This project is concerned with the development of implementing new matrix decomposition algorithms for solving the systems of linear algebraic equations arising when orthogonal spline collocation (that is, spline collocation at Gauss points) is applied to separable, second order, linear problems on rectangular regions. These algorithms have application in the solution of nonseparable boundary value problems, problems on general regions, and time dependent problems. The success of matrix decomposition algorithms depends on knowledge of the eigenvalues and eigenvectors of matrices arising in corresponding two-point boundary value problems in one space dimension. Knowledge of such an eigensystem with respect to one coordinate variable reduces the original two-dimensional discrete problem to solving a collection of independent discrete two-point boundary value problems with respect to the other coordinate variable. A software package is developed implementing orthogonal spline collocation algorithms with polynomials of arbitrary order on nonuniform partitions in each coordinate direction. The package includes, as a special case, a fast transform solver for piecewise Hermite bicubic orthogonal spline collocation for Poisson's equation in various coordinate systems.

Agency
National Science Foundation (NSF)
Institute
Division of Computer and Communication Foundations (CCF)
Application #
9403461
Program Officer
S. Kamal Abdali
Project Start
Project End
Budget Start
1994-09-15
Budget End
1996-08-31
Support Year
Fiscal Year
1994
Total Cost
$120,000
Indirect Cost
Name
University of Kentucky
Department
Type
DUNS #
City
Lexington
State
KY
Country
United States
Zip Code
40506