmolecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets.The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical andexperimental ones.
基金Project supported by the National Natural Science Foundation of China （Grant Nos. 61138004 and 61107068） and the National Basic Research Program of China （Grant No. 2012CB921904）.
文摘The effect of multipole resonance in the interaction between a spherical metallic nanoparticle （MNP） and an emitting dipole is studied with the Mie theory. The results show that the absorption peak of the MNP with respect to the field of the emitting dipole is blue-shifted with the decrease of the spacing between MNP and emitting dipole due to the enhanced multipole resonance. At a short distance, the enhanced multipole terms of scattering are not obvious compared with the dipole term. For the decay rate of the emitting dipole, multipole resonance brings about the enhancement of it largely at short spacing. For the radiative decay rate, the behavior is quite different. The dipole term is dominant at a short spacing, and the multipole term is dominant at a larger spacing.
文摘The interaction between a solute atom and an extended dislocation was investigated using a continuum approximation method with force multipoles.The dislocation core structure of extended dislocation was modeled with the Peierls-Nabarro model discretized with a number of infinitesimal Volterra dislocations.The interaction energy and force between a nickel solute atom and perfect and extended dislocation in copper were successfully calculated using the force multipoles.The results clearly show that the core structure of extended dislocation weakens the interaction with solute atoms.The interaction energy and force for extended dislocations are almost the half of those for perfect dislocations.
基金the National Natural Science Foundation of China(Grant Nos.21573112 and 21421001)。
文摘The Buckingham expansion is important for understanding molecular multipoles and(hyper)polarizabilities.In this study,we give a complete derivation of the Buckingham expansion in the traced form using successive Taylor series.Based on the derivation results,a general Buckingham expansion in the traced form is proposed,from which highly accurate numerical calculations using the finite field method can be achieved.The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient.The applications of thefinite field method in this study show good agreements with previous theoretical calculations and experimental measurements.
