3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method （FMM） is useful for calculating 3D traveltime and has proven to be effi...3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method （FMM） is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method （WFC）, which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models.展开更多
Microseismic(MS)event locations are vital aspect of MS monitoring technology used to delineate the damage zone inside the surrounding rock mass.However,complex geological conditions can impose significantly adverse ef...Microseismic(MS)event locations are vital aspect of MS monitoring technology used to delineate the damage zone inside the surrounding rock mass.However,complex geological conditions can impose significantly adverse effects on the final location results.To achieve a high-accuracy location in a complex cavern-containing structure,this study develops an MS location method using the fast marching method(FMM)with a second-order difference approach(FMM2).Based on the established velocity model with three-dimensional(3D)discrete grids,the realization of the MS location can be achieved by searching the minimum residual between the theoretical and actual first arrival times.Moreover,based on the calculation results of FMM2,the propagation paths from the MS sources to MS sensors can be obtained using the linear interpolation approach and the Runge–Kutta method.These methods were validated through a series of numerical experiments.In addition,our proposed method was applied to locate the recorded blasting and MS events that occurred during the excavation period of the underground caverns at the Houziyan hydropower station.The location results of the blasting activities show that our method can effectively reduce the location error compared with the results based on the uniform velocity model.Furthermore,the obtained MS location was verified through the occurrence of shotcrete fractures and spalling,and the monitoring results of the in-situ multipoint extensometer.Our proposed method can offer a more accurate rock fracture location and facilitate the delineation of damage zones inside the surrounding rock mass.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
Fast computation of the landing footprint of a space-to-ground vehicle is a basic requirement for the deployment of parking orbits, as well as for enabling decision makers to develop real-time programs of transfer tra...Fast computation of the landing footprint of a space-to-ground vehicle is a basic requirement for the deployment of parking orbits, as well as for enabling decision makers to develop real-time programs of transfer trajectories. In order to address the usually slow computational time for the determination of the landing footprint of a space-to-ground vehicle under finite thrust, this work proposes a method that uses polynomial equations to describe the boundaries of the landing footprint and uses back propagation(BP) neural networks to quickly determine the landing footprint of the space-to-ground vehicle. First, given orbital parameters and a manoeuvre moment, the solution model of the landing footprint of a space-to-ground vehicle under finite thrust is established. Second, given arbitrary orbital parameters and an arbitrary manoeuvre moment, a fast computational model for the landing footprint of a space-to-ground vehicle based on BP neural networks is provided.Finally, the simulation results demonstrate that under the premise of ensuring accuracy, the proposed method can quickly determine the landing footprint of a space-to-ground vehicle with arbitrary orbital parameters and arbitrary manoeuvre moments. The proposed fast computational method for determining a landing footprint lays a foundation for the parking-orbit configuration and supports the design of real-time transfer trajectories.展开更多
A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditiona...A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM.Moreover,a flow rate estimate method was developed for the project whose injection rate has not been clearly determined.A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project,which is a good practice verification of FEFDM.At last,this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure.The result shows that for deep wellbore,the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted.It is also shown that with flow rate increasing,the friction term can no longer be neglected.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
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
This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafuncti...This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafunctions and the Ishigami function are considered in the sensitivity analysis(SA).The effects of the input variables on the output variables are investigated,and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.展开更多
We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utiliz...We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.展开更多
The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to u...The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O（N^3） with direct solvers or O（N^2） with iterative solvers, as well as the memory requirement of O（N^2）. In this study, the first attempt was made to combine the fast multipole method （FMM） and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O（N）. Based on the complex variable represen- tation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.展开更多
