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

这个项目的目标是开发一个软件环境， 科学家和工程师不需要知道复杂的数字和 编程细节，以有效地解决计算 并行偏微分方程问题 电脑 基本前提是数值软件包括 两部分：一个核心，它对于一组相关的方法是不变的 设计用于不同的架构， 部分 传统的语言倾向于掩盖 软件和交织的两部分。 该项目旨在建设 一种基于断言编程范式的新语言， 寻找设计高效并行的统一原则 偏微分方程组的求解程序。 在断言编程范例中，计算被指定为 关于解决方案属性的断言集，而不是作为 详细的程序实现。 体系结构和实现 依赖于语言的过程是从 武断的描述 并行科学研究的断言编程 处理由等式语言支持，其中断言 用代数方程表示。 在这项研究中，一个方程式 正在构建编程语言（EPL）系统以（i）提供 工具，供用户指定并行数值算法在一个 架构独立的方式和（ii）开发工具，自动 生成那些数字的架构依赖部分， 算法 偏微分方程的自适应方法使用局部 关于计算解及其离散化误差的信息 自动细化网格、重新分布网格和/或改变 数值方法在问题域的不同部分。 的 项目继续研究并行自适应技术 对于二维和三维偏微分系统。 具体的研究包括动态调度和负载平衡 基于使用局部误差估计来预测工作的技术 剩下的解决问题，并行迭代技术， 代数系统和有限四叉树的并行算法， 八叉树结构网格。 新设计的程序将 使用EPL系统。

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.