| 摘要: |
| 本文研究了国产科学计算软件教学与科研应用适配性不足,以及偏微分方程有限元教学中理论与实践脱节的问题.利用北太天元(Baltamatica)数值计算软件,以一维和二维非稳态热传导方程为研究载体,采用有限元方法(FEM)与Crank-Nicolson时间离散格式相结合的方式,进行算法设计及编程数值求解,并探讨依托该软件开展相关教学的实施路径.获得了基于北太天元的热传导方程有限元求解完整流程,实现了算法编程与结果可视化,对比传统教学模式提出了“问题驱动+代码实践”的教学新模式.该教学新模式可有效提升学生数值建模能力与创新思维,为国产科学计算软件在偏微分方程教学中的推广应用提供了可行方案,丰富了有限元方法教学的实践路径. |
| 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;O241.3;G642.0 |
| 基金项目:国家自然科学基金资助(12471378). |
|
| INNOVATIONS AND PRACTICES IN TEACHING OF NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS BASED ON BALTAMATICA |
|
HUANG Bo1, LU Tiao2,3, YAO Wen-qi1
|
|
1.School of Mathematics, South China University of Technology, Guangzhou 510641, China;2.School of Mathematical Sciences, Peking University, Beijing 100871, China;3.Peking University Chongqing Big Data Research Institute, Chongqing 100871, China
|
| Abstract: |
| This paper studies the insufficient adaptability of domestic scientific computing software in teaching and scientific research applications, as well as the disconnection between theory and practice in the teaching of finite element method for partial differential equations. Using the Baltamatica (Baitai Tianyuan) numerical computing software, taking the one-dimensional and two-dimensional unsteady heat conduction equations as the research objects, the algorithm design and programmed numerical solution are carried out by combining the Finite Element Method (FEM) with the Crank-Nicolson time discretization scheme, and the teaching implementation path for carrying out relevant teaching relying on this software is explored. The complete process of finite element solution for heat conduction equations based on Baltamatica is obtained, the algorithm programming and result visualization are realized, and a new teaching mode centered on "Problem-Driven + Code Practice" is proposed by comparing with the traditional teaching mode. This new teaching mode can effectively improve students’ numerical modeling ability and innovative thinking, provide a feasible solution for the popularization and application of domestic scientific computing software in the teaching of partial differential equations, and enrich the practical path of finite element method teaching. |
| Key words: Baltamatica heat conduction equation finite element method Crank-Nicolson scheme teaching innovation numerical simulation |
