This paper presents a fast algorithm for solving the scattering problem from an open rectangular cavity embedded in the ground plane.The computational region is chosen as the union of two rectangular regions:one is a ...This paper presents a fast algorithm for solving the scattering problem from an open rectangular cavity embedded in the ground plane.The computational region is chosen as the union of two rectangular regions:one is a region above the ground,the other one is a region containing the cavity.The finite difference scheme is constructed in each region.An intermediate layer of the mesh is shared by both regions,which is the key of the algorithm.A cyclic reduction method is employed to solve the difference equation in the region above the ground.Then the numerical solution on the cavity aperture can be obtained.The numerical experiments are provided to verify the feasibility of the proposed algorithm.展开更多
To improve the performance of Saitou and Nei's algorithm (SN) and Studier and Keppler's improved algorithm (SK) for constructing neighbor-joining phylogenetic trees and reduce the time complexity of the computat...To improve the performance of Saitou and Nei's algorithm (SN) and Studier and Keppler's improved algorithm (SK) for constructing neighbor-joining phylogenetic trees and reduce the time complexity of the computation, a fast algorithm is proposed. The proposed algorithm includes three techniques. First, a linear array A[N] is introduced to store the sum of every row of the distance matrix (the same as SK), which can eliminate many repeated computations. Secondly, the value of A [i] is computed only once at the beginning of the algorithm, and is updated by three elements in the iteration. Thirdly, a very compact formula for the sum of all the branch lengths of operational taxonomic units (OTUs) i and j is designed, and the correctness of the formula is proved. The experimental results show that the proposed algorithm is from tens to hundreds times faster than SN and roughly two times faster than SK when N increases, constructing a tree with 2 000 OTUs in 3 min on a current desktop computer. To earn the time with the cost of the space and reduce the computations in the innermost loop are the basic solutions for algorithms with many loops.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
A fast algorithm is proposed to predict penetration trajectory in simulation of normal and oblique penetration of a rigid steel projectile into a limestone target. The algorithm is designed based on the idea of isolat...A fast algorithm is proposed to predict penetration trajectory in simulation of normal and oblique penetration of a rigid steel projectile into a limestone target. The algorithm is designed based on the idea of isolation between the projectile and the target. Corresponding factors of influence are considered, including analytical load model, cratering effect, free surface effect, and separation-reattachment phenomenon. Besides, a method of cavity ring is used to study the process of cavity expansion. Further, description of the projectile's three-dimensional gesture is coded for fast calculation, named PENE3D. A presented. As a result, the algorithm is series of cases with selected normal and oblique penetrations are simulated by the algorithm. The predictions agree with the results of tests, showing that the proposed algorithm is fast and effective in simulation of the penetration process and prediction of the penetration trajectory.展开更多
An iterative algorithm to calculate mutual correlation using hierarchical key points and the search space mark principle is proposed. An effective algorithm is designed to improve the matching speed. By hi-erarchical ...An iterative algorithm to calculate mutual correlation using hierarchical key points and the search space mark principle is proposed. An effective algorithm is designed to improve the matching speed. By hi-erarchical key point algorithm and mutual correlation coefficients of the matching images, the important points can be iteratively calculated in the images hierarchically, and the correlation coefficient can be ob-tained with satisfactory precision. Massive spots in the parameter space which are impossible to match can be removed by the search space mark principle. Two approximate continuities in the correlation image matching process, the image gray level distribution continuity and the correlation coefficient value in the parameter space continuity, are considered in the method. The experiments show that the new algorithm can greatly enhance matching speed and achieve accurate matching results.展开更多
Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to...Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I (the set of polynomials satisfying all the homogeneous interpolation conditions are zero) and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O(τ^3) where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions (presented by lower sets) and then use fast GEPP to solve the linear system with O((τ + 3)τ^2) operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ], where n is the number of variables.展开更多
Images captured outdoor usually degenerate because of the bad weather conditions,among which fog,one of the widespread phenomena,affects the video quality greatly.The physical features of fog make the video blurred an...Images captured outdoor usually degenerate because of the bad weather conditions,among which fog,one of the widespread phenomena,affects the video quality greatly.The physical features of fog make the video blurred and the visible distance shortened,seriously impairing the reliability of the video system.In order to satisfy the requirement of image processing in real-time,the normal distribution curve fitting technology is used to fit the histogram of the sky part and the region growing method is used to segment the region of sky.As for the non-sky part,a method of self-adaptive interpolation to equalize the histogram is adopted to enhance the contrast of the images.Experiment results show that the method works well and will not cause block effect.展开更多
