On Monday November 3rd at 3:30 in Math 357, Dr. Qin Shing from the Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research at Baylor University will be talking about “Numerical PDEs and the Legacy of ADI and LOD Methods”.
Abstract: Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations. They involve computational methods including the finite difference and finite element, finite volume, spectral, meshless, domain decomposition, multigrid, and in particular, splitting methods. The ADI and LOD approaches are two of them with extraordinary features in structure simplicity, computational efficiency and flexibility in applications. They look similar, but are fundamentally different. Naturally, they lead to different ways of operations, and offer different strategies in computational realizations. This talk will provide an insight into the glorious history of these numerical methods, and discuss some of their latest reinforcements including applications for highly oscillatory waves. (Flyer in PDF form)
About Dr. Qin Sheng: Dr. Sheng received his BS and MS in Mathematics from Nanjing University in 1982, 1985, respectively. Then he acquired his Ph.D. from the University of Cambridge under the supervision of Professor Arieh Iserles. After his postdoctoral research with Professor Frank T. Smith, FRS, in University College London, he joined National University of Singapore in 1990. Since then, Dr. Sheng was on faculty of several major universities till his joining Baylor University, which is one of the research institutions and the second largest private university in the United States. Dr. Sheng has been interested in splitting and adaptive numerical methods for solving linear and nonlinear partial differential equations. He is also known for the Sheng-Suzuki theorem in numerical analysis. He has published over 95 refereed journal articles as well as 6 joint research monographs. He has been an Editor-in-Chief of an SCI journal, International Journal of Computer Mathematics, published by Taylor and Francis in London since 2010. He gives invited presentations, including keynote lectures, in international conferences every year. Dr. Sheng’s projects have been supported by several U.S. research agencies. He currently advises 3 doctoral students and 1 postdoctoral research fellow. He also serves on Panelist Boards for several research agencies including the National Science Foundation, USA.
On Monday October 27th at 3:30 in Math 357, Dr. Tetyana Malysheva from the University of Oklahoma will be talking about “Modeling of Elastic Solids”. The talk will be accessible to undergraduates and grad students. Abstract: In this talk, we will consider a variational approach to the modeling and numerical analysis in linear elasticity and thermoelasticity. The presented method is based on physical principles, geometry of an object, and appropriate approximating assumptions. We will derive strong and weak formulations for the Timoshenko beam model, and discuss a finite element method for numerical solution of forward and inverse problems in linear elasticity. (Flyer in PDF form)
On Monday September 15th at 3:30 in Math 357, Dr. Matt Beauregard will be talking about “Surgical Splitting”. This talk will be interactive and interesting to all levels of students. Students with exposure to differential equations or numerical methods are especially encouraged to attend.
Abstract: Time dependent mathematical models are often written in terms of partial differential equations. The spatial derivatives can then be approximated to develop a system of first order differential equations in time. The solutions can formally be written in terms of an evolution operator. A final approximation can be formulated through approximating the underlying matrix exponential. Approximating the matrix exponential can be time-consuming, especially for high dimension problems. Is it possible to split the problem? If so, how is this influenced by forcing terms, nonlinearities, or geometric considerations? We’ll be investigating these questions with some toy problems. Students with exposure to differential equations are especially encouraged to attend! Come prepared with a few pieces of paper, pen/pencil, and water to stay hydrated as we sweat through this surgical splitting procedure. (flyer in PDF form)
On Monday April 28th at 3:30, Dr. Kalanka Jayalath will be talking about “Geometrical Pattern Identification Using a Bayesian Paradigm.”
Abstract: Identifying spatially distributed point patterns plays an important role in many scientific areas including pattern recognition, computer vision, image processing and some geological applications. Current methods of identifying conic structures depend solely on algebraic or geometric distances and are known as algebraic or geometric fits respectively. This talk focusses on a novel circle and ellipse fitting technique which elicits a Bayesian philosophy on geometric distance. Statistical methods will be discussed to investigate whether the spatial pattern is reasonably attributable to a circular or elliptical pattern. We compare classical and novel circle fitting methods under various error structures. In particular, we focus on their accuracy of estimates when in the presence of noisy data, a topic that is poorly documented in the literature. Finally, our findings will be applied to a pre-historic archeological site to identify the evident geometrical structure. (Flyer in PDF form)
On Monday April 14th at 3:30 in Math 357, Dr. Lynn Greenleaf will be talking about “Estimation and Analysis of Atmospheric Vortices”.
Abstract: Intense atmospheric vortices occur in dust devils, waterspouts, tornadoes, mesocyclones and tropical cyclones. Tangential wind models have been proposed that approximate the observed tangential wind profile of at atmospheric vortex for the purpose of data analysis and prediction. Data analysis is required to demonstrate in an objective way that a parameterized tangential wind model provides an acceptable description of the tangential wind profile of an atmospheric vortex and determine if the model can be used to make accurate predictions. Using the methodology of Information Theory and Sensitivity Analysis, information content of the parameters of a vortex model show that both parameters are essential in estimation of the tangential wind profile. Uncertainty in radial, tangential and vertical winds were examined and can be used effectively to predict these quantities and their uncertainties. (flyer in PDF form)
As part of his campus visit, on Thursday April 10th at 3:30 PM in Math 357, Dr. Mathew Beauregard will be giving a talk “Numerical Linear Algebra: Can you point me in the right direction?” This talk will be geared toward undergraduates and interesting to students with linear algebra or numerical analysis background.
Abstract: Numerical approximations to time-dependent differential equations often require spatial and temporal adaptive methods to resolve the solution accurately. In such methods, the numerical solution is advanced upon solving a, potentially large, linear algebraic system of equations. The adaptation in space and time generates new matrices at each iterate. Nevertheless, changes in the matrices are nominal, while the structure of the matrices often remains the same. GMRES is a common numerical linear algebraic solver, developed in the 1990s, that approximates the solution to a linear system. In this talk, a modified GMRES method is presented. The new method takes advantage of eigenvector information obtained from prior linear algebraic solves and then uses this to increase the rate of convergence in future linear solves. (flyer in PDF form)
As part of a campus visit on Monday February 24th at 3:30 PM, Rebecca-Anne Dibbs from the University of Northern Colorado will be talking about “The Effects of Formative Assessment on Students’ Zone of Proximal Development in Introductory Calculus”.
Abstract: One of the challenges of teaching introductory calculus is the large variance in student backgrounds. Formative assessment can be used to target which students need help, but little is known about why formative assessment is effective with adult learners. The purpose of this mixed methods study was to investigate which functions of formative assessment that enable instructors to provide the scaffolding needed to engage students in an introductory calculus course within their Zones of Proximal Development during weekly group labs. By regularly collecting information from low-stakes opportunities for students to demonstrate their current understanding, instructors were able to target subsequent class discussion on critical scaffolding for student growth. The formative assessments also enabled students to evaluate their own progress and ask clarifying questions and, provided students who would not ordinarily ask questions during class opportunities for legitimate peripheral participation. (flyer in PDF form)