@article{winton_pettway_kelley_howington_eslinger_2011, title={Application of Proper Orthogonal Decomposition (POD) to inverse problems in saturated groundwater flow}, volume={34}, ISSN={["1872-9657"]}, DOI={10.1016/j.advwatres.2011.09.007}, abstractNote={We develop a new Proper Orthogonal Decomposition (POD) reduced order model for saturated groundwater flow, and apply that model to an inverse problem for the hydraulic conductivity field. We use sensitivities as the POD basis. We compare the output when the optimizer uses the reduced order model against results obtained with a full PDE based model. The solutions generated using the POD reduced model are comparable in residual norm to the solutions formed using only the full-scale model. The material parameters are similarly comparable. The time to solution when using the reduced model is reduced by at least an order of magnitude, as are the number of calls to the full model.}, number={12}, journal={ADVANCES IN WATER RESOURCES}, author={Winton, Corey and Pettway, Jackie and Kelley, C. T. and Howington, Stacy and Eslinger, Owen J.}, year={2011}, month={Dec}, pages={1519–1526} }
@article{kelley_liao_qi_chu_reese_winton_2008, title={PROJECTED PSEUDOTRANSIENT CONTINUATION}, volume={46}, ISSN={["1095-7170"]}, DOI={10.1137/07069866X}, abstractNote={We propose and analyze a pseudotransient continuation algorithm for dynamics on subsets of $R^N$. Examples include certain flows on manifolds and the dynamic formulation of bound-constrained optimization problems. The method gets its global convergence properties from the dynamics and inherits its local convergence properties from any fast locally convergent iteration.}, number={6}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, author={Kelley, C. T. and Liao, Li-Zhi and Qi, Liqun and Chu, Moody T. and Reese, J. P. and Winton, C.}, year={2008}, pages={3071–3083} }