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Sequential function approximation for the solution of differential equations

✍ Scribed by Meade, Andrew J. ;Kokkolaras, Michael ;Zeldin, Boris A.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 185 KB
Volume: 13
Category: Article
ISSN: 1069-8299
DOI: 10.1002/(sici)1099-0887(199712)13:12<977::aid-cnm113>3.0.co;2-x

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✦ Synopsis

A computational method for the solution of dierential equations is proposed. With this method an accurate approximation is built by incremental additions of optimal local basis functions. The parallel direct search software package (PDS), that supports parallel objective function evaluations, is used to solve the associated optimization problem eciently. The advantage of the method is that, although it resembles adaptive methods in computational mechanics, an a priori grid is not necessary. Moreover, the traditional matrix construction and evaluations are avoided. Computational cost is reduced while eciency is enhanced by the low-dimensional parallel-executed optimization and parallel function evaluations. In addition, the method should be applicable to a broad class of interpolation functions. Results and global convergence rates obtained for one-and two-dimensional boundary value problems are satisfactorily compared to those obtained by the conventional Galerkin ®nite element method.

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