Parallel Adaptive Techniques for Transient Partial Differential Equations

Abstract

Our research aims to develop a framework for adaptive an and parallel computation on geometrically complex regions. In particular we investigated dynamic load balancing, transient solution techniques, and error estimation procedures for adaptive computation. Load balancing includes geometrically and topologically based procedures that are suitable for heterogeneous computation involving p and hp refinement, time dependence including local time stepping and method orders, diverse computing systems (e.g., clusters of workstations), and hierarchical networks (e.g., networks of MPs). Appropriate time integration techniques include explicit methods and implicit one and multi-step methods. The explicit methods are useful for problems having very rapid dynamics. Implicit multistep methods are generally more efficient than one step methods; however, this need not be the case when local time steps and method orders are used. A posteriori error estimation focus on procedures for transient problems with emphasis on singularly perturbed parabolic and hyperbolic problems, high order methods involving p and hp refinement, and the coordination of spatial and temporal errors.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1999
Accession Number
ADA369924

Entities

People

  • J. E. Flaherty
  • Mark S. Shephard

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Energy and Power Technologies
  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mechanics
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Science
  • Differential Equations
  • Dynamic Loads
  • Engineering
  • Equations
  • Finite Element Analysis
  • Geometry
  • Mathematics
  • Numerical Analysis
  • Parallel Computing
  • Partial Differential Equations
  • Three Dimensional
  • Time Dependence

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Parallel and Distributed Computing.