A radial basis function method for solving PDE-constrained optimization problems

Pearson, John W (2013) A radial basis function method for solving PDE-constrained optimization problems. Numerical Algorithms, 64 (3). pp. 481-506. ISSN 1017-1398. E-ISSN 1572-9265. (doi:10.1007/s11075-012-9675-6) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1007/s11075-012-9675-6

Abstract

In this article, we apply the theory of meshfree methods to the problem of PDE-constrained optimization. We derive new collocation-type methods to solve the distributed control problem with Dirichlet boundary conditions and also discuss the Neumann boundary control problem, both involving Poisson’s equation. We prove results concerning invertibility of the matrix systems we generate, and discuss a modification to guarantee invertibility. We implement these methods using Matlab, and produce numerical results to demonstrate the methods’ capability. We also comment on the methods’ effectiveness in comparison to the widely-used finite element formulation of the problem, and make some recommendations as to how this work may be extended.

Item Type: Article
DOI/Identification number: 10.1007/s11075-012-9675-6
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: John Pearson
Date Deposited: 30 Apr 2015 16:28 UTC
Last Modified: 29 May 2019 14:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48154 (The current URI for this page, for reference purposes)
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