Attempting to find a fast computing method to DHT （distinguished hyperbolic trajectory）, this study first proves that the errors of the stable DHT can be ignored in normal direction when they are computed as the tra...Attempting to find a fast computing method to DHT （distinguished hyperbolic trajectory）, this study first proves that the errors of the stable DHT can be ignored in normal direction when they are computed as the trajectories extend. This conclusion means that the stable flow with perturbation will approach to the real trajectory as it extends over time. Based on this theory and combined with the improved DHT computing method, this paper reports a new fast computing method to DHT, which magnifies the DHT computing speed without decreasing its accuracy.展开更多
Electromagnetic scattering from inhomogeneous three-dimensional( 3D) bi-anisotropic scatterers is formulated in terms of the volume integral equation( VIE) method. Based on the volume equivalence principle,the VIE is ...Electromagnetic scattering from inhomogeneous three-dimensional( 3D) bi-anisotropic scatterers is formulated in terms of the volume integral equation( VIE) method. Based on the volume equivalence principle,the VIE is represented in terms of a pair of coupled bi-anisotropic polarized volume electric and magnetic flux densities. The VIE is solved using the method of moments( MoM) combined with tetrahedral mesh. Then the fast dipole method( FDM) based on the equivalent dipole method( EDM) is extended to analyze the scattering of bi-anisotropic media by solving the VIE. Finally,some numerical results are given to demonstrate the accuracy of the developed method for the scattering analysis of the bi-anisotropic media.展开更多
Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternati...Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.展开更多
The N-1 criterion is a critical factor for ensuring the reliable and resilient operation of electric power distribution networks.However,the increasing complexity of distribution networks and the associated growth in ...The N-1 criterion is a critical factor for ensuring the reliable and resilient operation of electric power distribution networks.However,the increasing complexity of distribution networks and the associated growth in data size have created a significant challenge for distribution network planners.To address this issue,we propose a fast N-1 verification procedure for urban distribution networks that combines CIM file data analysis with MILP-based mathematical modeling.Our proposed method leverages the principles of CIM file analysis for distribution network N-1 analysis.We develop a mathematical model of distribution networks based on CIM data and transfer it into MILP.We also take into account the characteristics of medium voltage distribution networks after a line failure and select the feeder section at the exit of each substation with a high load rate to improve the efficiency of N-1 analysis.We validate our approach through a series of case studies and demonstrate its scalability and superiority over traditional N-1 analysis and heuristic optimization algorithms.By enabling online N-1 analysis,our approach significantly improves the work efficiency of distribution network planners.In summary,our proposed method provides a valuable tool for distribution network planners to enhance the accuracy and efficiency of their N-1 analyses.By leveraging the advantages of CIM file data analysis and MILP-based mathematical modeling,our approach contributes to the development of more resilient and reliable electric power distribution networks.展开更多
In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension s...In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension splitting method(DSM).By using the DSM,a 3D problem is converted to a series of 2D ones,and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems.The essential boundary conditions are treated by the penalty method.The splitting direction uses the finite difference method(FDM),which can combine these 2D problems into a discrete system.Finally,the system equation of the 3D elasticity problem is obtained.Some specific numerical problems are provided to illustrate the effectiveness and advantages of the FEFG method for 3D elasticity by comparing the results of the FEFG method with those of the IEFG method.The convergence and relative error norm of the FEFG method for elasticity are also studied.展开更多
With the increasingly stringent requirements for carbon emissions,countries have increased the scale of clean energy use in recent years.As an important new clean energy source,the ratio of wind power in energy utiliz...With the increasingly stringent requirements for carbon emissions,countries have increased the scale of clean energy use in recent years.As an important new clean energy source,the ratio of wind power in energy utilization has been increasing.The horizontal axis wind turbine is the main form of wind power generation,which is subject to random wind loads during operation and is prone to various failures after a long period of operation,resulting in reduced power generation efficiency or even shutdown.In order to ensure stable external power transmission,it is necessary to perform fault diagnosis for wind turbines.However,the traditional time-frequency analysis method is defective.This paper proposes a new LOD-ICA method to realize the resolution of the vibration signals mode mixing problem incorporated the merits of both methods.The LOD-ICA method and the LOD method based on noise-assisted analysis decompose the same signal to produce different signal components.The feasibility of the LOD-ICA method was verified by comparing the correlation coefficients between each of the signal components generated by the two methods and the original signal.In the field of wind turbine fault diagnosis,the LOD-ICA method is employed to the fault characteristics of gearboxes to extract the fault signs of vibration signals,further demonstrated the superiority of the LOD-ICA method in processing vibration signals of rotating machinery.展开更多
