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Sung Ha Kang, Georgia Tech, Variational image processing and computational challenges

SAS 4201

Starting with an introduction to variational/PDE based image processing, this talk will focus on new developments of fast algorithms for higher order variational imaging models.  For example, recent developments of fast algorithms, based on operator splitting, augmented Lagrangian, and alternating minimization, enabled us to revisit some of the variational image models, such as Euler's Elastica…

Murthy Gudatti, NC State, Efficient Forward and Inverse Algorithms for Guided Wave Inversion

SAS 4201

Guided waves are widely utilized in the fields of nondestructive testing and geophysical inversion, to estimate the medium properties through inversion of the dispersion curves. In this talk, we present improved methodologies for computing both dispersion curves and their derivatives, the two main ingredients of guided wave inversion. Specifically, a novel discretization approach based on Pade Approximants, named complex-length finite element…

Sercan Yildiz, SAMSI,Polynomial Optimization with Sums-of-Squares Interpolants

Sums-of-squares certificates define a hierarchy of relaxations for polynomial optimization problems which are parametrized with the degree of the polynomials in the sums-of-squares representation. Each level of the hierarchy generates a lower bound on the true optimal value, which can be computed in polynomial time via semidefinite programming, and these lower bounds converge to the…

Serkan Gugercin, Virginia Tech, Interpolatory model reduction with applications to flow control and nonlinear inversion

SAS 4201

Numerical simulation of large-scale dynamical systems plays a crucial role and may be the only possibility in studying a great variety of complex physical phenomena with applications ranging from heat transfer to fluid dynamics, to signal propagation and interference in electronic circuits, and many more. However, these large-scale dynamical systems present significant computational difficulties when…

Georg Stadler, Sparsity meets optimal control of PDEs

SAS 4201

I will discuss formulations and algorithms for computing sparse optimal controls in systems governed by PDEs. These sparse solutions can guide the placement of control devices in applications.  After reviewing results for elliptic and parabolic PDEs, I will focus on recent work on sparse optimal control governed by linear PDEs with uncertain coefficients. Here, we aim at finding stochastic controls that…

Grey Ballard, Wake Forest University, Tensor Decompositions for Multidimensional Data Analysis

SAS 4201

An increasing number of scientific and enterprise data sets are multidimensional, where data is gathered for every configuration of three or more parameters. For example, physical simulations often track a set of variables in two or three spatial dimensions over time, yielding 4D or 5D data sets. Tensor decompositions are structured representations of multidimensional data…

Wilkins Aquino, Duke University, A Locally Adapted Reduced Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems

SAS 4201

The numerical solution of large-scale risk-averse PDE-constrained optimization problems requires substantial computational effort due to the discretization in physical and stochastic dimensions. Managing the cost is essential to tackle such problems with high dimensional uncertainties. In this work, we combine an inexact trust-region (TR) algorithm from with a local, reduced basis (RB) approximation to efficiently solve risk-averse optimization problems…

Gabor Pataki, UNC-Chapel Hill, Bad semidefinite programs, linear algebra, and short proofs

SAS 4201

Semidefinite programs (SDPs) -- optimization problems with linear constraints, linear objective, and semidefinite matrix variables --  are some of the most useful, versatile, and pervasive optimization problems to emerge in the last 30 years. They find applications in combinatorial optimization, machine learning, and statistics, to name just a few areas. Unfortunately, SDPs often behave pathologically: the optimal values of the primal…

Yingwei Wang, University of Wisconsin, Madison, Introduction to Muntz Polynomial Approximation

SAS 4201

In general, solutions to the Laplacian equation enjoy relatively high smoothness. However, they can exhibit singular behaviors at domain corners or points where boundary conditions change type. In this talk, I will focus on the mixed Dirichlet-Neumann boundary conditions for Laplacian equation, and discuss how singularities in this case adversely affect the accuracy and convergence…

