| Date: | September 24, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 117 |
| Speaker: | Manuel Quezada de Luna, ERDC |
| Title: | A monolithic conservative level set method with built-in redistancing |
| Abstract: | In fluid mechanics the interaction of fluids with distinguishable material
properties (e.g. water and air) is referred as multiphase flow. In this
work we consider two-phase incompressible flow and concentrate on the
representation and time evolution of the interface. There is an extensive
list of methods to treat material interfaces. Popular choices include the
volume of fluid and level set techniques. We propose a novel level-set like
methodology for multiphase flow that preserves the initial mass of each
phase. The model combines and reconciles ideas from the volume of fluid and
level set methods by solving a non-linear conservation law for a
regularized Heaviside of the (distance function) level-set. This guarantees
conservation of the volume enclosed by the zero level-set. The equation is
regularized by a consistent term that assures a non-singular Jacobian. In
addition, the regularization term penalizes deviations from the distance
function. The result is a nonlinear monolithic model for a phase
conservative level-set where the level-set is given by the distance
function. The continuous model is monolithic (meaning that only one
equation is needed) and has only one parameter that controls the strength
of regularization/penalization in the model. We start the presentation
reviewing the main ingredients of this model: 1) a conservative level-set
method by [Kees et all (2011)], which combines a distanced,
non-conservative level-set method with the volume of fluid method via a
non-linear correction and 2) elliptic re-distancing by [Basting and
Kuzmin(2014)]. Afterwards, we manipulate the conservative level-set method
by [Kees et all (2011)] to motivate our formulation. We present a first
model which we then modify to resolve some difficulties. Finally, we
present a full discretization given by continuous Galerkin Finite Elements
in space and a high-order Implicit-Explicit time integration. We
demonstrate the behavior of this model by solving different benchmark
problems in the literature of level-set methods. T |
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| Date: | October 8, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 117 |
| Speaker: | Jonathan Tyler, Texas A&M |
| Title: | Mathematical Modeling in the Pharmaceuticals |
| Abstract: | Mathematical models are used in each step of the drug discovery process to expedite and optimize drug development. Currently, the TransQST (Translational Quantitative Systems Toxicology) consortium is facilitating one such effort to develop open source quantitative systems toxicology (QST) models of four organ systems: GI-immune, heart, kidney, and liver. In this talk, I will give a brief introduction to how math models are used in the drug development process. I will then talk about my summer internship project with Boehringer Ingelheim to make the current TransQST GI-immune model more precise and practical through the addition of key immune species such as cytokines and Th2 cells. Finally, I will present three simulations that address pharmacological issues: (1) Simulation of a Crohn’s patient taking a TNF-alpha inhibitor to address the drug's immunosuppressive action, (2) Sensitivity analysis to help guide in vivo and in vitro experiments, and (3) Generation of virtual parameter sets to address drug efficacy across a population. |
|
| Date: | October 29, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Timo de Wolff, TU Berlin |
| Title: | An Experimental Comparison of SONC and SOS Certificates for Unconstrained Optimization |
| Abstract: | Finding the minimum of a multivariate real polynomial is a well-known hard problem with various applications. We present a polynomial time algorithm to approximate such lower bounds via sums of nonnegative circuit polynomials (SONC). As a main result, we carry out the first large-scale comparison of SONC, using this algorithm and different geometric programming (GP) solvers, with the classical sums of squares (SOS) approach, using several of the most common semidefinite programming (SDP) solvers. SONC yields bounds competitive to SOS in several cases, but using significantly less time and memory. In particular, SONC/GP can handle much larger problem instances than SOS/SDP. This is joint work with Henning Seidler. |
|
| Date: | November 12, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Sourav Dutta, ERDC |
| Title: | Reduced Order Modeling for Coastal and Hydraulic Applications in the Corps of Engineers |
| Abstract: | Computational models are becoming increasingly
important for achieving the U.S. Army Corps of Engineer's
mission of delivering vital public and military engineering
services. The multiphysics and multiscale problems we solve
typically require sophisticated, model-specific numerical
methods that are based on rigorous mathematical models. The
Shallow Water Equations (SWE), for instance, are widely adopted
to study various flow regimes from dam breaks and riverine flows
to atmospheric processes. However, for multi-query, real-time and
slim-computing scenarios arising in optimal design, risk assessment
or ensemble forecasting problems, that can require thousands of
forward simulations, a fully resolved two-dimensional shallow water
model poses a significant computational challenge.
Formal model reduction techniques like the Proper Orthogonal
Decomposition (POD)-based methods are a popular choice to alleviate
the computational burden. In this talk, we will review some of the
work focused on the development of reduced order computational tools
for supporting research on both existing and new models for coastal
and hydraulic processes. We will present some efficient model
reduction strategies for such complex nonlinear flows that use a
combination of - 1) hyper-reduction (Discrete Empirical Interpolation
Method or gappy POD), 2) non-intrusive multivariate radial basis
function (RBF-NIROM) interpolation, and 3) POD in a Lagrangian frame
that can effectively capture the lower rank structure of wave-like
solutions even in the presence of large gradients and non-polynomial
nonlinearities. We will present results involving practical dam-break
scenarios and large-scale geophysical flows and discuss the accuracy,
computational performance, and robustness of these methods.
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|
| Date: | November 19, 2018 |
| Time: | 5:00pm |
| Location: | BLOC 220 |
| Speaker: | Angelica Torres, University of Copenhagen |
| Title: | Stability of steady states and algebraic parameterizations in chemical reaction networks |
| Abstract: | Criteria such as Routh-Hurwitz and Liénard-Chipart are used to
establish whether a steady state of a system of ordinary differential
equations is asymptotically stable, by computing the Jacobian of the system
and studying the sign of the real part of its eigenvalues.
I am interested in determining the stability properties of the steady
states of reaction networks (using mass-action kinetics), when the
values of the reaction rate constants are unknown.
To this end, I combine the Routh-Hurwtiz criterion and the
Lienard-chipart criterion, with the use of algebraic parameterizations
of the steady states.
In this talk I will give an overview of this approach, I will present
results obtained for particular networks and, also, conditions under
which bistability of networks can be determined.
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