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Supported by the Department of Energy.
This workshop is at capacity and closed to further registration.
Organizers:
Douglas N. Arnold
IMA
University of Minnesota
director@ima.umn.edu
http://www.ima.umn.edu/~arnold
Richard B.
Lehoucq
Computational Mathematics and Algorithms Department
Sandia National Laboratories
rblehou@sandia.gov
http://www.cs.sandia.gov/~rlehoucq
Roy A.
Nicolaides
Department of Mathematical Sciences
CarnegieMellon University
dept.head@math.cmu.edu
http://www.math.cmu.edu/people/fac/nicolaides.html
Mikhail
Shashkov
MSB284, Group T7, Theoretical Division
Los Alamos National Laboratory
shashkov@lanl.gov
http://cnls.lanl.gov/~shashkov
Workshop will begin 9:00 AM Tuesday and end by 3:15 PM Saturday. Participants should plan to attend the entire workshop.
The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop is to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic instrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE.
Particular points of emphasis will include:




TUESDAY,
MAY 11 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


8:30  Coffee and Registration  Reception Room EE/CS 3176 

9:15  IMA Directors and Organizers  Welcome and Introduction  
9:30  Douglas
N. Arnold IMA 
Differential Complexes and Stability of Finite Element Methods Slides: pdf 

10:20  

11:00  Roy
Nicolaides Carnegie Mellon University 
Compatible Discretizations, Covolume Algorithms and Differential Forms  
11:50  

1:30  Mikhail
Shashkov Los Alamos National Laboratory 
Slides: pdf 

2:20  

3:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
3:30  
3:40  IMA
Tea and more (Reception and Poster Session) 

WEDNESDAY,
MAY 12 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Pavel
Bochev Sandia National Laboratories 
Variational and Geometric Aspects of Compatible Discretizations 

10:20  

11:00  Alain
Bossavit Laboratoire de GÃ©nie Electrique de Paris (LGEP) 

11:50  

1:30  Ralf
Hiptmair Seminar of Applied Mathematics 
Higher
Order Whitney Forms Slides: pdf 

2:20  

3:00  Daniel
A. White Lawrence Livermore National Laboratory 
Development and Application of Compatible Discretizations of Maxwell's Equations Slides: pdf 

4:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
THURSDAY,
MAY
13
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Ivan
Yotov University of Pittsburgh 
Superconvergence in Some Locally Conservative Discretization Methods Slides: pdf 

10:20  

11:00  Thomas
F. Russell National Science Foundation 

11:50  

1:30  Mary
Fanett Wheeler The University of Texas at Austin 
Coupling of MFE or Mimetic Finite Differences with Discontinuous Galerkin for PoroElasticity 

2:20  

3:00  Ivar
Aavatsmark University of Bergen 
MPFA Discretization on Quadrilateral Grids Slides: pdf 

4:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
FRIDAY,
MAY
14
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Eitan
Tadmor University of Maryland, College Park 
Entropy Stability Theory For Difference Approximations of Quasilinear Problems Slides: pdf 

10:20  

11:00  Timothy
J. Barth NASA Ames Research Center 
Entropy Stable FEM Discretization of FirstOrder Systems of Conservation Laws Slides: pdf 

11:50  

1:30  Thomas
J. R. Hughes University of Texas at Austin 

2:20  

3:00  Blair
Perot University of Massachusetts 
Compatible Reconstructions of Vectors and their Application to the NavierStokes Equations 

4:00  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
6:00  Workshop Dinner  Bona
Vietnamese Restaurant 802 Washington Avenue SE, Minneapolis Phone: 6123315011 

SATURDAY,
MAY
15 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  Reception Room EE/CS 3176  
9:30  Jim
E. Morel Los Alamos National Laboratory 
AsymptoticPreserving Discretization Schemes Slides: pdf 

10:20  

11:00  Daniele
Boffi UniversitÃ di Pavia 
Compatible Discretizations for Eigenvalue Problems Slides: pdf 

11:50  

1:30  Ragnar
Winther University of Oslo, Norway 
From the de Rham Sequence to Mixed Elasticity Slides: pdf 

2:30  SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, reframe their main points, look toward future directions.  
3:15 
NAME  DEPARTMENT  AFFILIATION 

