Efficient and accurate numerical-projection of electromagnetic multipoles for scattering objects

In this paper,we develop an efcient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical integration.Firstly,we briefy review the principles of multipole decomposition,highlighting two numerical projection methods including surface and volume integration.Secondly,we discuss the Lebedev and Gaussian quadrature methods,provide a detailed recipe to select the quadrature points and the corresponding weighting factor,and illustrate the integration accuracy and numerical efciency(that is,with very few sampling points)using a unit sphere surface and regular tetrahedron.In the demonstrations of an isotropic dielectric nanosphere,a symmetric scatterer,and an anisotropic nanosphere,we perform multipole decomposition and validate our numerical projection procedure.The obtained results from our procedure are all consistent with those from Mie theory,symmetry constraints,and fnite element simulations.

竖直单U型地埋管换热器埋管间负热阻现象的参数化研究与分析

基于Mutipole方法对竖直单U型地埋管换热器钻孔内外的耦合传热过程进行求解,在钻孔内三热阻和四热阻简化传热模型基础上,详细地分析钻孔内的复杂稳态传热过程,参数化研究埋管布置结构、回填料与岩土热物性等因素对钻孔内埋管间直接传热热阻的影响规律,揭示导致钻孔内埋管间负热阻现象的本质原因,对钻孔内热阻传热模型的工程实践应用给出参考意见。

Analytical computation of magnetic field in coil-dominated superconducting quadrupole magnets based on racetrack coils

Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.

Effects of confining pressure and pore pressure on multipole borehole acoustic field in fluid-saturated porous media

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.

Aerodynamic/stealth design of S-duct inlet based on discrete adjoint method

It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.

Cumulative potential-derived atomic multipoles

A method to derive the atomic multipole moments cumulatively up to quadrupole mo- ments was developed.The multipole moments are obtained by least-square simulating the molecular electrostatic potentials.Only the components of the term of highest order in the atomic multipole expansion are optimized while the lower terms remain fixed.The calculations on HF,H_2O and NH_2 show that the cumulative method can give reasonable qualitative and fairly good quantitative results.

Molecular multipoles and (hyper) polarizabilities from the Buckingham expansion:revisited

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.

RCS测试中的低散射载体设计及仿真分析

在雷达散射截面(RCS)测试中,低散射载体的设计结果取决于被测目标的RCS量级;为进行细节性隐身设计,获得台阶与缝隙排除载体干扰后的RCS水平,提出一种在台阶与缝隙RCS测试中的低散射载体设计方法;采用多层快速多极子算法,对低散射载体相邻曲面连接方式、台阶与缝隙在载体上的位置、前缘尖削度、倒圆半径对散射特性的影响进行仿真分析;仿真计算结果表明,控制载体表面曲率的变化、加大前缘尖削度、减小拼接曲面倒圆半径能有效降低载体前向散射水平,由于载体曲面一侧的散射水平低于平面一侧散射水平,台阶与缝隙特征应位于曲面上;对RCS测试中低散射载体设计具有指导意义。

多技术系统基于VHDL-AMS的统一建模与仿真技术研究

机电一体化系统设计要求跨领域的统一建模与仿真 ,多刚体动力学是其中的一个难点 通常的做法是采用动力学专用软件建模 ,求得DAEs形式的运动方程后再转化为集成环境中的统一建模语言 首先基于广义基尔霍夫网络理论 ,提出了基于端口的多技术系统集成组件 ,并采用VHDL AMS混合系统建模语言进行描述 为了更有效的集成多刚体动力学 ,通过选取参考基作为端点 ,构造了计算多刚体系统动力学的广义基尔霍夫网络模型 ,具体阐述了基本组件的VHDL AMS行为模型 ,从而将多刚体系统纳入基于VHDL AMS的集成设计和仿真环境中

Trapped Modes in a Three-Layer Fluid

In this work,trapped mode frequencies are computed for a submerged horizontal circular cylinder with the hydrodynamic set-up involving an infinite depth three-layer incompressible fluid with layer-wise different densities.The impermeable cylinder is fully immersed in either the bottom layer or the upper layer.The effect of surface tension at the surface of separation is neglected.In this set-up,there exist three wave numbers:the lowest one on the free surface and the other two on the internal interfaces.For each wave number,there exist two modes for which trapped waves exist.The existence of these trapped modes is shown by numerical evidence.We investigate the variation of these trapped modes subject to change in the depth of the middle layer as well as the submergence depth.We show numerically that two-layer and single-layer results cannot be recovered in the double and single limiting cases of the density ratios tending to unity.The existence of trapped modes shows that in general,a radiation condition for the waves at infinity is insufficient for the uniqueness of the solution of the scattering problem.

Harmonic Polynomials Via Differentiation

It is well-known that if p is a homogeneous polynomial of degree k in n variables, p ∈ P;, then the ordinary derivative p（）(r;) has the form A;Y（x）r;where A;is a constant and where Y is a harmonic homogeneous polynomial of degree k, Y ∈ H;, actually the projection of p onto H;. Here we study the distributional derivative p（）(r;) and show that the ordinary part is still a multiple of Y, but that the delta part is independent of Y, that is, it depends only on p-Y. We also show that the exponent 2-n is special in the sense that the corresponding results for p（）(r;)do not hold if α≠2-n. Furthermore, we establish that harmonic polynomials appear as multiples of r;when p（） is applied to harmonic multipoles of the form Y’（x）r;for some Y ∈H;.

APPLICATION OF A NEW FAST MULTIPOLE BEM FOR SIMULATION OF 2D ELASTIC SOLID WITH LARGE NUMBER OF INCLUSIONS

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.

Improvement and performance of parallel multilevel fast multipole algorithm

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.

无线局域网IEEE 802.11的一种高效调度方案

深入分析了无线局域网IEEE 802.11系列标准的现有调度方案,提出了一种基于IEEE 802.11e标准中HCF接入模式的高效调度方案SA-Multipoll。设计了调度帧结构和调度时序,推导了满足时延和带宽要求的准入协商和调度效率公式。通过数值计算和仿真结果证实了SA-Multipoll的调度效率高于singlepoll,也高于现有multipoll方案中效率较高的CP-Multipoll方案。

A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites

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.

Band structure calculation of scalar waves in two-dimensional phononic crystals based on generalized multipole technique

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.

Cardiac magnetic source imaging based on current multipole model

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.

Application of A Fast Multipole BIEM for Flow Diffraction from A 3D Body

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.

Cylindrical vector beams reveal radiationless anapole condition in a resonant state

Nonscattering optical anapole condition is corresponding to the excitation of radiationless field distributions in open resonators,which offers new degrees of freedom for tailoring light-matter interaction.Conventional mechanisms for achieving such a condition relies on sophisticated manipulation of electromagnetic multipolar moments of all orders to guarantee superpositions of suppressed moment strengths at the same wavelength.In contrast,here we report on the excitation of optical radiationless anapole hidden in a resonant state of a Si nanoparticle utilizing a tightly focused radially polarized(RP)beam.The coexistence of magnetic resonant state and anapole condition at the same wavelength further enables the triggering of resonant state by a tightly focused azimuthally polarized(AP)beam whose corresponding electric multipole coefficient could be zero.As a result,high contrast inter-transition between radiationless anapole condition and ideal magnetic resonant scattering can be achieved experimentally in visible spectrum.The proposed mechanism is general which can be realized in different types of nanostructures.Our results showcase that the unique combination of structured light and structured Mie resonances could provide new degrees of freedom for tailoring light-matter interaction,which might shed new light on functional meta-optics.

General and efficient parallel approach of finite element-boundary integral-multilevel fast multipole algorithm

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.