A joint meeting of the Southeast MAAA Section and the Southeast Atlantic SIAM Section will be held 31 March to 01 April 2006 on the campus of Auburn University, in Auburn, Alabama. The web page for this meeting is http://www.auburn.edu/~govilnk/maa-siam1/index.html.
I don't know yet when our minisymposium will be held, nor when the contributed talks will be given. My best guess is that ALL minisymposia will be on Friday between 2 and 4, and that contributed talks will also be on Friday between 2 and 4, or on Saturday betwen 10:30 and 12. The organizers promise to have a specific schedule out soon!
Friday, 31 March:
| 11:15-12:45 | TA Rush | |
| 12:40-1:50 | General Session 1 | David Anderson, Can You See a Ring? |
| 2:00-4:00 | Minisymposiums and Contributed Talks | |
| 4:10-5:15 | General Session 2 | Susanne Brenner, Fast Solvers for C0 Penalty Methods |
Saturday, 01 April:
| 9:30-10:30 | General Session 3 | Ralph Smith, Model Development and Control Design for Nonlinear Smart Material Systems |
| 10:30-12:00 | Contributed Talks | |
| 1:15-2:15 | General Session 4 | Mathematics is Not a Spectator Sport |
Minisymposium speakers have 30 minutes; 25 minutes for a presentation and 5 minutes for questions.
Each room is equipped with an overhead transparency projector, a computer with Internet access and basis software including PowerPoint, and a computer projection system.
Minisymposium #1:
| Friday | 2:00-2:30 | ROOM | Catalin Trenchea | Optimal Control for an MHD System |
| Friday | 2:30-3:00 | ROOM | Hyung-Chun Lee | Feedback control of the Burgers equation by CVT-based reduced-order modeling |
| Friday | 3:00-3:30 | ROOM | Raul Tempone | Collocation for Stochastic PDE's: The Linear Case |
| Friday | 3:30-4:00 | ROOM | Clayton Webster | Collocation for Stochastic PDE's: The Nonlinear Case |
Minisymposium #2:
| Friday | 2:00-2:30 | ROOM | Lili Ju | Adaptive Finite Element Methods for Elliptic PDE's Based on Conforming Centroidal Voronoi/Delaunay Triangulations |
| Friday | 2:30-3:00 | ROOM | Traian Iliescu | A Bounded Artificial Viscosity Large Eddy Simulation Model |
| Friday | 3:00-3:30 | ROOM | Monika Neda | Time Relaxation for Turbulent Flow Problems |
| Friday | 3:30-4:00 | ROOM | Jason Howell | Iterative defect-correction strategies for viscoelastic fluid flow |
Contributed talks speakers have 20 minutes; 15 minutes for a presentation and 5 minutes for questions.
Contributed Talks:
| DAY? | TIME? | ROOM | Chris Harden | Adapting the Parareal Algorithm for Reduced Order Models |
| DAY | TIME | ROOM | Hoa Nguyen | Estimating Probability Densities from Numeric Samples |
We consider the mathematical formulation and the analysis of an optimal control problem associated with the tracking of the velocity and the magnetic field of a viscous, incompressible, electrically conducting fluid in a bounded two-dimensional domain through the adjustment of distributed controls. Existence of optimal solutions is proved and first-order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls. Finite element approximations are defined and a priori estimates are used to show their convergence to the exact optimal solution. Some results of the computational experiments are presented.
In this talk, we present a reduced-order model for feedback control of the Burgers equation. We present the background for a CVT (centroidal Voronoi tessellation) approach to reduced-order bases. CVT-reduced order modeling begins with a snapshot set of raw data. We then extract a basis using CVT methods, and determine a very low-dimensional approximation to the solution of the Burgers equation. This technique is demonstrated for some feedback control problems. Numerical experiments are presented which compare the results of the CVT-based algorithm with those using the full finite element model.
We present a stochastic collocation method to solve linear partial differential equations whose coefficients and forcing terms depend on a finite number of random variables. The method uses a Galerkin approximation in space and a collocation in the zeros of suitable tensor-product orthogonal polynomials (Gauss points) in the probability space. This naturally leads to the solution of uncoupled deterministic problems, as in the Monte Carlo approach. It can be seen as a generalization of the Stochastic Galerkin method proposed in [Babuska-Tempone-Zouraris, SIAM J. Num. Anal. 42(2004)]. We give a complete convergence analysis for the case of a linear elliptic operator. We demonstrate exponential convergence of the "probability error" with respect to the number of Gauss points, under some regularity assumptions on the random input data. Numerical examples will show the effectiveness of the method.
