The Stability and Multiplicity of the Monotonic Lagrangian Grid,
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 well-structured 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 well-structured tend to be extremely stable against perturbations of the node positions. It is this extreme stability of the well-structured MLG's that is responsible for both the utility of this approach in particle-based simulations and the success of stochastic grid regularization, a technique for restructuring from a poorly structured to a well-structured MLG. The high probability of encountering a well-structured MLG when the node dynamics is complex, even without stochastic grid regularization, is a result of this relative stability.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 28, 1997
- Accession Number
- ADA325866
Entities
People
- Elaine Oran
- Jay Paul Boris
- Robert S. Sinkovits
Organizations
- United States Naval Research Laboratory