Problem Solving Environments and Methods for the Developmentof PDE Based Applications on Parallel Machines

本研究项目有三个技术重点：1。面向偏微分方程应用的基于知识的问题求解环境设计。2. 开发一个软件工程框架，用于在具有多媒体前端的并行机器网络上快速有效地解决PDE问题。3. 开发可扩展算法的基础设施，以支持各种大规模并行机器上某些pde的解决方案。偏微分方程是描述科学和工程中许多应用过程的物理行为的基本数学工具。大多数现有的PDE软件系统主要处理序列机或向量机上特定类别的PDE问题的解决。该项目将研究软件工程平台ParPDElab的设计和实现，用于生成pse和相关的算法基础设施，用于任何类别的PDE问题和基于PDE的应用程序。假设的硬件设施由具有不同体系结构和软件环境的并行处理器网络组成。ParPDElab的主要设计目标是创建一个问题解决和编程环境，将重点从编程和硬件问题转移到科学和工程问题的分析。这个环境将几乎是机器独立的，并将尝试统一一些众所周知的并行计算范式。它将是基于知识的，因为它将了解其基础结构和所涉及的原子元素的兼容性要求。此外，它将能够为用户做出一些决定。该系统将是开放式的，与国外系统的易于接口将是ParPDElab设计的主要考虑因素之一。为了实现上述设计目标，必须解决数字、符号、多媒体和人工智能处理的集成问题。这种集成将通过利用现有技术来尝试，同时为将来开发一些新的方法。

This research project has three technical thrusts: 1. The design of knowledge based PSEs (Problem Solving Environments) for PDE (Partial Differential Equation) based applications. 2. The development of a software engineering framework for solving PDE problems quickly and efficiently on a network of parallel machines with multimedia front-ends. 3. The development of an infrastructure of scalable algorithms to support the solution of certain PDEs on a variety of massively parallel machines. PDEs are the fundamental mathematical tools for describing the physical behavior of many application processes in science and engineering. Most of the existing PDE software systems deal primarily with the solution of specific classes of PDE problems on sequential or vector machines. This project will study the design and implementation of the software engineering platform, ParPDElab, for generating PSEs and the related algorithmic infrastructure for any class of PDE problems and PDE based applications. The hardware facility assumed consists of a network of parallel processors with different architectures and software environments. The primary design goal in ParPDElab is to create a problem solving and programming environment that shifts the emphasis from programming and hardware issues to the analysis of science and engineering issues. This environment will be almost machine independent and will attempt to unify some of the well known parallel computational paradigms. It will be knowledge based in the sense that it will be aware of its infrastructure and the compatibility requirements of the atomic elements involved. Furthermore, it will be capable of making some decisions for the user. The system will be open ended and the easy interfacing of foreign systems will be one of the primary considerations in the design of ParPDElab. To achieve the above design objectives, one must address the issue of integration of numeric, symbolic, multimedia, and AI processing. This integration will be attempted by utilizing existing technologies while developing some new methodologies for the future.