Geophysical exploration methods are important tools for landslide disaster assessment,landslide treatment scheme design,and landslide prevention engineering.Seismic exploration,as an important geophysical exploration ...Geophysical exploration methods are important tools for landslide disaster assessment,landslide treatment scheme design,and landslide prevention engineering.Seismic exploration,as an important geophysical exploration method,plays an critical role in geological disaster evaluation.Traveltime is one of the most frequently used seismic attributes.Among many different traveltime calculation methods,the fast marching method(FMM)is featured for its advantages in high efficiency,high accuracy and strong stability.In this paper,the velocity models are established according to the real landslide models,and then the topography FMM is applied to these landslide models.The calculation results show that topography FMM outperforms in calculating the traveltime for landslides.展开更多
The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle li...The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle limitation. And, the vanishing point is detected robustly by using the fast M-estimation method. Proposed method could detect straight-line features associated with vanishing point detection efficient on the road. And the vanishing point was detected exactly by the effect of the fast M-estimation method when the straight-line features not associated with vanishing point detection were detected. The processing time of the proposed method was faster than the camera flame rate （30 fps）. Thus, the proposed method is capable of real-time processing.展开更多
Making use of this expression to calculate the phase grating in high resolution image simulation can greatly reduce the calculating time. In this paper, the derivation of the expression is introduced, and then the com...Making use of this expression to calculate the phase grating in high resolution image simulation can greatly reduce the calculating time. In this paper, the derivation of the expression is introduced, and then the computer routine is explained in details. Finally the potential projection map of Mg44Rh7 along [001] direction is shown as an illustration. All operations are carried out in real space, so we call the calculation method as the real space method.展开更多
基金supported by NSFC(Nos.41274120,41404085,and 41504084)
文摘3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method （FMM） is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method （WFC）, which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models.
基金the Key Program of National Natural Science Foundation of China(52039007)for providing financial support.
文摘Microseismic(MS)event locations are vital aspect of MS monitoring technology used to delineate the damage zone inside the surrounding rock mass.However,complex geological conditions can impose significantly adverse effects on the final location results.To achieve a high-accuracy location in a complex cavern-containing structure,this study develops an MS location method using the fast marching method(FMM)with a second-order difference approach(FMM2).Based on the established velocity model with three-dimensional(3D)discrete grids,the realization of the MS location can be achieved by searching the minimum residual between the theoretical and actual first arrival times.Moreover,based on the calculation results of FMM2,the propagation paths from the MS sources to MS sensors can be obtained using the linear interpolation approach and the Runge–Kutta method.These methods were validated through a series of numerical experiments.In addition,our proposed method was applied to locate the recorded blasting and MS events that occurred during the excavation period of the underground caverns at the Houziyan hydropower station.The location results of the blasting activities show that our method can effectively reduce the location error compared with the results based on the uniform velocity model.Furthermore,the obtained MS location was verified through the occurrence of shotcrete fractures and spalling,and the monitoring results of the in-situ multipoint extensometer.Our proposed method can offer a more accurate rock fracture location and facilitate the delineation of damage zones inside the surrounding rock mass.
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supported by the National Natural Science Foundation of China (61603398)。
文摘Fast computation of the landing footprint of a space-to-ground vehicle is a basic requirement for the deployment of parking orbits, as well as for enabling decision makers to develop real-time programs of transfer trajectories. In order to address the usually slow computational time for the determination of the landing footprint of a space-to-ground vehicle under finite thrust, this work proposes a method that uses polynomial equations to describe the boundaries of the landing footprint and uses back propagation(BP) neural networks to quickly determine the landing footprint of the space-to-ground vehicle. First, given orbital parameters and a manoeuvre moment, the solution model of the landing footprint of a space-to-ground vehicle under finite thrust is established. Second, given arbitrary orbital parameters and an arbitrary manoeuvre moment, a fast computational model for the landing footprint of a space-to-ground vehicle based on BP neural networks is provided.Finally, the simulation results demonstrate that under the premise of ensuring accuracy, the proposed method can quickly determine the landing footprint of a space-to-ground vehicle with arbitrary orbital parameters and arbitrary manoeuvre moments. The proposed fast computational method for determining a landing footprint lays a foundation for the parking-orbit configuration and supports the design of real-time transfer trajectories.
