Interpreting moving mesh methods and transformation techniques from various applications in terms of the mass transport problem
Year: 2003
Type: article
Abstract: Over the last twenty years, moving mesh methods have become a very useful tool for solving many partial differential equations (PDEs) numerically, in particular, PDEs having large solution variations such as boundary layers, shock waves, blow-up, and moving wave fronts. Various types of moving mesh methods have been developed to solve such problems. These methods generally use a non-uniform mesh with a fixed number of mesh points as time evolves. The points are concentrated in regions with steep solutions. In their recent paper, Cao, Huang and Russell introduce a moving mesh niethod based on specifying the Jacobian of the coordinate transformation, the geometric conservation law (GCL) and a curl condition. In this thesis, we study the relationship between the resulting GCL method and the hIonge-Kantorovich mass transfer problem: a civil engineering problem first formulated by hIonge in 1781. The transfer problem is concerned with finding the optimal path, in the sense of moving parcels of materials from one site to another one with minimal transportation cost. We also investigate the link between moving mesh theory and fluid dynamics, meteorology, computational anatomy and image registration by establishing a relationship between the coordinate transformations used in their formulations.
Source: Summit (Simon Fraser University)
Author: M. Sulman
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2303865423