Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering, September 1, 2003 - June 30, 2004

IMA "Hot Topics" Workshop:

Compatible Spatial Discretizations for Partial Differential Equations

May 11-15, 2004

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
Carnegie-Mellon University
dept.head@math.cmu.edu
http://www.math.cmu.edu/people/fac/nicolaides.html

Mikhail Shashkov
MS-B284, Group T-7, 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.

Description:

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.

LIST OF CONFIRMED PARTICIPANTS

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