Creating domain mappings

Atkinson, Kendall ; Hansen, Olaf

Electronic transactions on numerical analysis, Tome 39 (2012), pp. 202-230

Résumé

Consider being given a mapping $\varphi:S^{d-1}\% \overset{1-1}{\underset{onto}{\longrightarrow}}\partial\Omega$, with $\partial\Omega$ the $\left( d-1\right) $-dimensional smooth boundary surface for a bounded open simply-connected region $\Omega$ in $\mathbb{R}\% ^{d}, d\geq2$. We consider the problem of constructing an extension $\Phi:\overline{B}_{d}\overset{1-1}{\underset{onto}{\longrightarrow}}\% \overline{\Omega}$ with $B_{d}$ the open unit ball in $\mathbb{R}^{d}$. The mapping is also required to be continuously differentiable with a non-singular Jacobian matrix at all points. We discuss ways of obtaining initial guesses for such a mapping $\Phi$ and of then improving it by an iteration method.

Détail

Classification : 65D99
Keywords: domain mapping, multivariate polynomial, constrained minimization, nonlinear iteration