I³MS - Tempone Seminar
Prof. Dr. Raul F. Tempone - A Potpourri of Results from the KAUST Uncertainty Quantification Center
In this talk, we will present several results produced at the KAUST Strategic Research Initiative for Uncertainty Quantification.
These include, among others, contributions on Multi-level and Multi-index sampling techniques that address both direct and
inverse problems. We may also discuss efficient methods for Bayesian Inverse Problems and Optimal Experimental Design.
EU Regional School - Crane Seminar
Prof. Dr. Keenan Crane - Conformal Geometry Processing
Carnegie Mellon University, USA
Digital geometry processing is the natural extension of traditional signal processing to three-dimensional geometric data. In recent years, methods based on so-called conformal (i.e., angle-preserving) transformations have proven to be a powerful paradigm for geometry processing since (i) numerical problems are typically linear, providing scalability and guarantees of correctness and (ii) conformal descriptions of geometry are often dramatically simpler or lower-dimensional than traditional encodings. This lecture will touch on both the mathematical foundations of conformal geometry, as well as recent numerical techniques and applications in 3D geometry processing.
I³MS - Rossmanith Seminar
Prof. Dr. James Rossmanith - The Regionally-Implicit Discontinuous Galerkin Method: Improving the Stability of High-Order DG-FEM
Department of Mathematics,
Iowa State University, USA
Discontinuous Galerkin (DG) methods for hyperbolic partial differential equations (PDEs) with explicit time-stepping schemes such as strong stability-preserving Runge-Kutta (SSP-RK) suffer from time-step restrictions that are significantly worse than what a simple Courant-Friedrichs-Lewy (CFL) argument requires. In particular, the maximum stable time-step scales inversely with the highest degree in the DG polynomial approximation space and becomes progressively smaller with each added spatial dimension. In this work we introduce a novel approach that we have dubbed the regionally implicit discontinuous Galerkin method (RIDG) to overcome these small time-step restrictions. The RIDG is method is based on an extension of the Lax-Wendroff DG (LxW-DG) method, which previously had been shown to be equivalent (for linear constant coefficient problems) to a predictor-corrector approach, where the predictor is a locally implicit space-time method (i.e., the predictor is something like a block-Jacobi update for a fully implicit space-time DG method). The corrector is an explicit method that uses the space-time reconstructed solution from the predictor step. In this work we modify the predictor to include not just local information, but also neighboring information. With this modification we show that the stability is greatly enhanced; in particular, we show that we are able to remove the polynomial degree dependence of the maximum time-step and show vastly improved time-steps in multiple spatial dimensions. A semi-analytic von Neumann analysis is presented and several tests are shown to verify the efficiency of the proposed scheme.
This work is joint with Pierson Guthrey.
I³MS - Saxena Seminar
Prof. Dr. Anupam Saxena - On Potential Flow Approach Modeling Unsteady Flow Around and Wake Interaction with a Flapping Wing
Department of Mechanical Engineering
Indian Institute of Technology, Kanpur
Unsteady flow characteristics are incorporated within the potential flow
theory to estimate mean lift and drag forces per cycle on a flapping
winghcord. Creation and evolution of the attached vortices, vortex
shedding and subsequent wake capture, Kramer's and added mass effects, are
modeled. Position of the attached vortex is estimated by considering the
variation in vortex properties and centrifugal forces due to wing
rotation. Viscous effects are modeled via Kramer's effect and post vortex
shedding, via a three stage decay function of which the governing
parameters are determined optimally. Results on mean lift and drag are in
good agreement with the experimental results for fruitfly, oval and figure
of eight flap patterns available in literature. The presented analytical
model is envisaged to assist in and expedite the design process of various
sub-systems of say, a micro aerial vehicle.
I³MS - Firaha Seminar
Dr. Dzmitry Firaha - Reconstruction of the Microcanonical Rate Constant from Experimental Thermal Data
The modeling of the kinetics of gas-phase chemical processes with complex reactions is a challenging task. Before modeling, the mechanism of the process needs to be proposed in the form of simple steps with known or estimated rate constants. Some chemical processes like combustion and thermal decomposition are highly sensitive to temperature and external pressure. In the straightforward approach, the modeling of such processes is a nontrivial task. In a direct approach, a lot of experimental data is needed to provide a smooth function of the rate constant depending on temperature and pressure, k(T, p). In the alternative approach (a master equation approach) pressure and temperature are used to specify the energy distribution among particles and the number of collisions between them. In such the approach, the knowledge of the energy dependent rate constant, k(E), is required. The so-called microcanonical rate constant, k(E), is hard to obtain directly from the experiment. However, the measurements are usually performed at fixed temperature providing the energy distribution for the reacting molecules allowing for recovering k(E) from k(T, p) employing the real Laplace inversion together with regularization procedure. In the talk, a summary of the possible methods for the Laplace inversion of the input data will be presented. Also, the issue on the regularization of the input data will be discussed to overcome the ill-posedness of the inversion problem.