2 It is important to compute the Hilbert transform of a given function defined on a finite interval.In 2013,Micchelli and his collaborators proposed a fast algorithm,which is called the Hilbert spline transform,to cal...2 It is important to compute the Hilbert transform of a given function defined on a finite interval.In 2013,Micchelli and his collaborators proposed a fast algorithm,which is called the Hilbert spline transform,to calculate the Hilbert transform of a given function on a finite interval with the computational complexity O(n log n),where the spline knots were chosen to be the midpoints of sampling points.A natural question is that,whether or not the spline knots can be chosen to be the same as the sampling points.This paper gives a positive answer to this question.Besides,the analytic expression of the Hilbert transform of B-splines of any order is also established.Furthermore,the problem of how to choose spline coefficients,using the quasi-interpolation method or interpolation method,is also considered,although both make sure an optimal approximation order.Several interesting numerical examples are implemented and compared with most of the existing methods.Numerical results show that the proposed algorithm has a relatively high computational accuracy as well as a relatively low computational complexity.展开更多
In eld seismic data acquisition,seismic traces are often aected by substantial data gaps and strong noise interference due to environmental and instrumental factors,thus degrading the resolution and signalto-noise rat...In eld seismic data acquisition,seismic traces are often aected by substantial data gaps and strong noise interference due to environmental and instrumental factors,thus degrading the resolution and signalto-noise ratio(SNR)of the seismic profiles.Effective seismic data reconstruction and noise suppression techniques are therefore essential to recover missing signals and improve data quality.In this study,a fast projection onto convex sets(FPOCS)algorithm is proposed by incorporating an inertial parameter that involves a linear combination of the two preceding iterations based on the traditional projection onto convex sets(POCS)algorithm.Then,a weighting factor is introduced to achieve simultaneous data reconstruction and noise suppression using the weighted fast projection onto convex sets(WFPOCS)algorithm.To further suppress residual random noise in the updated solution,an optimization strategy is adopted by swapping the order of the iterative hard thresholding operator and the projection operator.The nal algorithm,termed the improved weighted fast projection onto convex sets(IWFPOCS),achieves high-efciency reconstruction and effective noise suppression.Compared with WFPOCS,the proposed method maintains fast reconstruction speed while demonstrating superior denoising performance on irregularly missing and noisy datasets.Field data experiments conrm that the proposed method signicantly improves the SNR and resolution of seismic data,oering strong practical potential for subsequent processing and interpretation.展开更多
The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh(TT-M)finite element(FE)method to ease the problem caused by strong nonlinearities.The TT-M ...The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh(TT-M)finite element(FE)method to ease the problem caused by strong nonlinearities.The TT-M FE algorithm includes the following main computing steps.First,a nonlinear FE method is applied on a coarse time-meshτc.Here,the FE method is used for spatial discretization and the implicit second-orderθscheme(containing both implicit Crank-Nicolson and second-order backward difference)is used for temporal discretization.Second,based on the chosen initial iterative value,a linearized FE system on time fine mesh is solved,where some useful coarse numerical solutions are found by Lagrange’s interpolation formula.The analysis for both stability and a priori error estimates is made in detail.Numerical examples are given to demonstrate the validity of the proposed algorithm.Our algorithm is compared with the traditional Galerkin FE method and it is evident that our fast algorithm can save computational time.展开更多
Conditional Nonlinear Optimal Perturbation (CNOP) is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector (LSV) to include nonlinearity. It has become a powerful tool for studyi...Conditional Nonlinear Optimal Perturbation (CNOP) is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector (LSV) to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function (EOF). The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System (GRAPES), an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity (target) area is evaluated through two observing system simulation experiments (OSSEs). The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors (ARPEs) in the verification region are reduced significantly compared with the "true state," when the initial conditions (ICs) in the sensitivity area are replaced with the "observations." The decrease of the ARPEs can be achieved for even longer prediction times (e.g., 72 h). Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon's initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.展开更多
An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalize...An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalizes the algorithm for computing the linear complexity of a binary sequence with period 2' and the algorithm for computing the linear complexity of a binary sequence with period pn, where 2 is a primitive root modulo p2.展开更多
