Adaptive Solution of Partial Differential Equations on Parallel Computers Using An Equational Language

使用方程语言在并行计算机上自适应求解偏微分方程

• 批准号: 8920694
• 负责人: Joseph Flaherty
• 金额: $ 6.4万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-04-15 至 1992-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8920694&HistoricalAwards=false
• 关键词: Adaptive; Solution; Partial; Differential; Equations; Adaptive; Solution; Partial; Differential; Equations

The goal of this project is to develop a software environment where scientists and engineers need not know intricate numerical and programming details in order to efficiently solve computational problems involving partial differential equations on parallel computers. The basic premise is that numerical software consists of two parts: a core which is invariant for a group of related methods designed for different architectures and an architecturally dependent part. Traditional languages tend to cloud common features of the software and interweave the two parts. This project aims at building a new language based on the assertive programming paradigm and at searching for unified principles for designing efficient parallel procedures for solving systems of partial differential equations. In the assertive programming paradigm, computations are specified as sets of assertions about properties of the solution, and not as detailed procedural implementations. Architecture and implementation language-dependent procedures are automatically generated from the assertive description. Assertive programming for parallel scientific processing is supported by equational languages in which assertions are expressed as algebraic equations. In this research, an Equational Programming Language (EPL) system is being built to (i) provide the tools for users to specify parallel numerical algorithms in an architecture-independent way and (ii) develop tools for automatic generation of architecturally dependent parts of those numerical algorithms. Adaptive methods for partial differential equations use local information about the computed solution and its discretization error to automatically refine meshes, redistribute meshes, and/or vary the numerical method in different parts of the problem domain. The project continues the investigation of parallel adaptive techniques for two- and three- dimensional partial differential systems. Particular studies include dynamic scheduling and load balancing techniques based on using local error estimates to predict the work remaining to solve a problem, parallel iterative techniques for algebraic systems, and parallel algorithms for finite quadtree and octree structured meshes. Newly designed procedures will be implemented using the EPL system.

该项目的目的是开发一个软件环境，其中科学家和工程师不需要了解复杂的数值和编程细节，以便有效地解决涉及并行计算机上部分微分方程的计算问题。 基本前提是数值软件由两个部分组成：一个核心，该核心是针对不同架构和架构依赖部分设计的一组相关方法不变的。 传统语言倾向于掩盖软件的共同特征，并将两部分交织在一起。 该项目旨在基于确定的编程范式来构建一种新语言，并旨在寻找统一的原则，以设计有效的并行程序来求解偏微分方程的系统。 在自信的编程范式中，计算被指定为有关解决方案属性的主张集，而不是详细的程序实现。 架构和实现语言依赖性过程是从自信描述中自动生成的。 平行科学处理的自信编程得到了对代数方程式表示主张的方程式语言的支持。 在这项研究中，正在构建一种方程式编程语言（EPL）系统（i）为用户提供工具，使用户以独立于架构的方式指定并行数值算法，并且（ii）开发工具，以自动生成这些数值算法的建筑依赖性部分。 部分微分方程的自适应方法使用有关计算解决方案的本地信息及其离散化误差，以自动改进网格，重新分布网格和/或在问题域的不同部分中使用数值方法。 该项目继续研究了两维部分差分系统的平行自适应技术。 特定的研究包括基于使用局部误差估算的动态调度和负载平衡技术，以预测解决问题的剩余工作，代数系统的平行迭代技术以及有限的Quadtree和Octree结构网格的并行算法。 新设计的过程将使用EPL系统实施。