| 摘要: |
| 针对国产科学计算软件教学与科研应用的现实需求,本文以一维和二维非稳态热传导方程为研究载体,基于北太天元(Baltamatica)数值计算软件,实现了有限元方法(FEM)与Crank-Nicolson时间离散格式相结合的算法设计及编程数值求解.研究重点探讨了依托北太天元软件开展偏微分方程有限元方法的算法设计、编程实现及结果可视化的教学实施路径.通过与传统教学模式的对比分析,提出“问题驱动+代码实践”为核心的教学新模式,为提升学生数值建模能力与创新思维提供可行方案. |
| 关键词: 北太天元 热传导方程 有限元 Crank-Nicolson格式 教学创新 数值仿真 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| Innovations and Practices in Teaching of Numerical Solutions of Partial Differential Equations Based on Baltamatica |
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Huang Bo,Yao Wenqi
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| Abstract: |
| In response to the practical demands of teaching and scientific research applications of domestic scientific computing software, this paper takes the one-dimensional and two-dimensional unsteady heat conduction equations as the research objects, and implements
the algorithm design and programmed numerical solution combining the Finite Element Method (FEM) with the Crank-Nicolson time discretization scheme, based on the Baltamatica (BaitaiTianyuan) numerical computing software. The research focuses on exploring the teaching implementation path for algorithm design, programming implementation, and result visualization of the finite element method for Partial Differential Equations (PDEs) by virtue of Baltamatica. Through comparative analysis with the traditional teaching mode, a new teaching mode centered on “Problem-Driven + Code Practice” is proposed, which provides a feasible solution for improving students’ numerical modeling ability and innovative thinking. |
| Key words: Baltamatica Heat Conduction Equation Finite Element Method Crank-Nicolson Scheme Teaching Innovation Numerical Simulation |
