ADAPT '03: Adaptive Methods for Partial Differential Equations and Large-Scale Computation

Conference in honor of the 60th birthday of Dean Joseph E. Flaherty

Early 1970's	Mid 1980's	Today

October 11-12, 2003
Rensselaer Polytechnic Institute
Troy, New York

Supported by the U.S. Army Research Office and by the National Science Foundation

Pictures

Objective

Many physical phenomena in science and engineering are modeled by partial differential equations with solutions that exhibit localized nonuniformities that form, evolve and decay during integration. Such applications include boundary layers and shock waves in fluids and reaction fronts in combustion. Applications such as thin film coating, composite media and nanoscale materials require mathematical models capable of capturing behavior at several different scales. The traditional approach via user designed meshes and methods with several iterations is no longer acceptable in terms of cost and understanding of process behavior. The problems are too complex and users can be fooled. In some situations problems can not be solved when using over-designed meshes.

Adaptive higher-order methods combine

• h-refinement, where meshes are refined and/or coarsened to achieve a prescribed accuracy and efficiency,
• p-refinement, where method orders are assigned to elements to achieve exponential convergence rates, and
• r-refinement where elements are moved and redistributed to track evolving nonuniformities.

This conference has two main goals:

• to bring together researchers working in this critical area of scientific computing to discuss new advances and challenges, and
• to introduce young researchers into the area of adaptive methods for solving partial differential equations.

Conference Themes

• Efficient adaptive refinement strategies. These are strategies that find solutions to prescribed levels of accuracy in minimal time, space, and/or other criteria and are dependent on the problems under consideration and the computational devices available for the solution.
• Data structures for parallel and adaptive computations. This includes the study of dynamic data structures that support efficient storage, retrieval and update of solution data, dynamic load balancing and support tools that make communication and data migration more efficient.
• A posteriori error estimation. These are techniques to estimate discretization errors in several norms and quantities of interest. These estimates are used to guide the adaptive process by indicating regions where more or less resolution is needed. They also help stop the adaptive process when the prescribed accuracy is achieved.
• Discontinuous Galerkin (DG) methods. DG methods consist of finite element approximations that are discontinuous across element boundaries which make order variation and mesh refinement much easier in the presence of hanging nodes. They also have a simple communication pattern that allows for efficient parallelization.
• Grid and mesh generation. This involves techniques that automate mesh generation and adaptivity which are necessary to simulate complex three-dimensional problems using fully adaptive methods on parallel computers.
• Multiscale applications. These include fluid dynamics and solid mechanics, combustion problems, thin film coating, composites and nanoscale materials.

• Ivo Babuška (UT-Austin)
• Randy Bank (UCSD)
• Marsha Berger (NYU)
• Martin Berzins (University of Leeds)
• Rupak Biswas (NASA Ames)
• Bernardo Cockburn (University of Minnesota, Twin Cities)
• Karen Devine (Sandia National Laboratories)
• William Mitchell (NIST)
• Tinsley Oden (UT-Austin)
• Robert O'Malley (University of Washington)
• Linda Petzold (UCSB)
• Mark Shephard (Rensselaer)
• Barna Szabo (Washington University in St. Louis)
• Jan Verwer (Netherlands)
• Mary Wheeler (UT-Austin)

• Slimane Adjerid (Virginia Tech)
• Peter Moore (Southern Methodist University)
• Jim Teresco (Williams College)