Implementation of Matrix Decomposition for Solving Linear Systems Arising in Orthogonal Spline Collocation for Separable Elliptic Boundary Value Problems

求解可分离椭圆边值问题正交样条配置中产生的线性系统的矩阵分解实现

• 批准号: 9103451
• 负责人: Graeme Fairweather
• 金额: $ 9.06万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-15 至 1994-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103451&HistoricalAwards=false
• 关键词: Implementation; Matrix; Decomposition; Solving; Linear

This project is concerned with the development of software implementing new matrix decomposition algorithms which have been formulated for solving the systems of linear algebraic equations arising when orthogonal spline collocation (that is, spline collocation at Gauss points) is applied to certain separable, second order, linear problems on rectangular regions. Two classes of algorithms will be examined. In the first, the approximate solution is a piecewise Hermite bicubic defined on a uniform mesh, while the second provides approximations of arbitrarily high order on nonuniform partitions. The new algorithms, which are modular and possess a great deal of natural parallelism, also have application in the solution of nonseparable boundary value problems, problems on general regions, and time dependent problems. The new software will be written in Fortran and developed for use on various shared memory machines.

该项目涉及开发实现新矩阵分解算法的软件，该算法是为了求解当正交样条配置（即高斯点处的样条配置）应用于矩形区域上的某些可分离二阶线性问题时产生的线性代数方程组而制定的。 将检查两类算法。 在第一个中，近似解是在均匀网格上定义的分段 Hermite 双三次，而第二个提供非均匀分区上任意高阶的近似。 新算法是模块化的，具有很强的自然并行性，也可用于解决不可分离的边值问题、一般区域问题和时间相关问题。 新软件将用 Fortran 编写，并开发用于各种共享内存机器。