An acoustic vector sensor(AVS)can capture more information than a conventional acoustic pressure sensor(APS).As a result,more output channels are required when multiple AVS are formed into arrays,making processing the...An acoustic vector sensor(AVS)can capture more information than a conventional acoustic pressure sensor(APS).As a result,more output channels are required when multiple AVS are formed into arrays,making processing the data stream computationally intense.This paper proposes a new algorithm based on the propagator method for wideband coherent sources that eliminates eigen-decomposition in order to reduce the computational burden.Data from simulations and lake trials showed that the new algorithm is valid:it resolves coherent sources,breaks leftight ambiguity,and allows inter element spacing to exceed a half-wavelength.展开更多
The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm(PMLFMA).Considering the main complements of multilevel fast multipole algorithm(M...The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm(PMLFMA).Considering the main complements of multilevel fast multipole algorithm(MLFMA) memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects.展开更多
An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival,which is the measurement of X-ray pulsar navigation.Epoch f...An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival,which is the measurement of X-ray pulsar navigation.Epoch folding is a classical period estimation method in the time domain;however,its computational complexity grows as the number of trail periods increases.In order to reduce the computational complexity,this paper improves the fast folding algorithm through segment correlation and amplitude accumulation,which is based on the post-order traversal of a binary tree.Compared with epoch folding,the improved fast folding algorithm can achieve a similar accuracy at the cost of a lower computational burden.Compared with the original fast folding algorithm,the improved algorithm can be applied to detectors with a much smaller effective area.The performance of the method is investigated by simulation data and observation data from the Neutron star Interior Composition Explorer(NICER).展开更多
Recently,a two-dimensional(2-D)Tsallis entropy thresholding method has been proposed as a new method for image segmentation.But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle t...Recently,a two-dimensional(2-D)Tsallis entropy thresholding method has been proposed as a new method for image segmentation.But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems.A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed.The key variables involved in calculating 2-D Tsallis entropy are written in recursive form.Thus,many repeating calculations are avoided and the computation complexity reduces to O(L2)from O(L4).The effectiveness of the proposed algorithm is illustrated by experimental results.展开更多
Although the genetic algorithm (GA) for structural optimization is very robust, it is very computationally intensive and hence slower than optimality criteria and mathematical programming methods. To speed up the de...Although the genetic algorithm (GA) for structural optimization is very robust, it is very computationally intensive and hence slower than optimality criteria and mathematical programming methods. To speed up the design process, the authors present an adaptive reanalysis method for GA and its applications in the optimal design of trusses. This reanalysis technique is primarily derived from the Kirsch's combined approximations method. An iteration scheme is adopted to adaptively determine the number of basis vectors at every generation. In order to illustrate this method, three classical examples of optimal truss design are used to validate the proposed reanalysis-based design procedure. The presented numerical results demonstrate that the adaptive reanalysis technique affects very slightly the accuracy of the optimal solutions and does accelerate the design process, especially for large-scale structures.展开更多
A full-wave analysis of the electromagnetic problem of a three-dimensional(3-D)antenna radiating through a 3-D dielectric radome is preserued.The problem is formulated using the Poggio-Miller-Chang-Harrington-Wu(PMCHW...A full-wave analysis of the electromagnetic problem of a three-dimensional(3-D)antenna radiating through a 3-D dielectric radome is preserued.The problem is formulated using the Poggio-Miller-Chang-Harrington-Wu(PMCHW)approach for homogeneous dielectric objects and the electric field integral equation for conducting objects.The integral equations are discretized by the method of moment(MoM),in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions.The resultant matrix equation is then solved by the multilevel fast multipole algorithm(MLFMA)and fast far-field approximation(FAFFA)is used to further accelerate the computation.The radiation patterns of dipole arrays in the presence of radomes are presented.The numerical results demonstrate the accuracy and versatility of this method.展开更多
A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm(FE-BI-MLFMA).Among many algorithms of FE-BI-MLFMA...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 Natural Science Foundation of China(12101205)the Natural Science Foundation of Heilongjiang Province of China(PL2024A010)。
摘要This paper presents a fast algorithm for solving the scattering problem from an open rectangular cavity embedded in the ground plane.The computational region is chosen as the union of two rectangular regions:one is a region above the ground,the other one is a region containing the cavity.The finite difference scheme is constructed in each region.An intermediate layer of the mesh is shared by both regions,which is the key of the algorithm.A cyclic reduction method is employed to solve the difference equation in the region above the ground.Then the numerical solution on the cavity aperture can be obtained.The numerical experiments are provided to verify the feasibility of the proposed algorithm.
