@article{kelley_liao_qi_chu_reese_winton_2008, title={PROJECTED PSEUDOTRANSIENT CONTINUATION}, volume={46}, ISSN={["1095-7170"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-55349118529&partnerID=MN8TOARS}, 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} }
@article{finkel_kuster_lasater_levy_reese_ipsen_2006, title={Communicating Applied Mathematics: Four Examples}, volume={48}, ISSN={0036-1445 1095-7200}, url={http://dx.doi.org/10.1137/s0036144504443523}, DOI={10.1137/S0036144504443523}, abstractNote={Communicating Applied Mathematics is a writing- and speaking-intensive graduate course at North Carolina State University. The purpose of this article is to provide a brief description of the course objectives and the assignments. Parts A--D of of this article represent the class projects and illustrate the outcome of the course:
* The Evolution of an Optimization Test Problem: From Motivation to Implementation, by Daniel E. Finkel and Jill P. Reese
* Finding the Volume of a Powder from a Single Surface Height Measurement, by Christopher Kuster
* Finding Oscillations in Resonant Tunneling Diodes, by Matthew Lasater
* A Shocking Discovery: Nonclassical Waves in Thin Liquid Films, by Rachel Levy
We introduce a water-supply problem considered by the optimization and hydrology communities for benchmarking purposes. The objective is to drill five wells so that the cost of pumping water out of the ground is minimized. Using the implicit filtering optimization algorithm to locate the wells, we save approximately $2,500 over the cost of a given initial well configuration.
The volume of powder poured into a bin with obstructions is found by calculating the height of the surface at every point. This is done using the fast marching algorithm. We look at two different bin geometries and determine the volumes as a function of the powder height under the spout. The surface of the powder satisfies a two-dimensional eikonal equation. This equation is solved using the fast marching method.
Resonant tunneling diodes (RTDs) are ultrasmall semiconductor devices that have potential as very high-frequency oscillators. To describe the electron transport within these devices, physicists use the Wigner--Poisson equations which incorporate quantum mechanics to describe the distribution of electrons within the RTD. Continuation methods are employed to determine the steady-state electron distributions as a function of the voltage difference across the device. These simulations predict the operating state of the RTD under different applied voltages and will be a tool to help physicists understand how changing the voltage applied to the device leads to the development of current oscillations.
When a thin film flows down an inclined plane, a bulge of fluid, known as a capillary ridge, forms on the leading edge and is subject to a fingering instability in which the fluid is channeled into rivulets. This process is familiar to us in everyday experiments such as painting a wall or pouring syrup over a stack of pancakes. It is also observed that changes in surface tension due to a temperature gradient can draw fluid up an inclined plane. Amazingly, in this situation the capillary ridge broadens and no fingering instability is observed. Numerical and analytical studies of a mathematical model of this process led to the discovery that these observations are associated with a nonclassical shock wave previously unknown to exist in thin liquid films.}, number={2}, journal={SIAM Review}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Finkel, Daniel E. and Kuster, Christopher and Lasater, Matthew and Levy, Rachel and Reese, Jill P. and Ipsen, Ilse C. F.}, year={2006}, month={Jan}, pages={359–389} }
@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} }