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Reference: John W. Pearson, (2011). A Radial Basis Function Method for Solving PDE Constrained Optimization Problems. Springer.Citable link to this page:

 

A Radial Basis Function Method for Solving PDE Constrained Optimization Problems

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 the Neumann boundary control problem, both involving Poisson's equation. We prove results concerning invertibility of the matrix systems we generate, and discuss a modication 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.

Bibliographic Details

Issue Date: 2011-07Identifiers

Urn: uuid:d8f95776-3af7-4798-b633-7d5c3338ab8a Item Description

Type: Technical Report;

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Author: John W. Pearson - - - - Bibliographic Details Issue Date: 2011-07 - Identifiers Urn: uuid:d8f95776-3af7-4798-b633-7d5c3338ab8a -

Source: https://ora.ox.ac.uk/objects/uuid:d8f95776-3af7-4798-b633-7d5c3338ab8a



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