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A fast algorithm for the multi-layer Boussinesq equations

COASTAL ENGINEERING JOURNAL 2025年

作者： Cai, Zhiwen He, Chunrong Zhang, Jiuming Zheng, Kun Chen, Wenwei Ji, Xinran China Ship Sci Res Ctr Dept Offshore Struct Wuxi Peoples R China China Ship Sci Res Ctr Shanghai Branch Shanghai Peoples R China Hainan Univ Coll Civil Engn & Architecture Haikou Peoples R China

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).

关键词： Multi-layer Boussinesq equations fast algorithm nonlinear wave deep water shallow water

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fast algorithm for viscous Cahn-Hilliard equation

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Frontiers of Mathematics in China 2022年第4期17卷 689-713页

作者： Danxia WANG Yaqian LI Xingxing WANG Hongen JIA College of Mathematics Taiyuan University of TechnologyTaiyuan030024China

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.

关键词： fast algorithm two time-mesh(TT-M)finite element(FE)method viscous Cahn-Hilliard equation stability CPU time

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Simulation of Precipitation Echoes From Airborne Dual-Polarization Weather Radar Based on a fast algorithm for Invariant Imbedding T-Matrix

IEEE TRANSACTIONS ON RADAR SYSTEMS

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IEEE TRANSACTIONS ON RADAR SYSTEMS 2025年 3卷 135-154页

作者： Li, Hai Xiong, Yu Zhang, Boxin Wu, Zihua Civil Aviat Univ China Coll Elect Informat & Automat Tianjin 300300 Peoples R China Peking Univ Sch Earth & Space Sci Beijing 100871 Peoples R China

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.

关键词： Scattering Precipitation Radar Meteorology Meteorological radar Airborne radar Radar scattering Iterative methods Computational efficiency Time-domain analysis Airborne dual-polarization weather radar echo simulation fast algorithm invariant imbedding T-matrix (IITM) Mie scattering scattering amplitude matrices

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A Pre-splitting Green's Function based Hybrid fast algorithm for Multiscale Problems

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2023年第9期38卷 652-666页

作者： Zhu, Guang-Yu Li, Wei-Dong Sha, Wei E. I. Zhou, Hou-Xing Hong, Wei Zhejiang Univ Coll Informat Sci & Elect Engn Hangzhou 310027 Peoples R China Southeast Univ Frontiers Sci Ctr Mobile Informat Commun & Secur State Key Lab Millimeter Waves Nanjing 210096 Peoples R China

- 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.

关键词： fast algorithm fast Fourier transform Green's function matrix compression multiscale prob- lems

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fast algorithm of Inductive Pulse Power Based on Multiple HTSPPT Modules

Fast Algorithm of Inductive Pulse Power Based on Multiple HT...

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2023 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices, ASEMD 2023

作者： Han, Meiyi Li, Zhenmei Zhou, Hui Li, Haitao Liu, Na Shandong University of Technology School of Electrical and Electronic Engineering Zibo China

ISBN: (纸本)9798350301571

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 theoretical formulas for selecting parameter values in topology. To analyze the discharge characteristics of pulse power supply circuits more intuitively, this paper presented a fast solution method based on Laplace transform to analyzes the discharge characteristics of pulsed power supply. The discharge characteristics of two HTSPPT modules using experiment and fast algorithm are compared in this paper. The results show that the fast algorithm based on Laplace transform can very close to the experimental results. The fast algorithm solves the problem that simulation software can not set parameters flexibly, and can not automatically give relevant waveform when changing parameters of pulse PS. © 2023 IEEE.

关键词： fast algorithm High-temperature superconducting pulsed power transformer Laplace transform pulsed power supply

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fast algorithm for Completion State Calculating of Wire Rope Cable Bridge 8th

Fast Algorithm for Completion State Calculating of Wire Rope...

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8th International Conference on Civil Engineering (ICCE)

作者： Feng, Yang Song, Dan Li, Minghui Power China Northwest Engn Corp Ltd Xian 710065 Peoples R China

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.

关键词： fast algorithm Wire rope Cable Bridge Catenary theory Parabola theory

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OpenfastVC: An Open Source Library for Video Coding fast algorithm Implementation 23

OpenFastVC: An Open Source Library for Video Coding Fast Alg...

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31st ACM International Conference on Multimedia (MM)

作者： Yuan, Hang Gao, Wei Peking Univ Shenzhen Grad Sch Peng Cheng Lab Beijing Peoples R China Peking Univ Shenzhen Grad Sch Beijing Peoples R China

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.

关键词： video coding low-complexity optimization fast algorithm open source software

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Barnes–Hut/Multipole fast algorithm in Lagrangian Vortex Method 49th

Barnes–Hut/Multipole Fast Algorithm in Lagrangian Vortex Me...

引用

Advanced Problem in Mechanics III - Proceedings of the 49th International Summer School-Conference "Advanced Problems in Mechanics", 2021

作者： Chernyh, Julia Marchevsky, Ilia Ryatina, Evgeniya Kolganova, Alexandra Bauman Moscow State Technical University Moscow105005 Russia Ivannikov Institute for System Programming of the Russian Academy of Sciences Moscow109004 Russia

ISBN: (纸本)9783031372452

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 computational complexity and allows for the accuracy flexible adjustment, similarly to the classical Barnes–Hut method. Four schemes are developed with different number of terms being hold in multipole and local expansions. All the necessary formulae are presented, expressed in terms of operations with complex numbers. If extremely high accuracy is not required, the proposed algorithm is more efficient in comparison to the traditional FMM methods. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： fast algorithm Multipoles n-body problem The barnes–hut algorithm Vortex method

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fast algorithm BASED ON TT-M FE METHOD FOR MODIFIED CAHN-HILLIARD EQUATION

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ROCKY MOUNTAIN JOURNAL OF MATHEMATICS 2021年第1期51卷 327-346页

作者： Wang, Danxia Wang, Xingxing Li, Yaqian Jia, Hongen Taiyuan Univ Technol Coll Math Taiyuan 030024 Peoples R China

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.

关键词： fast algorithm TT-M FE method modified Cahn-Hilliard equation stability priori error estimate CPU time

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A fast algorithm for the Schrödinger equation in quaternionic quantum mechanics

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APPLIED MATHEMATICS LETTERS 2024年 150卷

作者： Jiang, Tongsong Guo, Zhenwei Zhang, Dong Vasil'ev, V. I. Shandong Xiandai Univ Sch Elect Informat Jinan 250104 Peoples R China North Eastern Fed Univ Inst Math & Informat Sci Yakutsk 677000 Russia Linyi Univ Sch Math & Stat Linyi 276005 Peoples R China

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.

关键词： fast algorithm Schrodinger equation Hermitian quaternion matrix Real representation Eigenvalue problem

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