Fourier matrix decomposition methods for the least squares solution of singular Neumann and periodic hermite bicubic collocation problems

Journal Article · Wed Mar 01 04:00:00 EST 1995 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/0916027· OSTI ID:32069

Bialecki, B ^[1]; Remington, K A ^[2]

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1. Univ. of Kentucky, Lexington, KY (United States). Dept. of Mathematics
2. Oak Ridge National Lab., TN (United States)

The use of orthogonal spline collocation with piecewise Hermite bicubics is examined for the solution of Poisson`s equation on a rectangle subject to either pure Neumann or pure periodic boundary conditions. Emphasis is placed on finding a least squares solution of these singular collocation problems. The technique of matrix decomposition is applied and explicit formulas for the requisite eigensystems corresponding to two-point Neumann and periodic collocation boundary value problems are presented. The resulting algorithms use fast Fourier transforms for efficiency and are highly parallel in nature. On an N x N partition, a fourth order accurate least squares solution is computed at a cost of O(N{sup 2}log N) operations. The results of numerical experiments are provided that demonstrate that the implementations compare very favorably with recent fourth order accurate finite difference and finite element Galerkin codes.

• Sponsoring Organization: USDOE
• OSTI ID: 32069
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 2 Vol. 16; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
FOURIER TRANSFORMATION
LEAST SQUARE FIT
NUMERICAL SOLUTION
PARALLEL PROCESSING
POISSON EQUATION
SPLINE FUNCTIONS