Homeomorphism criteria for the theory of grid generation
Marina Prokhorova
TL;DR
This paper establishes general topological and smooth criteria for homeomorphisms and diffeomorphisms, with applications to grid generation in 2D and 3D.
Contribution
It introduces new criteria for identifying homeomorphisms and diffeomorphisms, specifically tailored for applications in grid generation.
Findings
Criteria for homeomorphisms of topological manifolds
Criteria for diffeomorphisms of smooth manifolds
Application to 2D and 3D grid generation
Abstract
We give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to the problems arising in two- and three-dimensional grid generation.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology