Search Research Symposium Abstracts

Existence Theory of Multi-Scale Interface Coupling between Deformable Porous Media and Lumped Hydraulic Circuits

We consider an elliptic-parabolic coupled partial differential equation connected to a nonlinear ODE through an interface. The model describes fluid flowing through biological tissues with the ODE accounting for global features of blood flow that affect the tissue. We discuss a modeling choice on the interface coming from the fact that the ODE is 0D and the [Read More...]

Presenter: Sarah Strikwerda, University of Pennsylvania
Authors: Lorena Bociu, Matthew Broussard, Giovanna Guidoboni
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 9:45 am

On the structure of the value function of optimal exit time problems

In this paper, we study an optimal exit time problem with general running and terminal costs and a target S having an inner ball property for a nonlinear control system that satisfies mild controllability assumptions. In particular, the Petrov's condition at the boundary of S is not required and the value function V fails to be locally [Read More...]

Presenter: Khai T. Nguyen, North Carolina State University
Authors: Piermarco Cannarsa, Marco Mazzola, Khai T. Nguyen
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 10:10 am

Singularity formation for models of fluids

Finite time singularity formation for fluid equations will be discussed. Built on extensive study of approximating models, breakthroughs on this topic have emerged recently for the Euler equation. Inspired by the progress for pure fluids, we attempt to understand this challenging issue for magnetohydrodynamics (MHD). Finite time singularity scenarios are [Read More...]

Presenter: Mimi Dai, University of Illinois at Chicago
Authors: Mimi Dai
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 10:35 am

Accelerating and enabling convergence of nonlinear solvers for Navier-Stokes equations by continuous data assimilation

This paper considers improving the Picard and Newton iterative solvers for the Navier-Stokes equations in the setting where data measurements or solution observations are available. We construct adapted iterations that use continuous data assimilation (CDA) style nudging to incorporate the known solution data into the solvers. For CDA-Picard, we prove the [Read More...]

Presenter: Elizabeth Hawkins, Clemson University
Authors: Xuejian Li, Elizabeth V. Hawkins, Leo G. Rebholz, and Duygu Vargun
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 11:00 am

Analysis of a Multiscale Model based on the Coupling of ODEs and PDEs for Tissue Perfusion

Complex problems in biomedicine often need to be modeled by multiscale couplings between partial differential equations (PDEs) and ordinary differential equations (ODEs), in order to combine the accurate three-dimensional (3D) description of a local region of interest with the global features of the problem represented by reduced lumped models. We focus on a [Read More...]

Presenter: Lorena Bociu, NC State University
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 2:00 pm

Higher Regularity Properties of certain Hyperbolic-Parabolic Systems

This talk will present recent results concerning the (partial) validation of a conjecture by the late Igor Chueshov: He surmised that a certain fluid-structure PDE dynamics, whose respective PDE components evolve on distinct geometries and interact strictly across a boundary interface, are associated with strongly continuous semigroups which manifest [Read More...]

Presenter: George Avalos, University of Nebraska-Lincoln
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 2:25 pm

Filtered Anderson Acceleration for Numerical PDE

The efficient solution of systems of nonlinear equations is an important tool for the modeling of physical phenomena. In this talk, we will discuss a powerful and low-cost method for accelerating the convergence of fixed-point iterations, known as Anderson acceleration (AA). First developed in 1965 in the context of integral equations, this method has become [Read More...]

Presenter: Sara Pollock, University of Florida
Authors: Sara Pollock and Leo Rebholz
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 2:50 pm

Global-in-time domain decomposition methods for the fluid-structure interaction system

We consider two global-in-time domain decomposition methods, the Steklov-Poincare method and the Robin method, for solving a fluid-structure interaction system. These methods allow us to formulate the coupled system as a space-time interface problem and apply iterative algorithms directly to the evolutionary problem. Each time-dependent subdomain problem is [Read More...]

Presenter: Hyesuk Lee, Clemson University
Authors: Hemanta Kunwar and Hyesuk Lee
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 3:15 pm

Harnessing Neural OC Framework for High-Dimensional HJB: Applications in PDE-Constrained Optimization

This talk will focus on the applications of DNNs in high-dimensional optimal control problems. Traditional methods for solving these problems often suffer from the Curse-of-Dimensionality, where computational complexity increases exponentially with the dimension of the problem. Utilizing DNNs to approximate the value function of control problems can [Read More...]

Presenter: Deepanshu Verma, Emory University
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: September 30, 2023; 3:40 pm

Global Solutions in Turbulent Regimes of the Hyper-Dissipative 3D NSE

The existence of singularities in the super-critical regime of the 3D hyper-dissipative (HD) Navier-Stokes equations (NSE), where the hyper-dissipation is generated by a fractional power of the Laplacian within the interval (1, 5/4), has been a longstanding question in the field of mathematical fluid dynamics since J.L. Lions' foundational work. In this [Read More...]

Presenter: Aseel Farhat, Florida State University
Authors: Aseel Farhat, Zoran Grujic
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: October 1, 2023; 2:00 pm

Compressible Oseen-structure Interaction PDE Dynamics

We consider the Oseen structure of the linearization of a compressible FSI system for which the interaction interface is under the effect of material derivative term. The flow linearization is taken with respect to an arbitrary, variable ambient vector field. This process produces an extra “convective derivative” and “material derivative” terms which [Read More...]

Presenter: Pelin G. Geredeli, Iowa State University
Authors: Pelin G. Geredeli
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: October 1, 2023; 2:25 pm

Optimal Control for Suppression of Singularity in Chemotaxis via Flow Advection

In this talk, we discuss the problem of optimal control for chemotaxis governed by the parabolic-elliptic Patlak-Keller-Segel (PKS) system via flow advection. The main idea is to utilize flow advection for enhancing diffusion to control the nonlinear behavior of the system. The objective is to determine an optimal strategy for adjusting flow strength for [Read More...]

Presenter: Weiwei Hu, University of Georgia
Authors: Weiwei Hu
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: October 1, 2023; 2:50 pm

Approximate Deconvolution Leray Reduced Order Modeling

In the field of reduced order modeling, filtering methods have received significant recent attention for treating poorly performing models as a method of regularization. However, filtering by itself can be susceptible to over-smoothing of generated solutions. We propose new reduced order models that integrate the methods of approximate deconvolution into [Read More...]

Presenter: Ian Moore, Virginia Tech
Authors: Ian Moore, Anna Sanfilippo, Traian Iliescu, Francesco Ballarin
Symposium Year: 2023
Session: Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]
Presentation Time: October 1, 2023; 3:15 pm