"Asymptotically Well-posed Boundary Conditions for Partitioned Fluid-Structure Algorithms"
Abstract: A new partitioned algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with elastic structures undergoing finite deformations. The new algorithm, referred to as the Added-Mass Partitioned (AMP) scheme, overcomes the added-mass instability that has for decades plagued partitioned FSI simulations of incompressible flows coupled to light structures. Within a Finite-Difference framework, the AMP scheme achieves fully second-order accuracy and remains stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The stability and accuracy of the AMP scheme is validated through mode analysis and numerical experiments. Aiming to extend the AMP scheme to a Finite-Element framework, we also develop an accurate and efficient Finite-Element Method for solving the Incompressible Navier-Stokes Equations with high-order accuracy up-to the boundary.
April 25, 2017
Air Force Research Laboratory
"MULTI-SCALE AND MULTI-PHYSICS SIMULATIONS USING THE MULTI-FLUID PLASMA MODEL"
Abstract: The multi-fluid plasma model represents electrons, multiple ion and neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. There is a broad range of timescales in the plasma model mainly due to the large mass ratio between the electrons and the ions, but also due to necessity to resolve the plasma frequency and the speed of light. To address this challenges a blended continuous and discontinuous Galerkin method (BFEM) is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutral physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. Distribution A: Approved for public release; distribution unlimited AFTC/PA clearance No. 16221.
Abstract: Neutron star mergers are among the most violent events in the Universe. Gravitational wave, electromagnetic, and neutrino signals from these mergers encode important aspects of the physics and astrophysics of neutron stars, which cannot be inferred from terrestrial laboratory experiments. For example, on the nature of the short-range interaction between nucleons, which is imprinted in the neutron star equation of state. However, harnessing these imminent detections will only be possible by combining the observational data with reliable theoretical predictions. The formers, in turn, rely on the availability of high-precision simulations. In this talk, I will review the current state-of-the art in the modeling of neutron star mergers and discuss future challenges and possibilities in this field.
"Algebraic Multigrid Methods for Computing Diffusion-Based Metrics on Graphs"
Abstract: Recently, diffusion-based metrics have been developed for protein-protein interaction networks and used for protein function prediction. In this talk, we focus on the challenges in computing these diffusion-based metrics, especially for large-scale networks. By exploring the algebraic properties of the distance metrics, we reformulate the computation of distances into solving a series of graph Laplacians systems. In particular, we develop algebraic multilevel methods for solving the resulting linear systems efficiently. Applications to the protein-protein networks will be presented and possible generalizations will be discussed.
April 10, 2017
Scripps Inst. Of Oceanography
"Satellite observations of interactions between atmospheric convection and surface Winds"
Abstract: Satellite scatterometers measure surface winds over the global oceans, but these observations have historically been limited by rain-related errors. We have recently developed techniques to circumvent these rain-related errors, allowing for direct observational study of convection-wind coupling over the ocean.
We use these corrected wind data to detect cool downdrafts from mesoscale convective systems (MCSs) for the first time. These wind observations are validated against surface buoys and satellite observations of cloud-top temperature.
Building on this study, we utilize satellite wind and rainfall observations to examine coupling between the land-sea breeze and the diurnal cycle of rainfall in the Bay of Bengal. Observations show co-propagation of surface convergence and rainfall anomalies from the eastern coast of India into the bay; surface convergence leads the rainfall anomalies by several hours, implying that the land breeze forces the diurnal cycle of convection over the bay.
"Measure transport for Bayesian inference: theory and applications."
Abstract: Measure transport is a valuable tool for characterizing, sampling and manipulating multivariate non-Gaussian target distributions [1,2,3]. This method has a broad range of applications -- e.g., the solution of Bayesian inverse problems, as well as filtering and smoothing of dynamical systems. The transport maps framework seeks a deterministic parametric map that pushes forward a tractable reference distribution to a potentially complex target distribution of interest. The construction of high-dimensional maps may be challenging due to the curse of dimensionality. In many cases, though, one can leverage a number of sources of low-dimensional structure: marginal independence, smoothness, separability, conditional independence , to just name a few. In this seminar we will outline the transport map framework and some of the key ingredients useful to tackle high-dimensional problems. The presentation will be accompanied by examples of Bayesian inference problems in geophysics and finance.
 El Moselhy, T. a., Marzouk, Y. M. (2012). Bayesian inference with optimal maps. Journal of Computational Physics, 231(23), 7815–7850.
 Parno, M., Marzouk, Y. (2014). Transport map accelerated Markov chain Monte Carlo. ArXiv:1412.5492
 Marzouk, Y., Moselhy, T., Parno, M., Spantini, A. (2016). Sampling via Measure Transport: An Introduction. In R. G. Ghanem, D. Higdon, H. Owhadi (Eds.), Handbook of Uncertainty Quantification (pp. 1–41). Cham: Springer International Publishing.
 Spantini, A., Bigoni, D., Marzouk, Y. (2017). Inference via low-dimensional couplings.