摘要To improve the performance of Saitou and Nei's algorithm (SN) and Studier and Keppler's improved algorithm (SK) for constructing neighbor-joining phylogenetic trees and reduce the time complexity of the computation, a fast algorithm is proposed. The proposed algorithm includes three techniques. First, a linear array A[N] is introduced to store the sum of every row of the distance matrix (the same as SK), which can eliminate many repeated computations. Secondly, the value of A [i] is computed only once at the beginning of the algorithm, and is updated by three elements in the iteration. Thirdly, a very compact formula for the sum of all the branch lengths of operational taxonomic units (OTUs) i and j is designed, and the correctness of the formula is proved. The experimental results show that the proposed algorithm is from tens to hundreds times faster than SN and roughly two times faster than SK when N increases, constructing a tree with 2 000 OTUs in 3 min on a current desktop computer. To earn the time with the cost of the space and reduce the computations in the innermost loop are the basic solutions for algorithms with many loops.
摘要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.
基金Project supported by the National Natural Science Foundation of China(No.11202236)
摘要A fast algorithm is proposed to predict penetration trajectory in simulation of normal and oblique penetration of a rigid steel projectile into a limestone target. The algorithm is designed based on the idea of isolation between the projectile and the target. Corresponding factors of influence are considered, including analytical load model, cratering effect, free surface effect, and separation-reattachment phenomenon. Besides, a method of cavity ring is used to study the process of cavity expansion. Further, description of the projectile's three-dimensional gesture is coded for fast calculation, named PENE3D. A presented. As a result, the algorithm is series of cases with selected normal and oblique penetrations are simulated by the algorithm. The predictions agree with the results of tests, showing that the proposed algorithm is fast and effective in simulation of the penetration process and prediction of the penetration trajectory.
摘要An iterative algorithm to calculate mutual correlation using hierarchical key points and the search space mark principle is proposed. An effective algorithm is designed to improve the matching speed. By hi-erarchical key point algorithm and mutual correlation coefficients of the matching images, the important points can be iteratively calculated in the images hierarchically, and the correlation coefficient can be ob-tained with satisfactory precision. Massive spots in the parameter space which are impossible to match can be removed by the search space mark principle. Two approximate continuities in the correlation image matching process, the image gray level distribution continuity and the correlation coefficient value in the parameter space continuity, are considered in the method. The experiments show that the new algorithm can greatly enhance matching speed and achieve accurate matching results.
基金Supported by the National Natural Science Foundation of China(11271156 and 11171133)the Technology Development Plan of Jilin Province(20130522104JH)
摘要Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I (the set of polynomials satisfying all the homogeneous interpolation conditions are zero) and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O(τ^3) where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions (presented by lower sets) and then use fast GEPP to solve the linear system with O((τ + 3)τ^2) operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ], where n is the number of variables.
摘要Images captured outdoor usually degenerate because of the bad weather conditions,among which fog,one of the widespread phenomena,affects the video quality greatly.The physical features of fog make the video blurred and the visible distance shortened,seriously impairing the reliability of the video system.In order to satisfy the requirement of image processing in real-time,the normal distribution curve fitting technology is used to fit the histogram of the sky part and the region growing method is used to segment the region of sky.As for the non-sky part,a method of self-adaptive interpolation to equalize the histogram is adopted to enhance the contrast of the images.Experiment results show that the method works well and will not cause block effect.
摘要2 It is important to compute the Hilbert transform of a given function defined on a finite interval.In 2013,Micchelli and his collaborators proposed a fast algorithm,which is called the Hilbert spline transform,to calculate the Hilbert transform of a given function on a finite interval with the computational complexity O(n log n),where the spline knots were chosen to be the midpoints of sampling points.A natural question is that,whether or not the spline knots can be chosen to be the same as the sampling points.This paper gives a positive answer to this question.Besides,the analytic expression of the Hilbert transform of B-splines of any order is also established.Furthermore,the problem of how to choose spline coefficients,using the quasi-interpolation method or interpolation method,is also considered,although both make sure an optimal approximation order.Several interesting numerical examples are implemented and compared with most of the existing methods.Numerical results show that the proposed algorithm has a relatively high computational accuracy as well as a relatively low computational complexity.
基金supported in part by the Foundation of National Key Laboratory of Uranium Resources Exploration-Mining and Nuclear Remote Sensing under Grant 2024QZ-TD-13in part by the National Natural Science Foundation of China under Grant 42564006+1 种基金in part by the Natural Science Foundation of Jiangxi Province under Grant 20242BAB26051in part by the Open Fund of SINOPEC Key Laboratory of Geophysics,and in part by support the plan of Ganpo Juncai under Grant 20243BCE51012.
摘要In eld seismic data acquisition,seismic traces are often aected by substantial data gaps and strong noise interference due to environmental and instrumental factors,thus degrading the resolution and signalto-noise ratio(SNR)of the seismic profiles.Effective seismic data reconstruction and noise suppression techniques are therefore essential to recover missing signals and improve data quality.In this study,a fast projection onto convex sets(FPOCS)algorithm is proposed by incorporating an inertial parameter that involves a linear combination of the two preceding iterations based on the traditional projection onto convex sets(POCS)algorithm.Then,a weighting factor is introduced to achieve simultaneous data reconstruction and noise suppression using the weighted fast projection onto convex sets(WFPOCS)algorithm.To further suppress residual random noise in the updated solution,an optimization strategy is adopted by swapping the order of the iterative hard thresholding operator and the projection operator.The nal algorithm,termed the improved weighted fast projection onto convex sets(IWFPOCS),achieves high-efciency reconstruction and effective noise suppression.Compared with WFPOCS,the proposed method maintains fast reconstruction speed while demonstrating superior denoising performance on irregularly missing and noisy datasets.Field data experiments conrm that the proposed method signicantly improves the SNR and resolution of seismic data,oering strong practical potential for subsequent processing and interpretation.
基金supported by the Research Project Supported by Shanxi Scholarship Council of China(No.2021-029)the Key Research and Development(R&D)Projects of Shanxi Province(No.201903D121038)the Natural Science Foundation of Shanxi Province(Nos.201801D121016,201901D111123).
摘要The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh(TT-M)finite element(FE)method to ease the problem caused by strong nonlinearities.The TT-M FE algorithm includes the following main computing steps.First,a nonlinear FE method is applied on a coarse time-meshτc.Here,the FE method is used for spatial discretization and the implicit second-orderθscheme(containing both implicit Crank-Nicolson and second-order backward difference)is used for temporal discretization.Second,based on the chosen initial iterative value,a linearized FE system on time fine mesh is solved,where some useful coarse numerical solutions are found by Lagrange’s interpolation formula.The analysis for both stability and a priori error estimates is made in detail.Numerical examples are given to demonstrate the validity of the proposed algorithm.Our algorithm is compared with the traditional Galerkin FE method and it is evident that our fast algorithm can save computational time.
基金Supported by the "973" Project of the Ministry of Science and Technology of China under Grant No. 2004CB418304the China Meteorological Administration R&D Special Fund for Public Welfare (meteorology) under Grant No. GYHY(QX)2007-6-15
摘要Conditional Nonlinear Optimal Perturbation (CNOP) is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector (LSV) to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function (EOF). The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System (GRAPES), an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity (target) area is evaluated through two observing system simulation experiments (OSSEs). The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors (ARPEs) in the verification region are reduced significantly compared with the "true state," when the initial conditions (ICs) in the sensitivity area are replaced with the "observations." The decrease of the ARPEs can be achieved for even longer prediction times (e.g., 72 h). Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon's initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.
