Creating domain mappings
arXiv:1106.3338
Abstract
Consider being given a mapping ϕfrom the unit sphere S^{d-1}, d>2, to the smooth boundary of a simply-connected region Ωin R^d. We consider the problem of constructing an extension Φfrom the unit ball B_d to Ω. 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 Φand of then improving it by an iteration method.
16 figures