April 4, 2017
University Of Southern California
"Software Development in Alzheimer’s Research"
Abstract: ccording to Alzheimer’s Association, Alzheimer Disease(AD) is the 6th leading cause of death in the United States that cannot be prevented or cured. A person suffering from AD shows different symptoms of memory loss to language disability (In later stage). To help millions of people and advance in the research of AD, Alzheimer’s Therapeutic Research Institute (ATRI) is an institute committed to advancing the development of new treatments for AD through innovation in clinical trials.
Software development, nowadays has become a vital factor in all research fields and I would like to introduce how it plays its role in Alzheimer’s Research. ATRI has been responsible in organizing more than 50 clinical trials and the Informatics team actively develops and maintains a secure data capture system to record and analyze the data received from trials. Being a software developer at ATRI, I would also like to share my experiences of different concepts and best programming practices that I have learnt.
"A ROM-HPC framework with analysis for stochastic wave propagation models"
Abstract: We consider a class of wave propagation models with aleatoric and epistemic uncertainties. Using mathematical analysis-based, shape-independent, a priori parameter estimates, we develop offline/online strategies to compute statistical moments of a key quantity of interest in such models. We present an efficient reduced order model (ROM) and high performance computing (HPC) framework with analysis for quantifying aleatoric and epistemic uncertainties in the propagation of waves through a stochastic media comprising a large number of three dimensional particles. Simulation even for a single deterministic three dimensional configuration is inherently difficult because of the large number of particles. The aleatoric uncertainty in the model leads to a larger dimensional system involving three spatial variables and additional stochastic variables. Accounting for epistemic uncertainty in key parameters of the input probability distributions leads to prohibitive computational complexity. Our hybrid ROM and HPC framework can be used in conjunction with any computational method to simulate a single particle deterministic wave propagation model.
March 29, 2017
"New Bernstein-Bezier bases for the finite element exact sequence on tetrahedra"
Abstract: We present a set of new Bernstein-Bezier bases, with a local exact sequence property, for the finite element exact sequence on tetrahedra.
March 6, 2017
University Of North Carolina At Charlotte
"Consistent coupling of nonlocal diffusion"
Abstract: Nonlocal models have been developed and received lot of attention in recent years to model systems with important scientific and engineering applications. While it is established that the nonlocal formulations can often provide more accurate descriptions of the systems, the nonlocality also increases the computational cost compared to conventional models based on PDEs. The goal is to combine the accuracy of nonlocal models with the computational and modeling efficiency of local PDEs.
In this talk, I will introduce a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with respect to the energy norms induced by the nonlocal diffusion kernels as well as the L2 norm, and it satisfies the maximum principle. A finite difference approximation is used to discretize the coupled system, which inherits the property from the continuous formulation. Furthermore, we design a numerical example which shows the discrepancy between the fully nonlocal and fully local diffusions, whereas the result of the coupled diffusion agrees with that of the fully nonlocal diffusion.
"Exploiting Low-Dimensional Structures for Sensing and Control of Fluids via Data-Driven Reduced-Order Modeling"
Abstract: Many applications in engineering and the sciences generate large-amounts of data to describe physical systems, e.g., via high-dimensional approximation or experimental measurements. Fortunately, the underlying dynamics of a complex system is often of much lower dimension than the data volume suggests. Thus, much progress has been made in deriving reduced-order models from system equations to enable (or speed up) engineering tasks such as control and optimization. Data-driven reduced-order modeling complements these intrusive, equation-based methods, and offers new pathways to work with real system data.
In this talk, I will discuss recent work on indoor airflow sensing through reduced-order models and the compressed sensing method to detect flow phenomena. We use simulated data to derive a low-dimensional basis for the fluid system via dynamic mode decomposition (DMD). We then extend the basis to account for time series of measurements, making the sensing method more robust. Results based-on a two dimensional Boussinesq equation are presented.
Building on this work, I will discuss recent results on control of parameter varying systems, where the physical parameters are uncertain and unknown. In this setting, we learn reduced-order models from system data that can then be used for reduced-order feedback control. The derived data-driven controllers successfully stabilize the considered convection-diffusion equation
"Wave breaking and modulational instability in full-dispersion shallow water models"
Abstract: In the 1960s, Benjamin and Feir, and Whitham, discovered that a Stokes wave would be unstable to long wavelength perturbations, provided that (the carrier wave number) x (the undisturbed water depth) > 1.363.... In the 1990s, Bridges and Mielke studied the corresponding spectral instability in a rigorous manner. But it leaves some important issues open, such as the spectrum away from the origin. The governing equations of the water wave problem are complicated. One may resort to simple approximate models to gain insights. \n I will begin by Whitham's shallow water equation and wave breaking conjecture, and move to modulational instability, the effects of surface tension and constant vorticity, turbulent bores, and I will indicate where numerical investigation may help for further understanding. I will discuss wave breaking and modulational instability in other related equations. I will say a few words about higher order corrections, extension to bidirectional propagation and two-dimensional surfaces, if time permits. This is based on the joint works with Jared Bronski (Illinois), Mat Johnson (Kansas), Ashish Pandey (Illinois), and Leeds Tao (UC Riverside).