基金This work was supported in part by the National Natural Science Foundation of China ( Grant No.60073051) the Natural Science Foundation of Education Council of Anhui Province.
摘要An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalizes the algorithm for computing the linear complexity of a binary sequence with period 2' and the algorithm for computing the linear complexity of a binary sequence with period pn, where 2 is a primitive root modulo p2.
基金the National 863 Plan Project of Ministry of Science and Technology of China under Grant No.2006AA09Z234
摘要An acoustic vector sensor(AVS)can capture more information than a conventional acoustic pressure sensor(APS).As a result,more output channels are required when multiple AVS are formed into arrays,making processing the data stream computationally intense.This paper proposes a new algorithm based on the propagator method for wideband coherent sources that eliminates eigen-decomposition in order to reduce the computational burden.Data from simulations and lake trials showed that the new algorithm is valid:it resolves coherent sources,breaks leftight ambiguity,and allows inter element spacing to exceed a half-wavelength.
基金supported by the National Basic Research Program of China (973 Program) (61320)
摘要The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm(PMLFMA).Considering the main complements of multilevel fast multipole algorithm(MLFMA) memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects.
基金the National Natural Science Foundation of China(No.61703413).
摘要An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival,which is the measurement of X-ray pulsar navigation.Epoch folding is a classical period estimation method in the time domain;however,its computational complexity grows as the number of trail periods increases.In order to reduce the computational complexity,this paper improves the fast folding algorithm through segment correlation and amplitude accumulation,which is based on the post-order traversal of a binary tree.Compared with epoch folding,the improved fast folding algorithm can achieve a similar accuracy at the cost of a lower computational burden.Compared with the original fast folding algorithm,the improved algorithm can be applied to detectors with a much smaller effective area.The performance of the method is investigated by simulation data and observation data from the Neutron star Interior Composition Explorer(NICER).
基金supported by the National Natural Science Foundation of China for Distinguished Young Scholars(60525303)Doctoral Foundation of Yanshan University(B243).
摘要Recently,a two-dimensional(2-D)Tsallis entropy thresholding method has been proposed as a new method for image segmentation.But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems.A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed.The key variables involved in calculating 2-D Tsallis entropy are written in recursive form.Thus,many repeating calculations are avoided and the computation complexity reduces to O(L2)from O(L4).The effectiveness of the proposed algorithm is illustrated by experimental results.
基金supported by the National Natural Science Foundation of China(50975121)the Project 2009-2007 of the Graduate Innovation Fund of Jilin University
摘要Although the genetic algorithm (GA) for structural optimization is very robust, it is very computationally intensive and hence slower than optimality criteria and mathematical programming methods. To speed up the design process, the authors present an adaptive reanalysis method for GA and its applications in the optimal design of trusses. This reanalysis technique is primarily derived from the Kirsch's combined approximations method. An iteration scheme is adopted to adaptively determine the number of basis vectors at every generation. In order to illustrate this method, three classical examples of optimal truss design are used to validate the proposed reanalysis-based design procedure. The presented numerical results demonstrate that the adaptive reanalysis technique affects very slightly the accuracy of the optimal solutions and does accelerate the design process, especially for large-scale structures.
基金the National Natural Science Foundation of China(60431010)
摘要A full-wave analysis of the electromagnetic problem of a three-dimensional(3-D)antenna radiating through a 3-D dielectric radome is preserued.The problem is formulated using the Poggio-Miller-Chang-Harrington-Wu(PMCHW)approach for homogeneous dielectric objects and the electric field integral equation for conducting objects.The integral equations are discretized by the method of moment(MoM),in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions.The resultant matrix equation is then solved by the multilevel fast multipole algorithm(MLFMA)and fast far-field approximation(FAFFA)is used to further accelerate the computation.The radiation patterns of dipole arrays in the presence of radomes are presented.The numerical results demonstrate the accuracy and versatility of this method.
摘要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.