A Software Tool for Analytical Solutions of Laplace's Equation

拉普拉斯方程解析解的软件工具

• 批准号: 9060714
• 负责人: Joseph Crowley
• 金额: $ 4.99万
• 依托单位: Electrostatic Applications
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-01-01 至 1991-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9060714&HistoricalAwards=false
• 关键词: Software; Tool; Analytical; Solutions; Laplace

A software tool which presents analytical solutions of Laplace's equation offers several advantages over numerical techniques. Students in many areas of engineering and physics will benefit from the opportunity to study parametric dependence of the solutions. Aspects of potential theory that are difficult for numerical techniques, such as highly curved surfaces and derivative variables, are simple for analytical methods, so both analysis and design of new structures and devices will become more accurate. The principal obstacles to the use of analytical solutions have been the difficulty of matching the shape to a solution, and the need to perform a large number of tedious symbolic calculations using algebra and calculus. These difficulties are overcome in the proposed work by implementing an interface which guides the user through a sequence of graphical menus leading to the desired solution in a variety of formats, including, graphs, computer subprograms, and word processing elements. Phase I of the project is devoted to working out the techniques which will enable the solutions of Laplace's equation to be generated using a computer based symbolic mathematics package (Mathematica), and to testing a minimal version of the program for the suitability of the interface for Junior level engineering students.

一个软件工具，提供分析解决方案， 拉普拉斯方程提供了几个优于数值 技术. 工程学和物理学许多领域的学生 将受益于研究参数的机会， 解决方案的依赖性。 潜在理论的各个方面， 对于数值技术来说是困难的，例如高度弯曲的 曲面和导数变量，对于分析 方法，因此新结构的分析和设计， 设备将变得更加精确。的主要障碍 使用解析解一直是困难的， 将形状与解决方案相匹配，以及需要执行 用代数进行的大量繁琐的符号计算 和微积分。 这些困难都克服了建议 通过实现引导用户的界面来工作 通过一系列图形菜单， 各种格式的解决方案，包括图表，计算机 子程序和字处理元件。 该项目的第一阶段致力于制定 技术，使解决方案的拉普拉斯的 使用基于符号的计算机生成的方程 数学软件包（Mathematica），并测试最小的 接口适用性的程序版本 为初级工程专业的学生。