@article{kergosien_barnhart_kees_danielson_brourman_dehoff_schertel_2004, title={Radiographic and clinical changes of the tibial tuberosity after tibial plateau leveling osteotomy}, volume={33}, ISSN={["0161-3499"]}, DOI={10.1111/j.1532-950X.2004.04066.x}, abstractNote={Objective— To investigate radiographic changes of the tibial tuberosity after tibial plateau leveling osteotomy (TPLO) surgery and identify clinical findings and risk factors associated with such changes.}, number={5}, journal={VETERINARY SURGERY}, author={Kergosien, DH and Barnhart, MD and Kees, CE and Danielson, BG and Brourman, JD and Dehoff, WD and Schertel, ER}, year={2004}, pages={468–474} }
 @article{fowler_kelley_miller_kees_darwin_reese_farthing_reed_2004, title={Solution of a well-field design problem with implicit filtering}, volume={5}, ISSN={["1573-2924"]}, DOI={10.1023/B:OPTE.0000033375.33183.e7}, abstractNote={Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this application field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web.}, number={2}, journal={OPTIMIZATION AND ENGINEERING}, author={Fowler, KR and Kelley, CT and Miller, CT and Kees, CE and Darwin, RW and Reese, JP and Farthing, MW and Reed, MSC}, year={2004}, month={Jun}, pages={207–234} }
 @article{farthing_kees_coffey_kelley_miller_2003, title={Efficient steady-state solution techniques for variably saturated groundwater flow}, volume={26}, ISSN={["0309-1708"]}, DOI={10.1016/S0309-1708(03)00076-9}, abstractNote={We consider the simulation of steady-state variably saturated groundwater flow using Richards’ equation (RE). The difficulties associated with solving RE numerically are well known. Most discretization approaches for RE lead to nonlinear systems that are large and difficult to solve. The solution of nonlinear systems for steady-state problems can be particularly challenging, since a good initial guess for the steady-state solution is often hard to obtain, and the resulting linear systems may be poorly scaled. Common approaches like Picard iteration or variations of Newton’s method have their advantages but perform poorly with standard globalization techniques under certain conditions. Pseudo-transient continuation has been used in computational fluid dynamics for some time to obtain steady-state solutions for problems in which Newton’s method with standard line-search strategies fails. Here, we examine the use of pseudo-transient continuation as well as Newton’s method combined with standard globalization techniques for steady-state problems in heterogeneous domains. We investigate the methods’ performance with direct and preconditioned Krylov iterative linear solvers. We then make recommendations for robust and efficient approaches to obtain steady-state solutions for RE under a range of conditions.}, number={8}, journal={ADVANCES IN WATER RESOURCES}, author={Farthing, MW and Kees, CE and Coffey, TS and Kelley, CT and Miller, CT}, year={2003}, month={Aug}, pages={833–849} }
 @article{farthing_kees_miller_2003, title={Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow}, volume={26}, ISSN={["1872-9657"]}, DOI={10.1016/S0309-1708(02)00187-2}, abstractNote={Richards’ equation (RE) is commonly used to model flow in variably saturated porous media. However, its solution continues to be difficult for many conditions of practical interest. Among the various time discretizations applied to RE, the method of lines (MOL) has been used successfully to introduce robust, accurate, and efficient temporal approximations. At the same time, a mixed-hybrid finite element method combined with an adaptive, higher order time discretization has shown benefits over traditional, lower order temporal approximations for modeling single-phase groundwater flow in heterogeneous porous media. Here, we extend earlier work for single-phase flow and consider two mixed finite element methods that have been used previously to solve RE using lower order time discretizations with either fixed time steps or empirically based adaption. We formulate the two spatial discretizations within a MOL context for the pressure head form of RE as well as a fully mass-conservative version. We conduct several numerical experiments for both spatial discretizations with each formulation, and we compare the higher order, adaptive time discretization to a first-order approximation with formal error control and adaptive time step selection. Based on the numerical results, we evaluate the performance of the methods for robustness and efficiency.}, number={4}, journal={ADVANCES IN WATER RESOURCES}, author={Farthing, MW and Kees, CE and Miller, CT}, year={2003}, month={Apr}, pages={373–394} }
 @article{kees_miller_jenkins_kelley_2003, title={Versatile two-level Schwarz preconditioners for multiphase flow}, volume={7}, ISSN={["1420-0597"]}, DOI={10.1023/A:1023514922877}, number={2}, journal={COMPUTATIONAL GEOSCIENCES}, author={Kees, CE and Miller, CT and Jenkins, EW and Kelley, CT}, year={2003}, pages={91–114} }