Journals
Resources
About Us
Open Access

ANOVA Expansions and Efficient Sampling Methods for Parameter Dependent Nonlinear PDEs

ANOVA Expansions and Efficient Sampling Methods for Parameter Dependent Nonlinear PDEs

Year:    2009

International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 2 : pp. 256–273

Abstract

The impact of parameter dependent boundary conditions on solutions of a class of nonlinear partial differential equations and on optimization problems constrained by such equations is considered. The tools used to gain insights about these issues are the Analysis of Variance (ANOVA) expansion of functions and the related notion of the effective dimension of a function; both concepts are reviewed. The effective dimension is then used to study the accuracy of truncated ANOVA expansions. Then, based on the ANOVA expansions of functionals of the solutions, the effects of different parameter sampling methods on the accuracy of surrogate optimization approaches to constrained optimization problems are considered. Demonstrations are given to show that whenever truncated ANOVA expansions of functionals provide accurate approximations, optimizers found through a simple surrogate optimization strategy are also relatively accurate. Although the results are presented and discussed in the context of surrogate optimization problems, most also apply to other settings such as stochastic ensemble methods and reduced-order modeling for nonlinear partial differential equations.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2009-IJNAM-766

International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 2 : pp. 256–273

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    ANOVA expansions nonlinear partial differential equations surrogate optimization parameter sampling methods.