Pearson, John W.
SIAM
Biology and other natural sciences
http://eprints.maths.ox.ac.uk/1619/
Systems theory
Numerical analysis
2012-11
2014-02-05T00:53:41.567000+00:00
uuid:3f317dfe-0165-4df4-a80f-7ca579edd64b
2012-11-16T00:30:19.129000+00:00
Technical Report
NonPeerReviewed
application/pdf
Stoll, Martin
fedoraAdmin
http://eprints.maths.ox.ac.uk/1619
http://eprints.maths.ox.ac.uk/
oai:eprints.maths.ox.ac.uk:1619
Fast iterative solution of reaction-diffusion control problems arising from chemical processes
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.