中国科学院数学与系统科学研究院期刊网

14 March 2025, Volume 46 Issue 1
    

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  • Yang Chao
    Journal on Numerica Methods and Computer Applications. 2025, 46(1): 1-2. https://doi.org/10.12288/szjs.2025.1.1
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  • Wang Shuai, Liu Hao, Liu Xiuping, Wu Meng
    Journal on Numerica Methods and Computer Applications. 2025, 46(1): 3-23. https://doi.org/10.12288/szjs.s2024-0962
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    Sweep surface generation is a key technique in the field of Computer-Aided Design (CAD), widely used in engineering design and other fields. To address this problem, this paper first presents the basic single-rail and dual-rail sweep algorithms for geometric splicing with a given B-spline surface, and then proposes a swept surface generation algorithm with controllable splicing errors. Subsequently, the surfaces generated by these algorithms are compared and analyzed with the results obtained by the commercial software Catia and Rhino. In the swept surface generation algorithm with controllable splicing error in this article, the boundary of the given surface is first sampled to obtain information such as derivatives and parameters, and then B-spline curve interpolation is performed on this information. Perform a sweep operation through this B-spline curve to obtain a swept surface. Finally, based on a preset threshold for splicing errors between the sweep surface and the given surface, the sampling points are adjusted to obtain a sweep surface within the acceptable error range. Experimental results show that the algorithm in this article is better than Rhino in generating surface quality, and can generate surfaces with a quality comparable to Catia with a smaller number of control points.
  • Li Di, Zhou Jingang
    Journal on Numerica Methods and Computer Applications. 2025, 46(1): 24-43. https://doi.org/10.12288/szjs.s2024-0968
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    This paper mainly introduces the development history of numerical computation, as well as the development and application of existing numerical computation software. In addition, the paper introduces the development history, main functionalities, development challenges, and importance of the domestically developed numerical software Baltamatica, and discusses the future development of domestic numerical software.
  • Zhou Zhenya, Zuo Chengjie, Hu Ran, Cheng Minghou, Zhang Jinyu, Liu Qiang, He Xaiofeng
    Journal on Numerica Methods and Computer Applications. 2025, 46(1): 44-59. https://doi.org/10.12288/szjs.s2024-0978
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    With the evolution of design processes and the increasing integration of circuits, the scale of circuit simulation has been continuously expanding, leading to an extended simulation and verification time. The limitations of traditional hardware architectures in performance enhancement pose significant challenges for design engineers. In recent years, with the development of artificial intelligence, general-purpose graphics processing units (GPGPUs) have rapidly advanced, offering computational power and memory bandwidth far exceeding that of contemporary CPUs, thus providing new opportunities for accelerating circuit simulation. This paper will explore the mathematical models corresponding to analog and radio frequency circuit simulations, as well as the commonly used solving algorithms in the industry, analyzing the opportunities and challenges faced in heterogeneous simulation environments. By integrating advanced computing platforms, circuit simulation can achieve a more efficient solving process. Nevertheless, effectively integrating these new technologies to meet the simulation demands of complex circuits remains a key focus of current research.
  • Bai Jiantao, Guo Huiqiang, Wang Bin, Huo Fuchang, Shan Ruitong, Lu Yuyuan, Zuo Wenjie, Zhang Ran
    Journal on Numerica Methods and Computer Applications. 2025, 46(1): 60-72. https://doi.org/10.12288/szjs.s2024-0979
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    Aircraft tires are crucial safety components during the takeoff and landing phases, which are widely recognized as the “crown jewel” of the tire industry. The design of aircraft tires is a “bottleneck” technical problem in our country. It is urgent to solve the mathematical modeling and CAE industrial software development. The aircraft tire is mainly composed of cord reinforced rubber composites, which needs to meet the complex conditions. Therefore, this paper studies the mathematical modeling of cord reinforced rubber composite for aircraft tire. According to the deformation characteristics of cord reinforced rubber composites, a modeling method of cord reinforced rubber composite is proposed to establish the embedded constraint relationship between cord and rubber structure. The finite element equations are derived for the rubber and cord structures, which are implemented in the industrial software of aircraft tire SuperTire to realize the inflation analysis. Numerical examples of aircraft tires demonstrate the modeling accuracy and solving efficiency.
  • Huang Yufeng, Hou Chaofeng, Ge Wei
    Journal on Numerica Methods and Computer Applications. 2025, 46(1): 73-84. https://doi.org/10.12288/szjs.s2024-0988
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    Lattice Boltzmann method is an efficient algorithm for solving Boltzmann transport equation, which has been widely applied in the fields of fluid flow and heat transport of phonon. Based on our previous work of effective correction for the relaxation time of phonon, several lattice structures with different symmetries and numbers of discrete velocities are designed for the lattice Boltzmann method of phonon heat transport. The correctness of the algorithm and program is verified by a macroscale heat transport process. Then, the influences of symmetry and number of discrete velocities for different lattice structures on square-cavity heat transport at nano/microscale are studied. The results indicate that the non-physical temperature jump cannot be effectively overcome only by improving the symmetry of lattice. However, it can be effectively weakened by simultaneously improving symmetry and increasing the number of discrete velocities.