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Explicit potential function and fast algorithm for computing potentials in α x β conic surface resistor network

EXPERT SYSTEMS WITH APPLICATIONS 2024年第PartE期238卷

作者： Jiang, Xiaoyu Zhang, Gaojun Zheng, Yanpeng Jiang, Zhaolin Linyi Univ Sch Informat Sci & Engn Linyi 276000 Peoples R China Linyi Univ Sch Automat & Elect Engn Linyi 276000 Shandong Peoples R China Linyi Univ Sch Math & Stat Linyi 276000 Peoples R China

Resistor network research is of great importance, yet many resistor networks and their large-scale fast computations have not received sufficient attention. This paper proposes a new resistor network with idiosyncratic shape, i.e., a alpha x beta conic surface (CS) resistor network that resembles the upper part of a three-dimensional Dirac function. Utilizing the Recursion Transform (RT-V) method of Tan, a recursive matrix equation model is constructed based on Kirchhoff's law and nodal voltages, which contains the modified tridiagonal Toeplitz matrix. By using the orthogonal matrix transformation, the eigenvalues and eigenvectors of the modified tridiagonal Toeplitz are obtained. The discrete sine transform of the fourth type (DST - IV) is utilized to solve node voltages, while the explicit potential function is represented by the Chebyshev polynomials of the second kind. In addition, explicit potential functions for some special cases are provided, and the potential distribution is illustrated using dynamic three-dimensional graph. To achieve a rapid calculation of the potential, a fast algorithm based on the multiplication of DST-IV with a vector is proposed. In the end, analysis of computational efficiency for the explicit potential function and the fast algorithm are shown.

关键词： Resistor network Chebyshev polynomials DST-IV fast algorithm

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A physics-based fast algorithm for structural responses of generalized rotationally axisymmetric structures: the generalized rotation-superposition method

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LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 2024年第6期21卷 1-22页

作者： Yang, Mao Zhang, Jun Chen, Hao Yang, Jialin Mao, Yongjian China Acad Engn Phys Inst Syst Engn Mianyang 621999 Sichuan Peoples R China

fast calculations are widely required in the traditional applications and the emerging digital twin fields. For those considerations, a novel physics-based fast algorithm, namely generalized rotation-superposition method, is proposed for fast calculating linear elastic responses of generalized rotationally axisymmetric structures under arbitrary mechanical loads. This improved method breaks through the limitations of the previous basic rotationsuperposition method in rotational similarity of load and structural axisymmetry, and greatly expands its application scope. In this paper, firstly, the basic theory of the rotation-superposition algorithm is introduced;secondly, the theoretical model of the generalized rotation-superposition method is established;thirdly, the effectiveness and accuracy are verified by using finite element simulations;finally, through a complex case study, the applicability of the generalized rotation-superposition method for complex engineering problems and its advantages in efficiently obtaining massive amounts of data are further illustrated.

关键词： fast algorithm structural response axisymmetric structure rotationally axisymmetric structure rotation-superposition method digital twin

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Accelerate Three-Dimensional Generative Adversarial Networks Using fast algorithm

Accelerate Three-Dimensional Generative Adversarial Networks...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Su, Ziqi Mao, Wendong Wang, Zhongfeng Lin, Jun Wang, Wenqiang Sun, Haitao Nanjing Univ Sch Elect Sci & Engn Nanjing Peoples R China SenseTime Res Hong Kong Peoples R China

ISBN: (纸本)9781665484855

Three-dimensional generative adversarial networks (3D-GAN) have attracted widespread attention in three-dimension (3D) visual tasks. 3D deconvolution (DeConv), as an important computation of 3D-GAN, significantly increases computational complexity compared with 2D DeConv. 3D DeConv has become a bottleneck for the acceleration of 3D-GAN. Previous accelerators suffer from several problems, such as large memory requirements and resource underutilization. To handle the above issues, a fast algorithm for 3D DeConv (F3DC) is proposed in this paper. F3DC applies a fast algorithm to reduce the number of multiplications and achieves a significant algorithmic strength reduction. Besides, F3DC removes the extra memory requirement for overlapped partial sums and avoids computational imbalance to fully utilize resources. Moreover, we design an F3DC-based hardware architecture, which consists of four fast processing units (FPUs). Each FPU includes a pre-process module, a EWMM module and a post-process module for F3DC transformation. By implementing our design on the Xilinx VC709 platform for 3D-GAN, we achieve a throughput up to 1700 GOPS and 4x computational efficiency improvement compared with prior works.

