Here are the final three CSE talks for the semester, SIAM @ Purdue is sponsoring the first two, but all should be interesting.
April 24th: David Gerberry, CSE-MATH doctoral student
Mathematical Models of Infectious Disease: Very different approaches for very different diseases
April 29th: Murat Manguoglu, CSE-CS doctoral student
Parallel Hybrid Sparse System Solvers
May 1st: Matthew J. Churchfield, CSE-AAE doctoral student and CSE-Lynn Fellow
The Lag RST Turbulence Model Applied to Vortical Flows
click Read more for abstracts and locations
Mathematical Models of Infectious Disease: Very different approaches for very different diseases
David J. Gerberry
CS&E Doctoral Student Department of Mathematics Purdue University
Friday, April 24, 2009 4:00 pm - 5:00 pm LWSN 1142
Abstract
In this presentation, we will begin by discussing a mathematical model for childhood diseases (e.g. measles, mumps, chicken pox, etc.) and then discuss modeling work done on tuberculosis. For the childhood disease model, we are interested in the recurrent outbreaks which have long been associated with these diseases. Taking a theoretical approach, we use dynamical systems theory to prove the existence of Hopf and homoclinic bifurcations which give rise to rich dynamics. For tuberculosis, the approach is more applied in nature. The work is motivated by the uncertainty that surrounds the use of the BCG vaccine for tuberculosis. Within the modeling framework, we examine conditions which justify the discontinuation of mass vaccination. The effort is datadriven and relies heavily on model simulations for eight countries with varying TB burdens. The model is analyzed via numerical experiments, statistical analysis and dynamical systems theory.
David Gerberry is a Ph. D. student in the Department of Mathematics registered in the interdisciplinary Computational Science and Engineering Program at Purdue University. His work is conducted under the supervision of Professor Fabio Milner, who is now at Arizona State University. His research interests are in mathematical models for biological processes, including: epidemiology, immunology and ecology. David is currently funded by a Bilsland Dissertation Fellowship for interdisciplinary research through the CS&E program. He has also been funded through both VIGRE and GAANN fellowships at different times in his graduate career.
A Parallel Hybrid Linear System Solver
Murat Manguoglu
CS&E Doctoral Student Seminar Department of Computer Science
Wednesday, April 29 4:00 pm - 5:00 pm LWSN 3102A/B
Abstract
We present a family of hybrid algorithms that are suitable for the solution of large sparse linear systems on parallel computing platforms. This study is motivated by the lack of robustness of Krylov subspace iterative schemes with “black-box” preconditioners, such as incomplete LU-factorizations and the lack of scalability of direct sparse system solvers. Our hybrid solver is as robust as direct solvers and as scalable as iterative solvers whose preconditioners are both effective and scalable. Our method relies on weighted symmetric and nonsymmetric matrix reordering for bringing the largest elements on or closer to the main diagonal resulting in a very effective extracted banded preconditioner. Systems involving the extracted banded preconditioner are solved via a member of the recently developed SPIKE family of algorithms. The effectiveness of our method is demonstrated by solving large sparse linear systems that arise in various applications such as computational fluid dynamics, oil reservoir simulations, and nonlinear optimizations. Finally, we present a highly accurate method for predicting the parallel scalability of our system solver on architectures with more nodes than the platform on which our experiments have been performed.
Murat Manguoglu received his bachelor’s degree in Electrical and Electronics Engineering from Middle East Technical University, Ankara, Turkey in June 2002. He received his master’s degree in Computational Engineering and Science from the University of Utah, Salt Lake City, Utah in May 2004. He joined the Department of Computer Science at Purdue University, West Lafayette, Indiana, as a doctoral student in August 2004. He completed his doctoral research specializing in ‘Computational Science’ through the Computational Science and Engineering program at Purdue University under the supervision of Professor Ahmed Sameh in May 2009.
The Lag RST Turbulence Model Applied to Vortical Flows
Matthew J. Churchfield CS&E –AAE Doctoral Student School of Aeronautics and Astronautics
Wednesday, May 1, 2009 11:00 am - 12:00 pm ARMS 3326
Abstract:
Turbulent vortical flows are common in nature and engineering applications–the motivating type of flow being wingtip vortices. Computational fluid dynamics (CFD) based on the Reynolds-averaged Navier-Stokes (RANS) equations is an increasingly used analysis tool. Therefore, RANS-based CFD must be able to predict turbulent vortices well. Many popular linear eddy viscosity turbulence models used with RANS-based CFD do not accurately predict the turbulence in vortices, often causing the mean flow to diffuse too quickly. Because such models rely on the Boussinesq approximation, they cannot account for the fact that the Reynolds stresses require time to react to the ever-changing mean strain-rates encountered along a helical vortex streamline. In other words, such models do not allow for misalignment of the principal axes of the Reynolds stress and strain rate tensors. Empirical rotation corrections improve mean predictions but are not a complete solution. More sophisticated models that can account for this “lag” in the Reynolds stresses also have problems in predicting the turbulence correctly. The lag RST model proposed by Olsen and Coakley, which is based on a two-equation k-ω model, shows promise in better predicting turbulent vortices than other current models with little added complexity over a two-equation model. The model has been applied to a q-vortex flow, which is an idealized representation of wingtip vortex flow. These results show that the model is able to control the excessive diffusion of mean momentum seen with linear eddy viscosity models. The lag RST model is also currently being applied to a more complex three dimensional wingtip vortex flow created by a wing in a wind tunnel.
Matthew J. Churchfield is a doctoral candidate in the School of Aeronautics and Astronautics, majoring in aerodynamics and specializing in ‘Computational Engineering’ through the Computational Science and Engineering (CS&E) program at Purdue University. He is the recipient of the CS&E-Lynn fellowship (2003-2004), the NSF Graduate Research Fellowship (2005-2008), the NSF GK-12 Fellowship (2008-2009), and CS&E Bilsland Dissertation Fellowship (2009). He is a native of Reno, Nevada and completed his bachelors degree in mechanical engineering there at the University of Nevada, Reno. Matt will go on to a post-doctoral research position at the National Renewable Energy Laboratory’s National Wind Technology Center.