
Accession Number : ADA325866
Title : The Stability and Multiplicity of the Monotonic Lagrangian Grid,
Corporate Author : NAVAL RESEARCH LAB WASHINGTON DC CENTER FOR REACTIVE FLOW AND DYNAMICAL SYSTE MS
Personal Author(s) : Sinkovits, Robert S. ; Oran, Elaine S. ; Boris, Jay P.
PDF Url : ADA325866
Report Date : 28 MAY 1997
Pagination or Media Count : 28
Abstract : The Monotonic Lagrangian Grid (MLG) is a data structure in which nodes are ordered in a monotonic way such that those nodes which are close in physical space also have nearby indices in the data structure arrays. An MLG ordering for a given system of nodes, as defined by the monotonicity constraints, is not unique. For all but the smallest systems, the number of allowed orderings is extremely large with many of the possible MLG's so badly structured that they lead to poor results when used in physical calculations. A wellstructured MLG ordering is one that corresponds well to the physical ordering of the system. This paper shows that the majority of the MLG's for a given set of node locations are poorly structured, but that the small fraction which are wellstructured tend to be extremely stable against perturbations of the node positions. It is this extreme stability of the wellstructured MLG's that is responsible for both the utility of this approach in particlebased simulations and the success of stochastic grid regularization, a technique for restructuring from a poorly structured to a wellstructured MLG. The high probability of encountering a wellstructured MLG when the node dynamics is complex, even without stochastic grid regularization, is a result of this relative stability.
Descriptors : *DATA MANAGEMENT, *SYSTEMS ANALYSIS, *LAGRANGIAN FUNCTIONS, DATA BASES, COMPUTERIZED SIMULATION, STOCHASTIC PROCESSES, GRIDS, STRUCTURED PROGRAMMING, MONOTONE FUNCTIONS.
Subject Categories : Operations Research
Computer Programming and Software
Distribution Statement : APPROVED FOR PUBLIC RELEASE