Paper Info
Title
An optimal two-step quadratic spline collocation method for the Dirichlet biharmonic problem
Abstract
A two-step quadratic spline collocation method is formulated for the solution of the Dirichlet biharmonic problem on the unit square rewritten as a coupled system of two second-order partial differential equations. This method involves fast Fourier transforms and, in comparison to its one-step counterpart, it has the advantage of requiring the solution a symmetric positive definite Schur complement system rather than a nonsymmetric one. As a consequence, the corresponding step of the new method is performed using a preconditioned conjugate gradient method. The total cost of the method on a N × N partition of the unit square is $O(N^{2}\log N)$ . To demonstrate the optimal accuracy of the method, the results of numerical experiments are provided.
Year
DOI
Venue
2022
10.1007/s11075-022-01294-y
Numerical Algorithms
Keywords
DocType
Volume
Biharmonic equation, Quadratic spline collocation, Fast Fourier transforms, Preconditioned conjugate gradient method, Optimal global convergence rates, Superconvergence, 65N35, 65N22, 65F05
Journal
91
Issue
ISSN
Citations 
3
1017-1398
0
PageRank 
References 
Authors
0.34
5
3
Name
Order
Citations
PageRank
Bialecki Bernard100.34
Fairweather Graeme200.34
Andreas Karageorghis320447.54