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
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 fast multipole method (FMM) has been used to reduce the computing operations and mem- ory requirements in large numerical analysis problems. In this paper, the FMM based on Taylor expansions is combined with the...The fast multipole method (FMM) has been used to reduce the computing operations and mem- ory requirements in large numerical analysis problems. In this paper, the FMM based on Taylor expansions is combined with the boundary element method (BEM) for three-dimensional elastostatic problems to solve thin plate and shell structures. The fast multipole boundary element method (FM-BEM) requires O(N) opera- tions and memory for problems with N unknowns. The numerical results indicate that for the analysis of thin structures, the FM-BEM is much more efficient than the conventional BEM and the accuracy achieved is sufficient for engineering applications.展开更多
This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with frict...This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM.展开更多
The fast multipole method was used to solve the traction boundary integral equation for 2-D crack analysis. The use of both multipole and local expansions reduces both the computational complexity and the memory req...The fast multipole method was used to solve the traction boundary integral equation for 2-D crack analysis. The use of both multipole and local expansions reduces both the computational complexity and the memory requirement to O(N). The multipole expansion uses a complex Taylor series expansion to reduce the number of multipole moments. The generalized minimum residual method solver (GMRES) was selected as the iterative solver. An improved preconditioner for GMRES was developed which uses less CPU time and less memory. A new initial candidate vector for the iterative solver was developed to further improve the efficiency. The numerical examples apply the method to the analysis of cracks in infinite 2-D space with the largest model having 900 000 degrees of freedom.展开更多
A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established usin...A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice,the Kelvin type model is introduced.The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration.Since all the integrals are evaluated analytically,high accuracy and fast convergence of the numerical scheme are obtained.Several numerical examples,including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented.The numerical results are compared with the developed analytical solutions,which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces.The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.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
The design and synthesis of plasmonic nanoparticles with Raman-active molecules embedded inside them are of significant interest for sensing and imaging applications. However, direct synthesis of such nanostructures w...The design and synthesis of plasmonic nanoparticles with Raman-active molecules embedded inside them are of significant interest for sensing and imaging applications. However, direct synthesis of such nanostructures with controllable shape, size, and plasmonic properties remains extremely challenging. Here we report on the preparation of uniform Au@Ag core/sheU nanorods with controllable Ag shells of 1 to 25 nm in thickness. 1,4-Aminothiophenol （4-ATP） molecules, used as the Raman reporters, were located between the Au core and the Ag shell. Successful embedding of reporter molecules inside the core/shell nanoparticles was confirmed by the absence of selective oxidation of the amino groups, as measured by Raman spectroscopy. The dependence of Raman intensity on the location of the reporter molecules in the inside and outside of the nanorods was studied. The molecules in the interior showed strong and uniform Raman intensity, at least an order of magnitude higher than that of the molecules on the nanoparticle surface. In contrast to the usual surface-functionalized Raman tags, aggregation and clustering of nanoparticles with embedded molecules decreased the surface-enhanced Raman scattering （SERS） signal. The findings from this study provide the basis for a novel detection technique of low analyte concentration utilizing the high SERS response of molecules inside the core/shell metal nanostructures. As an example, we show robust SERS detection of thiram fungicide as low as 10-9 M in solutions.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
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
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
An index-guiding photonic crystal fibre with a small hole in the core is fabricated. The simulated results show that the first higher order mode possesses two zero-dispersion wavelengths, and the phase-matching is pos...An index-guiding photonic crystal fibre with a small hole in the core is fabricated. The simulated results show that the first higher order mode possesses two zero-dispersion wavelengths, and the phase-matching is possible in the anomalous dispersion regime between the two zero-dispersion wavelengths. Using 200 fs Ti： sapphire laser of 820, 830 and 840nm, the anti-Stokes line around 530nm can be generated efficiently. The maximum ratio of the anti-Stokes signal energy to the pump component in the output spectrum is estimated to be 1.03 and the conversion efficiency is above 50%.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
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 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
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 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 Natural Science Foundation of China (No. 10172053)
文摘The fast multipole method (FMM) has been used to reduce the computing operations and mem- ory requirements in large numerical analysis problems. In this paper, the FMM based on Taylor expansions is combined with the boundary element method (BEM) for three-dimensional elastostatic problems to solve thin plate and shell structures. The fast multipole boundary element method (FM-BEM) requires O(N) opera- tions and memory for problems with N unknowns. The numerical results indicate that for the analysis of thin structures, the FM-BEM is much more efficient than the conventional BEM and the accuracy achieved is sufficient for engineering applications.
基金Supported by the National Natural Science Foundation of China(No. 50075075)
文摘This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM.
文摘The fast multipole method was used to solve the traction boundary integral equation for 2-D crack analysis. The use of both multipole and local expansions reduces both the computational complexity and the memory requirement to O(N). The multipole expansion uses a complex Taylor series expansion to reduce the number of multipole moments. The generalized minimum residual method solver (GMRES) was selected as the iterative solver. An improved preconditioner for GMRES was developed which uses less CPU time and less memory. A new initial candidate vector for the iterative solver was developed to further improve the efficiency. The numerical examples apply the method to the analysis of cracks in infinite 2-D space with the largest model having 900 000 degrees of freedom.
基金supported by the National Natural Science Foundation of China(Grant No.10725210)the National Basic Research Program of China(Grant No.2009CB623200)
文摘A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice,the Kelvin type model is introduced.The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration.Since all the integrals are evaluated analytically,high accuracy and fast convergence of the numerical scheme are obtained.Several numerical examples,including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented.The numerical results are compared with the developed analytical solutions,which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces.The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.
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The design and synthesis of plasmonic nanoparticles with Raman-active molecules embedded inside them are of significant interest for sensing and imaging applications. However, direct synthesis of such nanostructures with controllable shape, size, and plasmonic properties remains extremely challenging. Here we report on the preparation of uniform Au@Ag core/sheU nanorods with controllable Ag shells of 1 to 25 nm in thickness. 1,4-Aminothiophenol （4-ATP） molecules, used as the Raman reporters, were located between the Au core and the Ag shell. Successful embedding of reporter molecules inside the core/shell nanoparticles was confirmed by the absence of selective oxidation of the amino groups, as measured by Raman spectroscopy. The dependence of Raman intensity on the location of the reporter molecules in the inside and outside of the nanorods was studied. The molecules in the interior showed strong and uniform Raman intensity, at least an order of magnitude higher than that of the molecules on the nanoparticle surface. In contrast to the usual surface-functionalized Raman tags, aggregation and clustering of nanoparticles with embedded molecules decreased the surface-enhanced Raman scattering （SERS） signal. The findings from this study provide the basis for a novel detection technique of low analyte concentration utilizing the high SERS response of molecules inside the core/shell metal nanostructures. As an example, we show robust SERS detection of thiram fungicide as low as 10-9 M in solutions.
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.
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Supported by the National Key Basic Research Programme of China under Grant No 2003CB314905, and the National Natural Science Foundation of China under Grant No 60637010.
文摘An index-guiding photonic crystal fibre with a small hole in the core is fabricated. The simulated results show that the first higher order mode possesses two zero-dispersion wavelengths, and the phase-matching is possible in the anomalous dispersion regime between the two zero-dispersion wavelengths. Using 200 fs Ti： sapphire laser of 820, 830 and 840nm, the anti-Stokes line around 530nm can be generated efficiently. The maximum ratio of the anti-Stokes signal energy to the pump component in the output spectrum is estimated to be 1.03 and the conversion efficiency is above 50%.
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 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.