Mingchao Cai, Morgan State University, Some Fast Solvers for Poroelastic Models

SAS 4201

Poroelastic models have been widely used in Biomechanics. For example, modeling brain edema and cancellous bones. We aim at solving the Biot model under the MAC Finite Difference discretization and the stabilized finite element discretizations. To solve the resulting saddle point linear systems, some iterative methods are proposed and compared. In these methods, the outer iteration solver can be the GMRES…

Daniel B. Szyld, Temple University, Asynchronous Optimized Schwarz Methods for the solution of PDEs

SAS 4201

Asynchronous methods refer to parallel iterative procedures where each process performs its task without waiting for other processes to be completed, i.e., with whatever information it has locally available and with no synchronizations with other processes. In this talk, an asynchronous version of the optimized Schwarz method is presented for the solution of differential equations on a parallel computational environment. Convergence is…

Mario Ricchiuto, INRIA Bordeaux, On dispersive-like effects in channels with banks

SAS 4201

The study of the propagation of undular bores in channels is relevant to many applications which go from the propagation of tsunami waves, to that of tidal bores/waves, to the propagation of strong waves in manmade channels due to hazards (e.g. dam breaking). In absence of banks, the flow exhibits a transition across which undulating waves  start breaking and transform…

Pierre Gremaud, NC State, Advances and challenges in global sensitivity analysis

SAS 4201

What to do when the size and complexity of your model essentially  prevent you from using it? Well, get a smaller and simpler model... At the heart of this dimension reduction process is the notion of parameter importance which, ultimately, is part of the modeling process itself. Global Sensitivity Analysis (GSA) aims at efficiently  identifying important…

Susan Minkoff, UT Dallas, Microseismic Source Estimation via Seismic Inversion

SAS 4201

Accurate estimation of microseismic events (small earthquakes) generated during hydraulic fracturing of low permeability rocks such as shale enables important characterization of hydraulic fracture networks. Determining the orientation of the fracture is important in characterizing the effectiveness of the stimulation process. We consider the source as separable in time and space and invert for a…

Vladimir Druskin, Worcester Polytechnic Institute, Reduced Order Models, Networks and Applications to Modeling and Imaging with Waves

SAS 4201

Geophysical seismic exploration, as well as radar and sonar imaging, require the solution of large scale forward and inverse problems for hyperbolic systems of equations. In this talk, I will show how model order reduction can be used to address some intrinsic difficulties of these problems. In model order reduction, one approximates the response (transfer…

Jianfeng Lu, Duke University, Solving large-scale leading eigenvalue problem

SAS 4201

The leading eigenvalue problems arise in many applications. When the dimension of the matrix is super huge, such as for applications in quantum many-body problems, conventional algorithms become impractical due to computational and memory complexity. In this talk, we will describe some recent works on new algorithms for the leading eigenvalue problems based on randomized and coordinate-wise methods (joint work with…

Malgorzata Peszynska, Modeling hysteresis using ODEs with constraints: Numerical stability and other properties

SAS 4201

In nonlinear conservation laws the flux function f(u) is usually single valued, but in many important applications it is hysteretic, i.e., it assigns different values depending on whether the input u(t) is increasing or decreasing in t. We present our recent results on a hysteresis model built with a collection of auxiliary ODEs under constraints. The model shares some similarities…

Casey Dietrich, NC State, Forecasting and Mapping of Coastal Flooding during Hurricanes

SAS 4201

When a hurricane threatens North Carolina, researchers use computational models to predict how the ocean waters will rise, and what areas will be flooded.  Emergency managers rely on fast and accurate storm surge predictions from these models to make decisions and estimate damages during storm events.  These models use unstructured, finite-element meshes to describe the…

Troy Butler, University of Colorado Denver, Data Consistent Inversion: An Interactive Talk Using Jupyter Notebooks

(Brief Note: In this talk, we utilize Jupyter notebooks to re-create some of our published results in real-time and also build a "computational intuition" for the ideas presented. In this way, we are (mostly) transparent about all the computations involved in our work. I will email these materials to anyone interested after the presentation.) Models are useful for…