The following is a tentative schedule, still subject to change.

Friday March 9th

  • 6:30-8:30pm Registration Reception (Hampton Inn, Carrboro)
    • light hors d’oeuvres

Saturday March 10th

  • 7:30-8:15pm Breakfast/Registration (Phillips Hall 330, Math Lounge)
  • 8:15-9:15 Opening Remarks/Plenary Talk (Carroll Hall 111)
    • James Sethian (UC Berkeley) “New Methods for Tracking Evolving Interfaces: Voronoi Implicit Interface Methods with Applications to Industrial Foams, Biological Cell Clusters, and Domain Decomposition”
  • 9:30-10:50 Minisymposium Session I
  • 11-12:20 Minisymposium Session II
  • 12:20-1:45 Lunch (participants on their own)
  • 1:45-2:30 Plenary Talk (Carroll Hall 111)
    • Julianne Chung (Virginia Tech) “Efficient Methods for Large and Dynamic Inverse Problems”
  • 2:30-3:30 Coffee Break (Phillips Hall 330, Math Lounge)
  • 3:30-4:50 Minisymposium Session III
  • 6-6:30 Poster Set-up
  • 6:30-8:30 Poster Reception (Ackland Art Museum)

Sunday March 11th

  • 8:30-9:15 Plenary Talk (Carroll Hall 111)
    • Clint Dawson (UT Austin) “Algorithms for Hurricane Storm Surge Modeling: Current State and Future Outlook”
  • 9:30-10:30 Brunch (Phillips Hall 330, Math Lounge)
  • 10:30-11:50 Minisymposium Session IV
  • 12-12:45 Plenary Talk/Closing Remarks (Carroll Hall 111)
    • Ricardo Cortez (Tulane) “A Model of Collective Motion of Self-Propelled Organisms”
  • 1-2:30 AWM Lunch (Phillips Hall 330, Math Lounge)

Plenary Talks

New Methods for Tracking Evolving Interfaces: Voronoi Implicit Interface Methods with Applications to Industrial Foams, Biological Cell Clusters, and Domain Decomposition

J.A. Sethian
Dept. of Mathematics
University of California, Berkeley

Many scientific and engineering problems involve interconnected moving interfaces separating different regions, including dry foams, crystal grain growth,  and multi-cellular structures in man-made and biological materials. Producing consistent and well-posed mathematical models that capture the motion of these interfaces, especially at degeneracies, such as triple points and triple lines where multiple interfaces meet, is challenging.

Joint with Robert Saye of UC Berkeley, we have built the Voronoi Implicit Interface Method (VIIM), which is an efficient and robust mathematical and computational methodology for computing the solution to two and three-dimensional multi-interface problems involving complex junctions and topological changes in an evolving general multiphase system. We demonstrate the method on a collection of problems, including geometric coarsening flows under curvature, incompressible flow coupled to multi-fluid interface problems, and biological cell cluster growth under competing effects of geometry, fluid dynamics, and elasticity.

Finally, we compute the dynamics of unstable foams, such as soap bubbles, evolving under the combined effects of gas-fluid interactions, thin-film lamella drainage, and topological bursting.

Efficient Methods for Large and Dynamic Inverse Problems

Julianne Chung
Virginia Tech, Blackburg

In many physical systems, measurements can only be obtained on the exterior of an object (e.g., the human body or the earth’s crust), and the goal is to estimate the internal structures. In other systems, signals measured from machines (e.g., cameras) are distorted, and the aim is to recover the original input signal. These are natural examples of inverse problems that arise in fields such as medical imaging, astronomy, geophysics, and molecular biology.
In this talk, we describe efficient methods to compute solutions to large, dynamic inverse problems. We focus on addressing two main challenges. First, since most inverse problems are ill-posed, small errors in the data may result in significant errors in the computed solutions. Thus, regularization must be used to compute stable solution approximations, and regularization parameters must be selected. Second, in many realistic scenarios such as in passive seismic tomography or dynamic photoacoustic tomography, the underlying parameters of interest may change during the measurement procedure. Thus, prior information regarding temporal smoothness must be incorporated for better reconstructions, but this can become computationally intensive, in part, due to the large number of unknown parameters. To address these challenges, we describe efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. These methods can be more flexible than standard methods, and efficient implementations can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples demonstrate the range of applicability and effectiveness of the described approaches.


Algorithms for Hurricane Storm Surge Modeling: Current State and Future Outlook

Clint Dawson
University of Texas at Austin

Hurricane storm surge modeling, especially in forecast mode as hurricanes approach land, is critical for emergency management, evacuation or shelter-in-place planning, and deployment of first responders.  After the event, storm surge models are used in forensic studies, validation exercises, and for planning future response to potential hurricanes.  Over the past 20 years, storm surge models, particularly the Advanced Circulation Model (ADCIRC),  have advanced to the point that they can be used reliably to predict maximum surge in both forecast and hindcast mode.  We will highlight some of these achievements and show how HPC was critical to these efforts.  We will then demonstrate the performance of such models on recent events, such as Hurricanes Harvey and Irma, and show how the model is used to evaluate proposed mitigitation systems, focusing particularly on the Texas coast.

Even with these advances, there are still critical physical processes
that are missing in these models.  Moreover, efficient performance on future HPC architectures that utilize GPU or KNL chips must be addressed for these models to retain their relevance.  We will outline research on new algorithms based on discontinuous Galerkin methods and HPX which may serve as the basis for future simulation technology.  We will also discuss missing components in these modeling systems, including coupling with rainfall/runoff, sediment transport, etc., and the research needed to realize a more fully complete modeling system.

A model of collective motion of self-propelled organisms

Ricardo Cortez
Tulane University, New Orleans

We consider the motion and interaction of self-propelled microscopic swimmers, such as bacteria, immersed in a viscous fluid. Their motion is coupled through the fluid, producing complex flow structures such as wakes and eddies that are important to investigate due to their application in transport and mixing. In order to study collective motion, it is convenient to develop a reduced model for each organism so that computations are feasible. I will present a new reduced model of self propelled organisms in low Reynolds number viscous incompressible flows. The model is based on a particular limit of regularized Stokeslets (the fundamental solution of Stokes equation in free space) with built-in asymmetry in order to produce a swimming direction. The result is a single-particle model of a swimmer that does not require special treatment of the self velocity due to the regularization.  Modeling “pusher” and “puller” organisms is straightforward and the model can also be extended to flows bounded by a plane wall using a method of images. I will show numerical examples characterizing the particle dynamics and discuss the diffusion of these particles as a function of the concentration density.