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).
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 *** TT-M FE algorithm in...
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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 *** TT-M FE algorithm includes the following main computing ***,a nonlinear FE method is applied on a coarse time-meshτ_(c).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 ***,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 *** analysis for both stability and a priori error estimates is made in *** examples are given to demonstrate the validity of the proposed *** algorithm is compared with the traditional Galerkin FE method and it is evident that our fast algorithm can save computational time.
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.
- Based on the splitting form of the Green's function, a hybrid fast algorithm is proposed for efficient analysis of multiscale problems. In this algorithm, the Green's function is a priori split into two part...
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- Based on the splitting form of the Green's function, a hybrid fast algorithm is proposed for efficient analysis of multiscale problems. In this algorithm, the Green's function is a priori split into two parts: a spectrally band-limited part and a spatially localized part. Then, the fast Fourier transforms (FFT) utilizing the global Cartesian grid and the matrix compression method aided by an adaptive octree grouping are implemented for these two parts, respectively. Compared with the traditional methods which only employ the FFT for acceleration, the proposed hybrid fast algorithm is capable of maintaining low memory consumption in multiscale the proposed algorithm does not need cumbersome geometric treatment to implement the hybridization, and can be established in a concise and straightforward manner. performance of proposed hybrid fast algorithm.
At present, the research of inductive pulsed power supply (PS) based on the high-temperature superconducting pulsed power transformer (HTSPPT) has many qualitative descriptions, but there is a lack of direct theoretic...
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When determining the completion state of the main cable of a cable-way bridge, although the catenary theory can accurately consider the nonlinear mechanical effect of the cable, the iterative calculation is cumbersome...
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ISBN:
(纸本)9789811912603;9789811912597
When determining the completion state of the main cable of a cable-way bridge, although the catenary theory can accurately consider the nonlinear mechanical effect of the cable, the iterative calculation is cumbersome and not convenient for engineering applications. Although the calculation based on the parabola theory is simple, the calculation accuracy for long cables is low. In this paper, based on catenary theory and considering the calculation accuracy and avoiding iterative calculation, a fast algorithm for the completion state of the main cable of the wire rope cableway bridge is proposed. The results show that the bridge state can be quickly and accurately determined by approximating the horizontal component of the cable tension and avoiding multiple iterative calculations. The proposed algorithm can be used in engineering design and construction.
Despite the remarkable coding gains exhibited by the recently released new-generation video coding standards, their serious computational complexity will pose a significant challenge in coding latency to practical app...
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ISBN:
(纸本)9798400701085
Despite the remarkable coding gains exhibited by the recently released new-generation video coding standards, their serious computational complexity will pose a significant challenge in coding latency to practical applications. Therefore, the corresponding low-complexity optimizations assume paramount importance. To facilitate the research in this field, the first open source software library for video coding fast algorithm implementation, namely OpenfastVC, is proposed in this paper. Specifically, OpenfastVC offers the outputting and processing of the intermediate coding information, e.g., the CU partitioning results, which is indispensable to fast algorithm design. To facilitate the integration of the designed algorithms, OpenfastVC also provides application programming interfaces (APIs) for direct control over the encoding process. Moreover, the existing typical fast algorithms are further implemented in OpenfastVC, enabling researchers to evaluate the performance of their algorithm effortlessly. The release of this library is highly favorable for the design, implementation, and evaluation of video coding fast algorithms, thereby fostering the widespread adoption of the new coding standards. The open source library for OpenfastVC is available at https://***/OpenCompression/OpenfastV C.
New modification of the fast algorithm based on the Barnes–Hut (BH) and multipole (FMM) methods is developed for the problem of velocities calculation in vortex particle method. It provides a quasilinear computationa...
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We consider numerical methods for solving the modified Cahn-Hilliard equation involving strong nonlinearities. A fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme is proposed to overcome the time...
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We consider numerical methods for solving the modified Cahn-Hilliard equation involving strong nonlinearities. A fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme is proposed to overcome the time-consuming computation of the nonlinear terms. The TT-M FE algorithm includes three main steps: Firstly, a nonlinear FE scheme is solved on a coarse time-mesh pi(c). Here, the FE method is used for spatial discretization and the implicit second-order theta scheme (containing both implicit Crank-Nicolson scheme and second-order backward difference method) is used for temporal discretization. Secondly, the Lagrange's interpolation is used to obtain the interpolation result on the fine time-mesh. Finally, a linearized FE system is solved on a fine time-mesh tau.(tau < tau(c)). The stability analysis and priori error estimates are provided in detail. Numerical examples are given to demonstrate the validity of the proposed scheme. The TT-M FE method is compared with the traditional Galerkin FE method and it is evident that the TT-M FE method can save the calculation time.
The eigenvalue problem of a Hermitian quaternion matrix plays a crucial role in quaternion quantum mechanics because it is closely related to the solution of Schrodinger equation. In this paper, a fast algorithm is pr...
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The eigenvalue problem of a Hermitian quaternion matrix plays a crucial role in quaternion quantum mechanics because it is closely related to the solution of Schrodinger equation. In this paper, a fast algorithm is proposed for finding the eigenvalues and corresponding eigenvectors of a Hermitian quaternion matrix based on the real representation of a quaternion matrix as well as the special structure and properties of a Hermitian quaternion matrix. Numerical experiments demonstrate that, compared with the existing computational methods for the eigenvalue problem of a Hermitian quaternion matrix, the proposed method in this paper not only greatly improves the computational efficiency, but also achieves better experimental results in terms of the corresponding computational errors.
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