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PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs.
Pearson, John W.
http://eprints.maths.ox.ac.uk/1619
2012-11-16T00:30:19.129000+00:00
http://eprints.maths.ox.ac.uk/1619/
application/pdf
SIAM
Numerical analysis
NonPeerReviewed
Systems theory
Stoll, Martin
Fast iterative solution of reaction-diffusion control problems arising from chemical processes
2012-11
http://eprints.maths.ox.ac.uk/
2014-02-05T00:53:41.567000+00:00
Biology and other natural sciences
Technical Report
uuid:3f317dfe-0165-4df4-a80f-7ca579edd64b
oai:eprints.maths.ox.ac.uk:1619