PARTIAL DIFFERENTIAL EQUATIONS SOFTWARE FOR PCS

这项研究的最终目标是生成一个软件包PDEsys 用于提供交互式图形环境的个人计算机 用于定义、求解和查看抛物型方程组和 任意1-和2-上的椭圆型偏微分方程 多维空间域。有限元方法将被用来 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都将是 可用。 拟由PDEsys软件处理的PDE类型为 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，神经冲动传递， 毛细血管/组织交换和组织中的大分子渗流 在这些方程式产生的众多领域中，只有几个。 现有的解决PDE的包都很大，很难使用，而且 它们都不适用于微型计算机。这些包裹很有效率 仅针对特殊问题，并提供不友好的用户界面。 我们打算设计一个方便、灵活和 效率很高。它将适合技术含量较低的用户 精通数值分析。这个包裹的区别是什么？ 另一种是，当在方便性和 效率，我们将向便利倾斜。PDEsys将使用MLAB 建模语言作为其交互的图形外壳。

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.