Data Structures and Algorithms for Self Adaptive Local Grid Refinement

Abstract

ABSTRACT Many models of important physical pehnomena are described using numerical schemes. Often, these numerical models are time dependent. Important active aspects of the phenomena are localized in small areas of the domain. These locations change often with time. Uniform gridding requires very small grid size. Very large domains would require large amounts of computer memory. Since the important changing areas are localized, grid size should be reduced only in the areas of high activity. Local refinement permits implementation of the model with significantly less storage allowing analysis of larger problems. Since the simulation procedes with time, the local refinement must also be able to dynamically adapt to reflect the movement of the active areas. Our aim is the development of high quality variational software capable of dynamic local grid refinement for general distribution. Herein, we discuss the data structure and algorithms needed to support the dynamic placing or removal of local refinement. The ability of a problem independent grid analysis to trigger the placement or removal of local refinement for an accurate local representation of temporal changes in the solution will be illustrated in a moving front situation.