Seminars are held Tuesdays and Thursdays in POB 6.304 from 3:30-5:00 pm, unless otherwise noted. Speakers include scientists, researchers, visiting scholars, potential faculty, and ICES/UT Faculty or staff. Everyone is welcome to attend. Refreshments are served at 3:15 pm.
Thursday, Jul 30, 2015 from 3:30PM to 4:30PM
Volume and neighbors algorithm for finding elimination trees for two and three dimensional h-adaptive grids
by Anna Paszynska
Jagiellonian University, Poland
In this talk Professor Paszynska will present an algorithm called "volume & neighbors" for finding elimination trees for multi-frontal solver algorithm applied for two and three-dimensional h-adaptive finite element method computations. The algorithm constructs the elimination tree in a bottom-up approach, starting from degrees of freedom related to "smallest" finite elements from the highest refinement level, ending with degrees of freedom related to "largest" finite elements. The algorithm has been tested in two and three dimensional h-adaptive finite element method code and tested on a sequence of representative grids, namely uniform grid, grid with point singularity, grid with edge singularity and grid with face singularity. The number of floating point operations for the multi-frontal solver algorithm working with the elimination trees generated by the volume & neighbors algorithm is compared with the number of floating-point operations resulting from execution of the state-of-the-art multi-frontal direct solver MUMPS with state-of-the-art algorithms for construction of elimination tree like nested-dissection from METIS library and approximate minimum degree AMD algorithm as well as PORD algorithm. In all the cases the volume & neighbors algorithm outperforms other state-of-the art algorithm. The only exception is the case of the uniform grid, where the algorithm results in a similar number of FLOPS than nested dissection algorithm.
This algorithm uses the bottom-up approach, which is not typical in classical top-down ordering algorithms. Thus, this bottom-up approach is more suited for implementation with graph grammar productions.
Anna Paszynska is an assistant professor Faculty of Physics, Astronomy and Applied Computer Science at Jagiellonian University, Krakow, Poland. She got her PhD in 2007 in Computer Science from Institute of Fundamental Technological Research Polish Academy of Sciences. Her current research interests include graph grammars modeling finite element method, as well as tree and ordering algorithms for multi-frontal solvers. She published over 20 papers indexed by Web of Science. She worked as visiting scientist and gave invited talks at King Abdullah University of Science and Technology (KAUST), at Thuwal, Saudi Arabia, Basque Center for Applied Mathematics (BCAM), and The University of the Basque Country, Bilbao, Spain.
Hosted by Keshav Pingali
Thursday, Aug 6, 2015 from 3:30PM to 5PM
Domain Decomposition and Time-partitioned Methods for Flow in Fractured Poroelastic Media
by Ivan Yotov
Professor, Department of Mathematics, University of Pittsburgh
We discuss a computational framework for modeling multi physics systems of coupled flow and mechanics problems. The simulation domain is decomposed into a union of subdomains, each one associated with a physical, mathematical, and numerical model. Physically meaningful interface conditions are imposed on the discrete level via mortar finite elements or Nitsche's coupling. We present applications of the framework to modeling flow in fractured poroelastic media and arterial flows based on Navier Stokes/Stokes/Brinkman flows coupled with the Biot system of poroelasticity. We discuss stability and accuracy of the spatial discretizations and loosely coupled non-iterative time-split formulations. We further study the use of the loosely coupled scheme as a preconditioner for the monolithic scheme and establish a spectral equivalence of the two formulations. A reduced-dimension fracture model will also be discussed.
Hosted by Mary Wheeler
Thursday, Aug 13, 2015 from 3:30PM to 5PM
Modeling The Pressure Strain Correlation Under Uncertainties
by Aashwin Mishra
Texas A&M University
The cardinal issues forestalling a better understanding of the turbulence phenomenon are the nonlinearity of the inertial cascade physics and the non-local nature of the action of pressure. In this talk, we focus on analyzing, understanding and modeling the latter, manifested in the pressure strain correlation.
