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.
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