基金Project(Z110803)supported by the State Key Laboratory of Geomechanics and Geotechnical Engineering,ChinaProject(2008AA062303)supported by the National High Technology Research and Development Program of China
文摘A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM.Moreover,a flow rate estimate method was developed for the project whose injection rate has not been clearly determined.A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project,which is a good practice verification of FEFDM.At last,this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure.The result shows that for deep wellbore,the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted.It is also shown that with flow rate increasing,the friction term can no longer be neglected.
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 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This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafunctions and the Ishigami function are considered in the sensitivity analysis(SA).The effects of the input variables on the output variables are investigated,and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.
基金The NNSF (10371137 and 10201034) of Chinathe Foundation (20030558008) of Doctoral Program of National Higher Education, Guangdong Provincial Natural Science Foundation (1011170) of China and the Advanced Research Foundation of Zhongshan UniversityThe US National Science Foundation (9973427 and 0312113)NSF (10371122) of China and the Chinese Academy of Sciences under the program of "Hundred Distinguished Young Chinese Scientists."
文摘We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.
基金Project supported by the National Basic Research Program of China(973 ProjectNo.2010CB832702)+4 种基金the National Science Funds for Distinguished Young Scholars of China(No.11125208)the National Natural Science Foundation of China(Nos.11125208 and 11302069)the 111 project under Grant B12032Jiangsu Province Graduate Students Research and Innovation Plan(No.KYZZ 0138)the scholarship from the China Scholarship Council(CSC)(No.201306710026)
文摘The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O（N^3） with direct solvers or O（N^2） with iterative solvers, as well as the memory requirement of O（N^2）. In this study, the first attempt was made to combine the fast multipole method （FMM） and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O（N）. Based on the complex variable represen- tation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.
基金supported by the National Natural Science Foundation of China (Grant No. 60872159)
文摘Attempting to find a fast computing method to DHT （distinguished hyperbolic trajectory）, this study first proves that the errors of the stable DHT can be ignored in normal direction when they are computed as the trajectories extend. This conclusion means that the stable flow with perturbation will approach to the real trajectory as it extends over time. Based on this theory and combined with the improved DHT computing method, this paper reports a new fast computing method to DHT, which magnifies the DHT computing speed without decreasing its accuracy.
基金Supported by the National Natural Science Foundation of China(61071019)the Joint Funding Project of the Aerospace Science Foundation Office of China(2008ZA52006)
文摘Electromagnetic scattering from inhomogeneous three-dimensional( 3D) bi-anisotropic scatterers is formulated in terms of the volume integral equation( VIE) method. Based on the volume equivalence principle,the VIE is represented in terms of a pair of coupled bi-anisotropic polarized volume electric and magnetic flux densities. The VIE is solved using the method of moments( MoM) combined with tetrahedral mesh. Then the fast dipole method( FDM) based on the equivalent dipole method( EDM) is extended to analyze the scattering of bi-anisotropic media by solving the VIE. Finally,some numerical results are given to demonstrate the accuracy of the developed method for the scattering analysis of the bi-anisotropic media.
基金Research was supported by the NSFC Grant 11872210Research was supported by the NSFC Grant 11872210 and Grant No.MCMS-I-0120G01+1 种基金Research supported in part by the AFOSR Grant FA9550-20-1-0055NSF Grant DMS-2010107.
文摘Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.