The Reynolds stresses provide an insufficient basis to describe the internal structure of turbulent flows, leading to an inherent degree of uncertainty in predictions using classical turbulence models. We carry out a detailed Dynamical Systems analysis of modal ensembles and individual modes in Fourier space to identify the range of possible behavior and the underlying physics. Based on this insight, Different aspects of the dynamics of pressure are discussed, individually and sequentially, vis-a-vis their amenability to the single point modeling paradigm. Thereon, a set of pragmatic compromises is constituted within the form and the scope of the model to outline a modeling framework. The predictions of an illustrative model are compared to numerical and experimental data while being contrasted against established modeling paradigms.
We conclude by quantifying the uncertainty in the modeling framework. For a spectrum of different states of the mean gradient and the Reynolds stress tensors, we establish the range of this uncertainty for rapid pressure strain closures, identify statistically most likely behavior and their evolution.
Hosted by Robert Moser
Tuesday, Nov 24, 2015 from 3:30PM to 5PM
The Time Dimension, “iIntegrators” and Next Generation State-of-the-Art for First/Second Order ODE/DAE Systems
by Kumar K. Tamma
Professor, Department of Mechanical Engineering; University of Minnesota
Each computational science and engineering simulation, whether it is the analysis of a single discipline or a multi-physics application involving, first or second order system or combination thereof, has its own emphasis and analysis requirements; wishful thinking is that a “wish list” of desired attributes by the analyst to meet certain required analysis needs is desirable. Optimal design developments of algorithms are not trivial; and alternately, how to foster, select, and determine such optimal designs for a targeted application if such an optimal algorithm does not readily exist, is a desirable goal and a challenging and daunting task; not to mention the added complexity of additionally designing a general purpose unified framework – a one size fits all philosophy. Under the notion of Algorithms by Design and the theoretical basis emanating from a generalized time weighted residual philosophy, we have developed under the umbrella of "isochronous time integrators [iIntegrators]" representing the use of the "same time integration framework/architecture", novel designs for first/second order ODE /DAE transient/dynamic systems for the general class of LMS methods . The framework not only encompasses most of the research to-date developed over the past 50 years or so, but additionally encompasses more new and novel schemes and solution procedures with improved physics such as energy-momentum or symplectic-momentum conservation and other optimal attributes with/without controllable numerical dissipation. All formulations within the "iIntegration framework of individual or mixed algorithms and designs" yield the much coveted second-order time accuracy in all kinematic and algebraic variables for ODE’s and DAE’s of any index. Under the umbrella of a single unified architecture, the iIntegration framework is envisioned as the next generation toolkit; and illustrative examples are highlighted as well for computational science and engineering.
Dr. Kumar K. Tamma, is currently - Professor in the Dept. of Mechanical Engineering, College of Science and Engineering at the University of Minnesota. He has published over 200 research papers in archival journals and book chapters; and over 300 in refereed conference proceedings, and conference abstracts. His primary areas of research encompass: Computational mechanics with emphasis on multi-scale/multi-physics and fluid-thermal-structural interactions; structural dynamics and contact-impact-penetration; computational aspects of microscale/nanoscale heat transfer; composites and manufacturing processes and solidification; computational development of finite element technology and time dependent algorithms by design; and development of techniques for applications to large-scale problems and high performance parallel computing environments; and virtual surgery applications in medicine. He serves on the editorial boards for over 20 archival national/international journals, Editor-in-Chief (co-shared) of an online journal, and is the Fellow of IACM, USACM, and the Minnesota Supercomputing Institute. He is the recipient of numerous research awards including the “ICCES Outstanding Research Medal for Contributions to Computational Structural Dynamics, June 2014”; and the "George Taylor Research Award" and selected for the University of Minnesota/Institute of Technology Award for Significant and Exceptional Contributions to Research. He is also the recipient of numerous Outstanding Teaching and other national and university awards. His recent book is titled “Advances in Computational Dynamics of Particles, Materials and Structures”, John Wiley & Sons publication.
Hosted by Leszek Demkowicz