Creating domain mappings
Abstract
Consider being given a mapping ϕfrom the unit sphere Sd-1, d>2, to the smooth boundary of a simply-connected region Ωin Rd. We consider the problem of constructing an extension Φfrom the unit ball Bd 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.
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