2014-02-05T00:53:41.567Z
SIAM
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Systems theory
Biology and other natural sciences
Numerical analysis
2012-11-16T00:30:19.129Z
2012-11
NonPeerReviewed
Technical Report
oai:eprints.maths.ox.ac.uk:1619
http://eprints.maths.ox.ac.uk/1619
http://eprints.maths.ox.ac.uk/1619/
application/pdf
Stoll, Martin
Pearson, John W.
uuid:3f317dfe-0165-4df4-a80f-7ca579edd64b
Fast iterative solution of reaction-diffusion control problems arising from chemical processes
http://eprints.maths.ox.ac.uk/
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.