关键词： Three-Dimensional Generative Neural Networks Deconvolution Transposed Convolution Hardware Architecture fast algorithm

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A fast algorithm for Fractional QCQP and Applications to Secure Beamforming in Cognitive Nonorthogonal Multiple Access Networks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 6237-6250页

作者： Luo, Hualiang Li, Quanzhong Yang, Liang Qin, Jiayin Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou 510006 Peoples R China Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Hunan Univ Coll Comp Sci & Elect Engn Changsha 410082 Hunan Peoples R China

In this paper, we investigate a nonconvex fractional quadratically constrained quadratic problem (fractional QCQP), which has a wide application to the resource allocation optimization in wireless communication systems. Different from the state-of-the-art methods needing to solve semidefinite programmings or second-order cone programmings, we propose a fast algorithm for solving fractional QCQP by combining the successive convex approximation method and the consensus alternating direction method of multipliers, which has only simple computations and works very fast in applications with modest accuracy. We also apply the proposed fast algorithm to secure beamforming design for enhancing physical layer security in cognitive nonorthogonal multiple access (NOMA) networks, where secrecy rate optimization problems in both underlay and overly cognitive NOMA networks are typical fractional QCQPs and have not been well studied. Simulation results have shown that our proposed fast algorithm achieves almost the same performance as the state-of-the-art methods, however, the proposed fast algorithm has very low computation complexity.

关键词： NOMA Signal processing algorithms Optimization Array signal processing Programming Resource management Multicast communication Fractional quadratically constrained quadratic problem (Fractional QCQP) fast algorithm secure beamforming cognitive radios nonorthogonal multiple access

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A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern recognition

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2021年第2期32卷 431-464页

作者： El Ogri, O. Karmouni, H. Yamni, M. Daoui, A. Sayyouri, M. Qjidaa, H. Univ Sidi Mohamed Ben Abdellah Fac Sci Dhar El Mahrez Lab Elect Signals & Syst Informat LESSI CED STSTIC Fes Morocco Sidi Mohamed Ben Abdellah Univ Natl Sch Appl Sci Engn Syst & Applicat Lab BP 72My Abdallah AveKm 5Imouzzer Rd Fes Morocco

Orthogonal moments are the projections of image functions on particular functions of the kernel. They play an essential role in image extraction: rotation, scaling, translation invariance, object recognition, image classification, image noise robustness, and low information redundancy. These moments are derived from orthogonal polynomials that can be continuous or discrete. This paper focuses on the fractional-order modified generalized Laguerre moment invariants (FMGLMIs), which is a generalization of the traditional integer order one. In this research, we have developed a new algorithm to compute the 3D invariant moments of FMGLMIs based on the 3D image cuboid representation, our proposed calculation method can improve the efficiency of 3D invariant moment calculation to maintain numerical stability and significantly reduce calculation time with very satisfactory accuracy. To check this new algorithm, the calculation of 3D invariant moments gives very encouraging results for the invariability property of the proposed method with respect to different geometric transformations and noise degradations of 3D images, classification and recognition of 3D images and the calculation time of fractional-order invariants proposed. Finally, the experimental results show that the proposed method makes it possible to construct fractional-order modified generalized Laguerre invariant moments offering better performances for image analysis and pattern recognition.

关键词： Fractional-order modified generalized Laguerre polynomials Fractional-order moment Invariants fast algorithm Accurate computation 3D image classification Pattern recognition

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A Reconfigurable Approach for Deconvolutional Network Acceleration with fast algorithm

A Reconfigurable Approach for Deconvolutional Network Accele...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Yang, Peixiang Mao, Wendong Wang, Zhongfeng Lin, Jun Nanjing Univ Sch Elect Sci & Engn Nanjing Peoples R China

ISBN: (纸本)9781665484855

Recently, deconvolutional neural network (DeCNN) has attracted widespread attention in various applications. The deconvolution (DeConv), as the main operation in DeCNN, has become the bottleneck of acceleration, due to its high computational complexity. Previous works have introduced fast algorithms such as the cascaded fast FIR algorithm (CFFA) and the Winograd algorithm to reduce the computational complexity of DeConv for the applications on mobile devices. Since these fast algorithms need different computing parameters to accelerate various operations, directly applying these methods to process DeCNNs with different kernels usually causes limited flexibility. To address this problem, we propose a reconfigurable scheme based on the fast transformation algorithm (FTA) to accelerate multiple types of DeConvs, minimizing the hardware overhead for reconfigurability. Based on this scheme, a reconfigurable hardware architecture is developed to support several types of DeConvs. In addition, an adaptive dataflow is proposed to handle different convolutional layers. The presented design can support several types of operations and achieve up to 222.54 GOPS under 210 MHz on the Intel Arria 10SX FPGA platform, which shows our design can obtain better flexibility and computational efficiency compared with prior arts.

关键词： Deconvolutional neural network deconvolution transposed convolution hardware architecture acceleration reconfigurable design fast algorithm

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Development of Embedded Temperature Regulator Based on DMC fast algorithm 34

Development of Embedded Temperature Regulator Based on DMC F...

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34th Chinese Control and Decision Conference (CCDC)

作者： Wu, Zhen-He Zhao, Thong Beijing Univ Chem Technol Coll Informat Sci & Technol Beijing 100029 Peoples R China

ISBN: (纸本)9781665478960

A fast Dynamic Matrix Control (DMC) algorithm is proposed to satisfy the requirements of the embedded temperature regulator. There exists online high-dimension matrix inversion in the DMC control algorithm, so it is difficult to apply to the embedded temperature regulator with limited computing capacity. In this work, the high-dimension matrix is decomposed into the product of a triangular matrix and its transpose matrix by Cholesky decomposition, and the inversion of the matrix calculation could be calculated recursively. Based on the proposed algorithm, an embedded temperature regulator has been developed. Therefore, the computation cost of the fast algorithm is greatly reduced compared to the traditional DMC algorithm. The experimental results have verified that the algorithm can be applied to the embedded temperature regulator and provides better regulation effect than that with the PID control algorithm.

关键词： Dynamic Matrix Control fast algorithm Embedded Regulator Temperature Control

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fast algorithm for nonlocal Allen-Cahn equation with scalar auxiliary variable approach

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APPLIED MATHEMATICS LETTERS 2022年第0期126卷 107805-107805页

作者： Yao, Changhui Fan, Huijun Zhao, Yanmin Shi, Yanhua Wang, Fenling Zhengzhou Univ Sch Math & Stat Zhengzhou 450001 Peoples R China Xuchang Univ Sch Sci Xuchang 461000 Peoples R China

Numerical analysis is presented for the nonlocal Allen-Cahn equation, which contains spatial nonlocal operator and time-fractional derivative. By employing the spatial quadrature-based finite difference method and the nonuniform L1 formula jointed with the scalar auxiliary variable (SAV) approach in temporal discretization, a nonuniform numerical scheme is established. The nonlinear solver can be transformed into linear one effectively due to the SAV approach. And, the proposed scheme is proven to be energy stable by use of the positive definiteness of the kernel function. Moreover, the fast algorithm based on the nonuniform L1 formula is applied in the numerical example to improving computational efficiency. Finally, the numerical results demonstrate the temporal convergence of numerical scheme, energy property, comparisons with the nonlocal cases and local cases and maximum principle of the numerical solution. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Nonlocal Allen-Cahn equation SAV approach Energy stable fast algorithm

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An L1 Legendre-Galerkin spectral method with fast algorithm for the two-dimensional nonlinear coupled time fractional Schrodinger equation and its parameter estimation

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2021年 82卷 13-35页

作者： Jia, Junqing Jiang, Xiaoyun Zhang, Hui Shandong Univ Sch Math Jinan 250100 Peoples R China

In this paper, we derive an L1 Legendre-Galerkin spectral method with fast algorithm based on an efficient sum-of-exponentials (SOE) approximation for the kernel t(-1-alpha) to solve the two-dimensional nonlinear coupled time fractional Schrodinger equations. The numerical method is stable without the Courant-Friedrichs-Lewy (CFL) conditions based on the error splitting argument technique and the discrete fractional Gronwall type inequality. At the same time, we use the fully implicit method to deal with the nonlinear terms. For the non-smooth solution, we employ the graded mesh method. Moreover, we estimate the parameters including fractional derivative index and the coefficients of the nonlinear term in the equations by applying the Cuckoo Search algorithm related to Levy flights. Numerical examples are given to verify the theoretical analysis and confirm the effectiveness of the fast algorithm and the estimation method. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Two-dimensional nonlinear coupled time fractional Schrodinger equations L1 Legendre-Galerkin spectral method Optimal error estimate fast algorithm Parameter estimation

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Multi-stage affine motion estimation fast algorithm for versatile video coding using decision tree

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JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION 2023年第1期96卷

作者： Huang, Xiaofeng Zhou, Fangtao Niu, Weihong Li, Tianci Lu, Yu Zhou, Yang Yin, Haibing Yan, Chenggang Hangzhou Dianzi Univ Sch Commun Engn 2 St Hangzhou 310018 Peoples R China Peking Univ Adv Inst Informat Technol Hangzhou 311215 Peoples R China

Affine motion estimation (AME) which is newly introduced in versatile video coding (VVC) plays a significant role in the bit-rate reduction for rotation and zooming scenes. However, it brings the complexity extremely increased. In this paper, a fast AME algorithm is designed to cope with the high-complexity problem. Three crucial stages are involved in the fast algorithm, which is the optimal inter-mode decision based on the coding unit (CU) partition, the fast algorithm in affine motion search (AMS), and the fast inter-mode decision based on a decision tree. Specifically, the optimal inter-mode will be determined straightforwardly when the parent CU is checked whether it is translational motion estimation (TME). Then, three fast algorithms are made in AMS, which are early termination based on control point motion vector (CPMV), early termination of the iteration process, and fast fine granularity CPMV search. Finally, the optimal inter-mode is predicted using a decision tree based on eight essential features. Experimental results show that the proposed algorithm achieves 10.20% and 10.33% encoding time-saving on average under Low Delay B (LDB) and Random Access (RA) configuration, while the BD-Rate loss is only 0.12% and 0.14%, respectively.

关键词： Affine motion estimation Versatile video coding Inter-mode decision Decision tree fast algorithm

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