Olaf Hansen
Creating domain mappings.
Mon, 06/20/2011 - 15:01 — SomNambulAuthors: Kendall Atkinson, Olaf Hansen
Subjects: Numerical Analysis
AbstractConsider 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.A Spectral Method for the Eigenvalue Problem for Elliptic Equations.
Tue, 09/22/2009 - 14:09 — SomNambulAuthors: Kendall Atkinson, Olaf Hansen
Subjects: Numerical Analysis
AbstractLet $\Omega$ be an open, simply connected, and bounded region in
$\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth.
Consider solving the eigenvalue problem $Lu=\lambda u$ for an elliptic partial
differential operator $L$ over $\Omega$ with zero values for either Dirichlet
or Neumann boundary conditions. We propose, analyze, and illustrate a 'spectral
method' for solving numerically such an eigenvalue problem. This is an
extension of the methods presented earlier in [5],[6].
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