基金supported by the National Natural Science Foundation of China(52207105)。
文摘The N-1 criterion is a critical factor for ensuring the reliable and resilient operation of electric power distribution networks.However,the increasing complexity of distribution networks and the associated growth in data size have created a significant challenge for distribution network planners.To address this issue,we propose a fast N-1 verification procedure for urban distribution networks that combines CIM file data analysis with MILP-based mathematical modeling.Our proposed method leverages the principles of CIM file analysis for distribution network N-1 analysis.We develop a mathematical model of distribution networks based on CIM data and transfer it into MILP.We also take into account the characteristics of medium voltage distribution networks after a line failure and select the feeder section at the exit of each substation with a high load rate to improve the efficiency of N-1 analysis.We validate our approach through a series of case studies and demonstrate its scalability and superiority over traditional N-1 analysis and heuristic optimization algorithms.By enabling online N-1 analysis,our approach significantly improves the work efficiency of distribution network planners.In summary,our proposed method provides a valuable tool for distribution network planners to enhance the accuracy and efficiency of their N-1 analyses.By leveraging the advantages of CIM file data analysis and MILP-based mathematical modeling,our approach contributes to the development of more resilient and reliable electric power distribution networks.
基金supported by the National Natural Science Foundation of China(Grant Nos.52004169 and 11571223).
文摘In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension splitting method(DSM).By using the DSM,a 3D problem is converted to a series of 2D ones,and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems.The essential boundary conditions are treated by the penalty method.The splitting direction uses the finite difference method(FDM),which can combine these 2D problems into a discrete system.Finally,the system equation of the 3D elasticity problem is obtained.Some specific numerical problems are provided to illustrate the effectiveness and advantages of the FEFG method for 3D elasticity by comparing the results of the FEFG method with those of the IEFG method.The convergence and relative error norm of the FEFG method for elasticity are also studied.
文摘With the increasingly stringent requirements for carbon emissions,countries have increased the scale of clean energy use in recent years.As an important new clean energy source,the ratio of wind power in energy utilization has been increasing.The horizontal axis wind turbine is the main form of wind power generation,which is subject to random wind loads during operation and is prone to various failures after a long period of operation,resulting in reduced power generation efficiency or even shutdown.In order to ensure stable external power transmission,it is necessary to perform fault diagnosis for wind turbines.However,the traditional time-frequency analysis method is defective.This paper proposes a new LOD-ICA method to realize the resolution of the vibration signals mode mixing problem incorporated the merits of both methods.The LOD-ICA method and the LOD method based on noise-assisted analysis decompose the same signal to produce different signal components.The feasibility of the LOD-ICA method was verified by comparing the correlation coefficients between each of the signal components generated by the two methods and the original signal.In the field of wind turbine fault diagnosis,the LOD-ICA method is employed to the fault characteristics of gearboxes to extract the fault signs of vibration signals,further demonstrated the superiority of the LOD-ICA method in processing vibration signals of rotating machinery.
基金Supported by projects of National Natural Science Foundation of China(No.41804100)Fundamental Research Funds for the Central Universities(No.2682018CX36)+1 种基金China Postdoctoral Science Foundation(No.2020T130080)China Postdoctoral Science Foundation(No.2018M640910).
文摘Geophysical exploration methods are important tools for landslide disaster assessment,landslide treatment scheme design,and landslide prevention engineering.Seismic exploration,as an important geophysical exploration method,plays an critical role in geological disaster evaluation.Traveltime is one of the most frequently used seismic attributes.Among many different traveltime calculation methods,the fast marching method(FMM)is featured for its advantages in high efficiency,high accuracy and strong stability.In this paper,the velocity models are established according to the real landslide models,and then the topography FMM is applied to these landslide models.The calculation results show that topography FMM outperforms in calculating the traveltime for landslides.
文摘The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle limitation. And, the vanishing point is detected robustly by using the fast M-estimation method. Proposed method could detect straight-line features associated with vanishing point detection efficient on the road. And the vanishing point was detected exactly by the effect of the fast M-estimation method when the straight-line features not associated with vanishing point detection were detected. The processing time of the proposed method was faster than the camera flame rate （30 fps）. Thus, the proposed method is capable of real-time processing.
文摘Making use of this expression to calculate the phase grating in high resolution image simulation can greatly reduce the calculating time. In this paper, the derivation of the expression is introduced, and then the computer routine is explained in details. Finally the potential projection map of Mg44Rh7 along [001] direction is shown as an illustration. All operations are carried out in real space, so we call the calculation method as the real space method.
