Hi,

I want to learn flow optimization... What should I study...?? fluid dynamics or CFD...etc...

Thank you...

I am biased due to an interest in scalability for problems with mesh-dependent design space. This two-part paper is excellent.

@article{biros2005pln1, title={{Parallel Lagrange-Newton-Krylov-Schur methods for PDE constrained optimization. Part I: The Krylov-Schur solver}}, author={Biros, G. and Ghattas, O.}, journal={SIAM Journal on Scientific Computing}, volume={27}, number={2}, pages={687--713}, year={2005}, publisher={Society for Industrial and Applied Mathematics Philadelphia, PA, USA} }

@article{biros2005pln2, title={{Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part II: The Lagrange Newton solver, and its application to optimal control of steady viscous flows}}, author={Biros, G. and Ghattas, O.}, journal={SIAM Journal on Scientific Computing}, volume={27}, number={2}, pages={714--739}, year={2005}, publisher={Society for Industrial and Applied Mathematics Philadelphia, PA, USA} }

Thank you Jed.

Is there any text book to recommend...???

Sorry, I don't have a textbook recommendation. LNKS is pretty new and the Biros & Ghattas 2-part paper is very good. It has a survey of traditional reduced space methods (more in the book by Kelley below, but this book doesn't target fluid flow specifically). I know very little about problems with small design space. There are some recent papers (most/all involve Volkan Akcelik) an large-scale inversion of time-dependent problems (advection-diffusion of airborne contaminants, seismic inversion) which are too big to apply LNKS (>10^11 space-time unknowns). They have developed some multilevel preconditioners for the inverse operators which make the number of iterations manageable even when the design space is mesh-dependent (and >10^7 unknowns).

@book{kelley1999imo, title={{Iterative Methods for Optimization}}, author={Kelley, CT}, year={1999}, publisher={Society for Industrial Mathematics} }

@article{akcelik2005ddd, title={{Dynamic data-driven inversion for terascale simulations: real-time identification of airborne contaminants}}, author={Ak\c{c}elik, V. and Biros, G. and Draganescu, A. and Hill, J. and Ghattas, O. and van Bloemen Waanders, B.}, journal={Proceedings of the 2005 ACM/IEEE conference on Supercomputing}, year={2005}, publisher={IEEE Computer Society Washington, DC, USA} }

@article{akcelik2006pap, title={{Parallel algorithms for PDE-constrained optimization}}, author={Ak\c{c}elik, V. and Biros, G. and Ghattas, O. and Hill, J. and Keyes, D. and van Bloemen Waanders, B.}, journal={Frontiers of Parallel Computing. SIAM}, year={2006} }

@article{epanomeritakis2008ncm, title={{A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion}}, author={Epanomeritakis, I. and Ak\c{c}elik, V. and Ghattas, O. and Bielak, J.}, journal={Inverse Problems}, volume={24}, number={034015}, pages={034015}, year={2008}, publisher={Institute of Physics Publishing} }

Thank you Jed.