Ivar Aavatsmark  Center for Integrated Petroleum Research  University of Bergen 
Scot Adams  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Peter Arbenz  Institut für Wissenschaftliches Rechnen  Zentrum für Umfragen, Methoden und Analysen (ZUMA) e.V. 
Douglas Arnold  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Donald Aronson  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Gerard Awanou  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Randolph Bank  Department of Mathematics  University of California, San Diego 
Timothy Barth  NASA Ames Research Center  
Martin Berggren  Department of Scientific Computing  Uppsala University 
Pavel Bochev  Applied Mathematics and Applications  Sandia National Laboratories 
Daniele Boffi  Dipartimento di Matematica  Università di Pavia 
Alain Bossavit  Laboratoire de Génie Electrique de Paris  
Olga Brezhneva  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Franco Brezzi  I. A. N. del C. N. R.  
Zhiqiang Cai  Department of Mathematics  Purdue University 
Jose Castillo  Department of Mathematics & Statistics  San Diego State University 
Panagiotis Chatzipantelidis  Department of Mathematics  Texas A & M University 
Snorre Christiansen  Department of Mathematics  Centre of Mathematics for Applications 
Mark Christon  Sandia National Laboratories  
Bernardo Cockburn  School of Mathematics  University of Minnesota, Twin Cities 
Robert Crone  Mechanical Research and Development  Seagate Technology 
Leszek Demkowicz  Institute for Computational Engineering and Sciences  University of Texas, Austin 
Yalchin Efendiev  Department of Mathematics  Texas A & M University 
Richard Falk  Department of Mathematics  Rutgers, The State University Of New Jersey 
Juergen Geiser  IWR  Texas A & M University 
Anne Gundel  Institute for Mathematics  HumboldtUniversität 
Hazem Hamdan  School of Mathematics  University of Minnesota, Twin Cities 
Bo He  Department of Electrical Engineering  The Ohio State University 
Jan Hesthaven  Division of Applied Mathematics  Brown University 
Ulrich Hetmaniuk  Sandia National Laboratories  
Ralf Hiptmair  Seminar of Applied Mathematics  Zentrum für Umfragen, Methoden und Analysen (ZUMA) e.V. 
Anil Hirani  Department of Control and Dynamical Systems  California Institute of Technology 
Michael Holst  Department of Mathematics  University of California, San Diego 
Ronald Hoppe  Department of Mathematics  University of Houston 
Paul Houston  Department of Mathematics and Computer Science  University of Leicester 
Thomas Hughes  Institute for Computational Engineering and Sciences  University of Texas, Austin 
E. Hyde  School of Mathematics  University of Minnesota, Twin Cities 
Lili Ju  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Ruben Juanes  Department of Petroleum Engineering  Stanford University 
HyeRyoung Kim  Seoul National University  
Joseph Koning  Department of Engineering  Lawrence Livermore National Laboratory 
P. Robert Kotiuga  Department of Electrical and Computer Engineering  Boston University 
Thomas Kurtz  Department of Mathematics  University of Wisconsin, Madison 
Yuri Kuznetsov  Department of Mathematics  University of Houston 
Raytcho Lazarov  Department of Mathematics  Texas A & M University 
Richard Lehoucq  Computational Mathematics and Algorithms  Sandia National Laboratories 
Melvin Leok  Department of Control and Dynamical Systems  California Institute of Technology 
Konstantin Lipnikov  Los Alamos National Laboratory  
Mitchell Luskin  School of Mathematics  University of Minnesota, Twin Cities 
Antoinette Maniatty  Department of Mechanical, Aerospace, and Nuclear Engineering  Rensselaer Polytechnic Institute 
Elizabeth Mansfield  Institute of Mathematics and Statistics  University of Kent at Canterbury 
Donatella Marini  Dipartimento di Matematica  Università di Pavia 
Ilya Mishev  ExxonMobil  
Julie Mitchell  Departments of Mathematics and Biochemistry  University of Wisconsin, Madison 
Jim Morel  Los Alamos National Laboratory  
J. Moulton  Los Alamos National Laboratory  
JeanClaude Nédélec  Centre de Mathématiques Appliquées  École Polytechnique 
Roy Nicolaides  Department of Mathematical Sciences  Carnegie Mellon University 
Philippe Pebay  Sandia National Laboratories  
Blair Perot  Department of Mechanical and Industrial Engineering  University of Massachusetts 
Ilaria Perugia  Dipartimento di Matematica  Università di Pavia 
Edward Ratner  Department of Optical CD Metrology  KLA  Tencor 
Fernando Reitich  School of Mathematics  University of Minnesota, Twin Cities 
JeanFrancois Remacle  Scientific Computation Research Center  Rensselaer Polytechnic Institute 
Robert Rieben  Institute for Scienftic Computing Research  Lawrence Livermore National Laboratory 
Beatrice Riviere  Department of Mathematics  University of Pittsburgh 
Allen Robinson  Computational Physics Research and Development Department  Sandia National Laboratories 
Thomas Russell  Division of Mathematical Sciences  National Science Foundation 
Fadil Santosa  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Rolf Schuhmann  TEMF Laboratory  TU Darmstadt 
Mikhail Shashkov  XCP  XComputational Physics  Los Alamos National Laboratory 
ShagiDi Shih  Department of Mathematics  University of Wyoming 
Rajen Sinha  Institute for Scientific Computation  Texas A & M University 
Stanly Steinberg  Department of Mathematics & Statistics  University of New Mexico 
Srdjan Stojanovic  Department of Mathematical Sciences  University of Cincinnati 
Eitan Tadmor  CSCAMM  University of Maryland 
Fernando Teixeira  Department of Electrical Engineering  The Ohio State University 
JeanMarie Thomas  Laboratory of Applied Mathematics  Université de Pau et des Pays de l'Adour 
Kathryn Trapp  Department of Mathematical Sciences  Carnegie Mellon University 
Jukka Tuomela  Department of Mathematics  University of Joensuu 
Panayot Vassilevski  Center for Applied Scientific Computing  Lawrence Livermore National Laboratory 
Jing Wang  Institute for Mathematics and its Applications  University of Minnesota, Twin Cities 
Timothy Warburton  Department of Mathematics & Statistics  University of New Mexico 
Mary Wheeler  Institute for Computational Engineering and Sciences  University of Texas, Austin 
Daniel White  Center for Applied Scientific Computing  Lawrence Livermore National Laboratory 
Ragnar Winther  Centre of Mathematics for Applications  University of Oslo 
Jinchao Xu  Department of Mathematics  The Pennsylvania State University 
Ivan Yotov  Department of Mathematics  University of Pittsburgh 
Jun Zhao  Institute of Mathematics and its Application  University of Minnesota, Twin Cities 
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