PARTIAL DIFFERENTIAL EQUATIONS SOFTWARE FOR PCS

本研究的最终目标是产生PDESTIM，一个软件包 对于提供交互式图形环境的个人计算机 用于定义、求解和查看抛物方程组的解， 任意1-和2-上的椭圆型偏微分方程 三维空间域 有限元法将用于 在二维域上求解这些方程。 对于一维 域，有限元和有限差分方法将 available. 拟由所提议的PDE软件处理的PDE类型如下 在生物医学、科学和工程中无处不在。 心脏移植， 电扩散、反应扩散、神经脉冲传递、 毛细血管/组织交换和组织中的大分子渗透是 只是这些方程出现的众多领域中的一小部分。 用于求解PDE的现有软件包很大且难以使用， 它们中没有一个可用于微型计算机。 这些包是高效的 仅针对特殊问题，并提供不友好的用户界面。 我们打算设计一个系统，这将是方便，灵活， 高效. 它将适合那些技术上不那么熟练的用户 精通数值分析。 这个包与 另一个是，当在便利性和 效率，我们将向方便倾斜。 政策制订和执行局将利用多边实验室 建模语言作为其交互式图形外壳。

The ultimate goal of this research is to produce PDESYS, a software package for personal computers which provides an interactive graphical environment for defining, solving and viewing the solutions to systems of parabolic and elliptic partial differential equations (pde's) on arbitrary 1- and 2- dimensional spatial domains. The finite element method will be used to solve these equations on 2-dimensional domains. For 1-dimensional domains, both finite element and finite difference methods will be available. Pde's of the type to be handled by the proposed PDESYS software are ubiquitous in biomedicine, science, and engineering. Heart transfer, electro-diffusion, reaction-diffusion, nerve-impulse transmission, capillary/tissue exchange, and macro-molecular percolation in tissue are only a few of the many areas in which these equations arise. Existing packages for solving pde's are large and difficult to use, and none of them is available for microcomputers. These packages are efficient only on special problems and provide unfriendly user interfaces. We intend to design a system which will be convenient, flexible, and efficient. It will be suitable for users who are less technically proficient in numerical analysis. What will distinguish this package from others is that, when there is a tradeoff between convenience and efficiency, we will tilt toward convenience. PDESYS will use the MLAB modeling language as its interactive graphical shell.