Tuesday, September 15, 2009 at 3:00 PM in SAS 4201
Tom Hagstrom, Southern Methodist University
Plane Wave Expansions, Optimal Local Radiation Boundary Conditions, and Propagation Algorithms
The fundamental feature of waves is their ability to propagate
long distances relative to their wavelength. Efficient algorithms
for simulating waves deal with this fact by:
i. Employing high-resolution discretizations;
ii. Avoiding the sampling of wave fields where possible via the
use of accurate radiation boundary conditions and fast
far-field propagation algorithms.
In this talk we will focus on the second issue, reviewing the disparate
representations which have been proposed and developing a new technique,
the complete plane wave representation, which we prove leads to local
radiation boundary conditions of optimal complexity for isotropic systems.
We will also discuss the prospects for the development of fast propagation
algorithms using the complete plane wave representation as well as other
solution forms. Finally we will list some of the difficult issues which arise when
considering more complex models.
Tuesday, September 22, 2009 at 3:00 PM in SAS 4201
Anita Layton, Duke
A Velocity Decomposition Approach for Moving Interfaces in Viscous Fluids
We present a second-order accurate method for computing the
coupled motion of a viscous fluid and an elastic material interface with
zero thickness. The fluid flow is described by the Navier-Stokes
equations, with a singular force due to the stretching of the moving
interface. We decompose the velocity into a "Stokes" part and a "regular"
part. The first part is determined by the Stokes equations and the
singular interfacial force. The Stokes solution is obtained using the
immersed interface method, which gives second-order accurate values by
incorporating known jumps for the solution and its derivatives into a
finite difference method. The regular part of the velocity is given by the
Navier-Stokes equations with a body force resulting from the Stokes part.
The regular velocity is obtained using a time-stepping method that
combines the semi-Lagrangian method with the backward difference formula.
Because the body force is continuous, jump conditions are not necessary.
We will also briefly discuss an on-going project, where the velocity
decomposition approach is applied to problems with coupled fluid and
solid.Tuesday, October 6, 2009 at 3:00 PM in SAS 4201
Junping Wang, National Science Foundation
On maximum value principles for finite element approximations
The purpose of this talk is to discuss how the classical
maximum value principles in PDEs be extended to their numerical
approximations arising from finite element methods. In particular, the
discussion will be primarily focused on the second order elliptic
problem, and the finite element methods shall include standard Galerkin,
P1 non-conforming, and mixed finite elements methods.Thursday, November 5, 2009 at 4:00 PM in Burlington Labs
Brian Adams, Sandia National Laboratories
Uncertainty Quantification Methods Enabling Credible Simulation
To be credible, computational models must be verified in their software implementation, validated with data, and deliver a best estimate of performance, together with its degree of variability or uncertainty. Estimates of variability or uncertainty require enhancing science-based simulations with non-deterministic analysis methods accounting for both aleatory (inherent/probabilistic) and epistemic (lack-of-knowledge) uncertainties.
In this talk, I will offer an accessible introduction to uncertainty quantification (UQ) methods that assess model output responses as a function of input parameter uncertainty. These typically yield information on response means, standard deviations, level probabilities, reliability indices, or belief/plausibility bounds. I will survey such forward uncertainty propagation approaches as Latin hypercube sampling, reliability methods, and polynomial chaos/stochastic collocation. These can treat simulations as "black boxes," assessing them without intrusive code modification. I will demonstrate how advanced UQ methods employ a mix of probability, nonlinear optimization, quadrature, and surrogate (meta-) modeling, and indicate Sandia's UQ research directions.
Tuesday, November 10, 2009 at 3:00 PM in SAS 4201
Michael Pernice, Idaho National Laboratory
Adjoint-based error estimates for a Cartesian grid finite volume method for diffusion problems with discontinuous coefficients
Finite volume methods on Cartesian grids are widely used in scientific
and engineering applications due to their simplicity and local
conservation properties. Diffusion operators with discontinuous
coefficients are encountered in many application areas such as heat
conduction, diffusion approximations to radiation transport, and
subsurface flow. Convergence analysis and error estimation for such
operators is difficult due to lack of smoothness in the solution.
However, adjoint-based techniques are well suited for developing sharp
error estimates.
Our approach is based on replacing the original problem by a surrogate
problem in which the discontinuous coefficient is replaced by a smooth
one. We then combine an adjoint-based estimate of the error in the
surrogate problem with an estimate of the difference between the
solutions of the original and surrogate problems. The adjoint-based
estimate exploits a well-known equivalence between the finite volume
discretization and a mixed finite element discretization with
appropriate quadrature rules. Numerical results demonstrate the
effectiveness of our approach.
This is joint work with H. Wang (Michigan Technological University)
and D. Estep (Colorado State University).Tuesday, November 17, 2009 at 3:00 PM in SAS 4201
Jian-Guo Liu, Duke
Controlling numerical dissipation and time stepping in some multi-scale fluid simulations
In the Eulerian description of fluid dynamics such as compressible gas dynamics and kinetic equation, numerical dissipations are necessarily introduced to have a stable discretization. One severe difficulty in multi-scale fluid simulations is the amplification and accumulation
of these numerical dissipations due to the dynamics in small scale motions such as fast waves and small mean free path.
Another known difficulty in multi-scale fluid simulations is the inhibitively small time stepping.
In this talk, we will show that with some proper decompositions of the underlying, governing equations, these two difficulties can be removed in the gas dynamics uniformly
with respect to the Mach number, and in the neutron transport equation uniformly with respect to the mean free path. I will also discuss an effective way to carry out localized kinetic upscaling in a global fluid model .Thursday, December 3, 2009 at 2:00 PM in SAS 4201
Paul Van Dooren, Catholic University of Louvain, Belgium
TBA
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Seminar Organizers: Pierre Gremaud, Ilse Ipsen, Tim Kelley