The multi-layer Boussinesq equation proposed by Liu and Fang [Zhongbo Liu and Fang 2016] extends the applicability of the Boussinesq equation to deep-water waves. However, the model contains a large number of Poisson ...
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The multi-layer Boussinesq equation proposed by Liu and Fang [Zhongbo Liu and Fang 2016] extends the applicability of the Boussinesq equation to deep-water waves. However, the model contains a large number of Poisson type equations, making the model computationally inefficient. By solving some of the equations in preparation stage, a fast algorithm is proposed for the model in this paper. Compared with Liu and Fang's algorithm [Z B Liu and Fang 2019], the computational efficiency of the proposed algorithm is improved by 2.95-4 times. Finally, the accuracy of the algorithm is verified by three examples (including a horizontal two-dimensional example).
Modeling nonspherical precipitation targets and calculating their scattering properties are key for simulating dual-polarization weather radar echoes and remote sensing. The invariant imbedding T-matrix (IITM) method,...
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Modeling nonspherical precipitation targets and calculating their scattering properties are key for simulating dual-polarization weather radar echoes and remote sensing. The invariant imbedding T-matrix (IITM) method, due to its accuracy and practicality in computing nonspherical precipitation targets, is the most promising approach. However, accurate echo simulation requires repeated calculations of the scattering amplitude matrices for precipitation targets at various diameters, involving iterative computations, which leads to significant memory usage and long computation times when using the IITM. Hence, enhancing the computational efficiency of the IITM in simulations of nonspherical precipitation targets in dual-polarization weather radars is urgent. This article improves upon the traditional method of using ellipsoids for modeling precipitation targets by precisely considering particle shapes, employing various nonspherical particles, and dividing these targets into an inscribed homogeneous domain and an extended heterogeneous domain. For the homogeneous domain, the logarithmic-derivative Mie scattering method is used to improve computational efficiency, while the heterogeneous domain utilizes conventional iterative methods, rotational symmetry fast algorithms, and N-fold symmetry fast algorithms. The computed scattering amplitude matrices are integrated with the weather radar equation and pulse covariance matrix to complete echo simulations. Analyzing the computational results from individual particles and overall calculations, experiments show that fast algorithms can increase the computational efficiency of simulating various nonspherical precipitation targets in airborne dual-polarization weather radars by more than tenfold.
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...
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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.
Moment invariants are important shape descriptors in computer vision. The method of decomposing the trigonometric function is suggested to obtain various moment invariants. Based on this method, the "multi-filter...
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Moment invariants are important shape descriptors in computer vision. The method of decomposing the trigonometric function is suggested to obtain various moment invariants. Based on this method, the "multi-filter" algorithm is introduced as an efficient way to generate large numbers of moment invariants. A great deal of repeated computation on sub-polynomial is avoided. General explicit constructions of basic moment invariants are also provided. Furthermore, the proposed magnitude-normalized method makes invariants more stable and easier for classification. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
Segmented image coding segments an image into non-rectangular regions and approximates the texture in each region by a weighted sum of orthonormal base functions. These orthonormal base functions, which are region-spe...
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Segmented image coding segments an image into non-rectangular regions and approximates the texture in each region by a weighted sum of orthonormal base functions. These orthonormal base functions, which are region-specific, used to be generated by the Gram-Schmidt (GS) algorithm, which is unfortunately very time-consuming. This paper presents the polynomial recursive orthogonalization (PRO) algorithm which generates the same orthonormal base functions as GS, but which is faster than GS because it is based on a recurrence which has fewer terms than the corresponding GS equation. The paper presents theoretical and experimental results which show that PRO is two to three times faster in practice (depending on the number of computed base functions).
In this paper, we propose a fast algorithm for speeding up the process of template matching that uses M-estimators for dealing with outliers. We propose a particular image hierarchy called the p-pyramid that can be ex...
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In this paper, we propose a fast algorithm for speeding up the process of template matching that uses M-estimators for dealing with outliers. We propose a particular image hierarchy called the p-pyramid that can be exploited to generate a list of ascending lower bounds of the minimal matching errors when a nondecreasing robust error measure is adopted. Then, the set of lower bounds can be used to prune the search of the p-pyramid, and a fast algorithm is thereby developed in this paper. This fast algorithm ensures finding the global minimum of the robust template matching problem in which a nondecreasing M-estimator serves as an error measure. Experimental results demonstrate the effectiveness of our method.
Many combinatorial (optimization) problems of graphs (e.g., finding maximal independent sets or maximum matchings) and acyclic networks (e.g., finding shortest paths or maximum flows) can be solved by means of decompo...
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Many combinatorial (optimization) problems of graphs (e.g., finding maximal independent sets or maximum matchings) and acyclic networks (e.g., finding shortest paths or maximum flows) can be solved by means of decomposition of the graph (network) into autonomous subsets. (Given a relation R on A, a subset B of A is called autonomous, if for each α ∈ A\B the following holds: (i) if $(\alpha,\beta _algorithm)\in R$ for some $\beta _algorithm\in B$, then (α, β) ∈ R for all β ∈ B; (ii) if $(\beta _algorithm,\alpha)\in R$ for some $\beta _algorithm\in B$, then (β, α) ∈ R for all β ∈ B). We present an algorithm which finds all autonomous subsets of graphs and posets with p points in $O(p^{3})$ time and $O(p^{2})$ space. The ideas behind this algorithm reveal rather strong connections between graph decomposition, homomorphisms of graphs and posets, and comparability graph recognition. Furthermore, the well-known series-parallel decomposition for graphs and posets is contained as a special case.
This paper proposes a fast algorithm for Walsh Hadamard Transform on sliding windows which can be used to implement pattern matching most efficiently. The computational requirement of the proposed algorithm is about 1...
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This paper proposes a fast algorithm for Walsh Hadamard Transform on sliding windows which can be used to implement pattern matching most efficiently. The computational requirement of the proposed algorithm is about 1.5 additions per projection vector per sample, which is the lowest among existing fast algorithms for Walsh Hadamard Transform on sliding windows.
fast algorithms are presented for multi-dimensional discrete Hartley transform (MD-DHT) with size q(l1) x q(l2) x...x q(lr). where q is an odd prime number, and r > 1 is the number of dimensions. By using the multi...
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fast algorithms are presented for multi-dimensional discrete Hartley transform (MD-DHT) with size q(l1) x q(l2) x...x q(lr). where q is an odd prime number, and r > 1 is the number of dimensions. By using the multi-dimensional polynomial transform. the MD-DHT can be converted into a series of reduced one-dimensional DHT. Compared to other fast algorithms, the proposed one substantially reduces the overall computational complexity and has a simple computational structure. (C) 2002 Elsevier Science B.V. All rights reserved.
A fast algorithm for electromagnetic scattering by buried three dimensional (3-D) dielectric objects of large size is presented by using the conjugate gradient (CG) method and fast Fourier transform (FFT), In this alg...
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A fast algorithm for electromagnetic scattering by buried three dimensional (3-D) dielectric objects of large size is presented by using the conjugate gradient (CG) method and fast Fourier transform (FFT), In this algorithm, tbe Galerkin method is utilized to discretize the electric field integral equations, where rooftop functions are chosen as both basis and testing functions. Different from the 3-D objects in homogeneous space, the resulting matrix equation for the buried objects contains both cyclic convolution and correlation terms, either of which can be Solved rapidly by the CG-FFT method. The near-scattered field on the observation plane in the upper space has been expressed by two-dimensional (2-D) discrete Fourier transforms (DFT's), which also can be rapidly computed. Because of the use of FFT's to handle the Toeplitz matrix, the Sommerfeld integrals' evaluation which is time consuming yet essential for the buried object problem, has been reduced to a minimum. The memory required in this algorithm is of order N (the number of unknowns), and the computational complexity is of order NiterN log N, in which N-iter is the iteration number, and N-iter << N is usually true far a large problem.
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