We propose and analyze a stochastic collocation method to solve nonlinear partial differential equations whose coefficients and forcing terms depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This work is an extension of [Babuska, Nobile and Tempone, Submitted SIAM J. Num. Anal. (2005)] a collocation method for linear elliptic PDEs with random input data. Our methods allow one to treat easily a wider range of situations, such as: input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, random variables that are correlated or have unbounded support. We provide a rigorous convergence analysis. Numerical examples will demonstrate the effectiveness of the method.
In this talk, we will discuss a new mesh adaptivity algorithm for elliptic PDE's that combines a posteriori error estimation with centroidal Voronoi/Delaunay tessellations of domains in two dimensions. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features. In particular: errors are equidistributed over the triangles; the triangles remain very well-shaped, (even if the grid size varies by several orders of magnitude); and the convergence rates are the best obtainable when using piecewise linear finite elements.
In this talk, we present a rigorous numerical analysis for a bounded artificial viscosity model for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model is overly dissipative, and yields unphysical results. To date, several methods for "clipping" the Smagorinsy viscosity have proved useful in improving the physical characteristics of the simulated flow. However, such heuristic strategies rely strongly upon a priori knowledge of the flow regime. The bounded artificial viscosity model relies on a highly nonlinear, but monotone and smooth, semilinear elliptic form for the artificial viscosity. For such a bounded model, we have introduced a variational computational strategy, provided finite element error convergence estimates, and included several computational examples indicating its improvement over the overly diffusive Smagorinsky model.
A fluid's velocity at higher Reynolds numbers contains many spatial scales not economically resolvable. The question that arises is: How can we truncate the small scales without altering appreciably the solution's large scales. We address this important question by applying the phenomenology of homogeneous, isotropic turbulence to a time relaxation regularization flow problem. A time-discretization relaxation model will be presented, followed by the error analysis and numerical experiments of flows in transition from equilibrium to the time dependent regime via eddy shedding behind the forward-backward step.
The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge. In this work we study defect correction methods for the Johnson-Segalman model of steady viscoelastic fluid flow.
As an extension of the work by Lee (Comp. Math. Appl. 2004) and Ervin and Lee (Numer. Meth. PDE 2006), we develop and analyze a twin-parameter defect correction method for the full nonlinear Johnson-Segalman case. In the defect step, we artificially reduce the Weissenberg number to solve a stable nonlinear problem. We then determine the residual correction by solving a linearized version of the problem using a Picard-like iterative corrector. Numerical experiments verify the theoretical results of the method and extend the range of Weissenberg number for which flows can be computed. We also discuss and implement the incorporation of multigrid methods into the defect correction algorithm.
The Parareal algorithm was introduced by Lions, Maday and Turinici as an innovative parallel approach to solving time dependent differential equations. The computation is divided across multiple processors, which work on separate but connected parts of the problem. As a result, accurate solutions can be computed in much reduced time.
The key step in the Parareal algorithm is the decomposition of the temporal domain into a coarse grid shared by all processors, and fine grids unique to each processor. Data on the coarse grid may be regarded as boundary or initial data, which is passed back and forth between processors as it is computed and updated.
We are interested in examining the behavior of this algorithm as a function of the number of processors for a variety of complex systems. We will present results based on standard test cases. It is our intention to employ this procedure in a parallel implementation of Reduced Order Modeling.
A fundamental problem of statistics is to estimate an unknown probability density function (PDF) that has generated a given set of sample points. There are several possible levels of knowledge of the PDF imaginable: we might be allowed to sample it a certain number of times; we might be given a pointset of equally spaced percentiles of the PDF; or our only information might be a set of random deviates generated by the PDF. It is this last case that concerns us. We propose a simple method to construct an approximate model of the unknown PDF, based only on the set of random samples, and to resample the model to produce pointsets that are well distributed under the PDF.
We will probably drive up on Thursday 30 March and leave on Sunday morning, 02 April. It looks like the drive to Auburn will take between 5 and 6 hours. Check-in time at the hotel is 3.
| Name | Drive/Ride |
|---|---|
| John Burkardt | riding with ? |
| Chris Harden | driving with ? |
| Hyung-Chun Lee | driving with family |
| Hoa Nguyen | driving with friend |
| Raul Tempone | driving with family |
| Catalin Trenchea | driving with ? |
| Clayton Webster | driving with ? |
We are staying at The Hotel at Auburn University and Dixon Conference Center. We have reservations for six rooms and three nights: 30 March, 31 March, and 01 April.
| Name | Roommate |
|---|---|
| John Burkardt | share with Chris |
| Chris Harden | share with John |
| Hyung-Chun Lee | share with family |
| Hoa Nguyen | |
| Raul Tempone | share with family |
| Catalin Trenchea | share with Clayton |
| Clayton Webster | share with Catalin |
We must all register for the conference, the prices are: