**Speaker:** Professor Mark S. Shephard, Director, Scientific Computation
Research Center (SCOREC), Rensselaer Polytechnic Institute

**Abstract:**

A great number of codes have been developed for the solution of partial differential equations. Increasingly the users of these codes are requesting that they include support for adaptive discretization error control. Three key data components that must be addressed in the development of an adaptive loop are:

1. The problem definition that links to a high level geometry and physical attribute specification of the simulation problem. 2. The mesh that provides the services for storing and modifying mesh data during the adaptive process. 3. The fields that provides the functions needed to obtain the solution information needed for error estimation and to support the transfer of solution fields as the mesh is adapted.

The presentation will overview these structures and their interactions with specific emphasis on the requirements placed on the mesh structure to support general mesh adaptivity as well as the possibilities of variable order methods (e.g., directional p-version).

Options for adding adaptive simulations capabilities to a code range from a tight integration of all components into the analysis code to the use interoperable components to construct an adaptive loop leaving the analysis code unaltered. The presentation will demonstrate examples of both approaches with emphasis on the use interoperable components to construct automated adaptive simulation loops for:

(a) An electromagnetics frequency domain solver used by in the design of multiple cavity accelerator systems.

(b) Forming simulations of parts that undergo large deformations resulting in major changes in the domain geometry. The adaptive procedure sets the mesh size field accounting for discretization errors, control of element shape, geometric approximation and the transfer of history dependent variables.

Last modified: Thu Feb 10 10:29:16 EST 2005