Creating domain mappings
Numerical Analysis
2011-06-20 v1
Abstract
Consider being given a mapping \phi from the unit sphere S^{d-1}, d>2, to the smooth boundary of a simply-connected region \Omega in R^d. We consider the problem of constructing an extension \Phi from the unit ball B_d to \Omega. The mapping is required to be 1-1 and continuously differentiable with a nonsingular Jacobian matrix. We discuss ways of obtaining initial guesses for such a mapping \Phi and of then improving it by an iteration method.
Cite
@article{arxiv.1106.3338,
title = {Creating domain mappings},
author = {Kendall Atkinson and Olaf Hansen},
journal= {arXiv preprint arXiv:1106.3338},
year = {2011}
}
Comments
16 figures