中国科学院数学与系统科学研究院期刊网

14 September 2024, Volume 45 Issue 3
    

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  • Xia Qing, Yu Qian, Li Yibao
    Journal on Numerica Methods and Computer Applications. 2024, 45(3): 189-236. https://doi.org/10.12288/szjs.s2024-0948
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    Component design (“digitalization”), performance optimization (“optimization”), and process simulation (“simulation”) are three critical modules in the 3D printing process. “Digitalization” refers to the transformation of design drawings or pre-processed physical objects into editable digital components through means such as images, videos, and scanning processes. “Optimization” involves the application of constraints from physical fields such as mechanics and thermodynamics to enhance the performance of digital components. “Simulation” entails the digital simulation and twin modeling of physicochemical changes during the manufacturing process, based on the optimized components, to emulate real-world physical conditions. This research aims to introduce integrated modeling and algorithmic studies in design, optimization, and simulation within the phase field framework. In the “digitalization” module, we will present three-dimensional reconstruction models, repair models, and lightweight support structure design models that correspond to common data types in computer-aided design. In the “optimization” module, we will introduce a series of multi-scale, multi-physical field, and multi-material coupled topology optimization problems and their corresponding solutions. In the “simulation” module, we will discuss macroscopic (phase transition) to microscopic (grain boundary) scale coupling theories and the physical field couplings such as laser-thermal-flow-solid, in addition to simulating methods for processes like Fused Deposition Modeling (FDM) and Selective Laser Melting (SLM), integrating 3D printing parameters and techniques. The integrated research approach to design, optimization, and simulation based on the phase field model framework aims to shorten the product development cycle, enhance design efficiency, and provide a theoretical basis and algorithmic support for quality traceability and root cause analysis of 3D printed components.
  • Sun Chao, Guo Xiaoxia
    Journal on Numerica Methods and Computer Applications. 2024, 45(3): 237-248. https://doi.org/10.12288/szjs.s2023-0922
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    In this paper, we first provide a new convergence theorem for the greedy Kaczmarz (GK) method in reference [14]. Secondly, in order to improve the efficiency of solving consistent linear equations, a new greedy block Kaczmarz (RDBK) method based on the greedy strategy of the GK method is proposed, and the convergence theorem of the RDBK method is provided. Finally, the numerical results demonstrate that the RDBK method is significantly superior to the GK method in terms of iteration steps and computation time.
  • Zhang Huiwen, Wang Jialing
    Journal on Numerica Methods and Computer Applications. 2024, 45(3): 249-261. https://doi.org/10.12288/szjs.s2023-0931
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    In this present work, we propose two local energy-preserving schemes for the CamassaHolm equation, which can preserve both the local energy conservation law and the local mass conservation law, that is to say, these two schemes can accurately preserve energy and mass in any time and space regions. The local energy-preserving scheme is an extension of the global energy-preserving scheme, which eliminates the dependence on boundary conditions of the latter. Moreover, under suitable boundary conditions, such as periodic or homogeneous boundary condition, the local energy conservation law and local mass conservation law can be transformed into the corresponding global conservation laws. Finally, numerical experiments verify the splendid effect of the proposed schemes.
  • Liu Chao
    Journal on Numerica Methods and Computer Applications. 2024, 45(3): 262-272. https://doi.org/10.12288/szjs.s2023-0932
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    This paper proposes a partial linear regression model based on Fourier basis by combining nonparametric regression model and quantile regression model. We use the Fourier approximation of function model of the nonlinear function, and combined with quantile regression model estimation method of the model are given, under some basic assumptions The consistency of parameter vector and nonlinear function estimation is proved.The effectiveness of this method is demonstrated by simulation studies.At the end of the paper, the meteorological data of Beijing Capital International Airport are empirically analyzed with this model, and a new method will be proposed to accurately predict the diffusion of PM2.5 by this model.
  • Wang Jiandong, Kong Linghua, Xu Qiaomeng, Guo Huacheng
    Journal on Numerica Methods and Computer Applications. 2024, 45(3): 273-287. https://doi.org/10.12288/szjs.s2024-0935
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    It designs a combined high-order compact method for KdV equation in this work. This method simultaneously and compactly calculates the first-order and third-order spatial derivatives which overcomes many shortcomings of classic high-order compact methods. The KdV equation is discretized by the combined high-order compact method in space, and is approximated by the Crank-Nicolson scheme combined with extrapolation method in time. In addition, projection method is used to pull the numerical solution back to the energy-preserving manifold. Finally, some numerical experiments are conducted to verify the numerical accuracy, computational efficiency, and the property of energy-preserving.
  • Wen Xin, Li Feng, Sui Peng, Zou Yongkui
    Journal on Numerica Methods and Computer Applications. 2024, 45(3): 288-300. https://doi.org/10.12288/szjs.s2024-0956
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    Reconstructing clear images from blurred and noisy ones is a typical ill-posed problem. When the blurring kernel is unknown, reconstructing both the blurring kernel and the image is required. Such blind denoising and deblurring problems have attracted widespread attention in academia. Using variational methods, we established a partial differential equation model for the blind denoising and deblurring problem of remote sensing images. Then, combining alternating direction method and finite difference method, we constructed a fully discrete numerical format for solving unknown kernel functions and clear images. Numerical experiments were conducted to analyze the effect of parameters on image processing performance and to determine reasonable parameters. Finally, numerical experiments were conducted on several remote sensing images, and the results demonstrated the effectiveness of the model.