1er Symposium canadien en analyse numérique et calcul scientifique
Parabolic Monge-Ampere and Mesh Alignment
Walsh, Emily (1), Chris Budd (2) and Bob Russell (1)
(1) Simon Fraser University, (2) Bath University, UK

The Parabolic Monge-Ampere Moving Mesh Method combines equidistribution with optimal transport. We demonstrate that this method can produce an anisotropic mesh along a given feature by equidistributing a suitably chosen scalar monitor function. We define the general metric $M$, in physical space, that a mesh generated by this method aligns to. We then derive expressions for the eigenvalues and eigenvectors of $M$ for a linear feature and a feature with curvature that is radially symmetric. The eigenvectors of $M$ are shown to be orthogonal and tangential to the feature, and the ratio of the eigenvalues is shown to depend on the value of the scalar monitor density function, both locally and globally. Numerical results will be presented in 2D to verify these results.

Mardi, 18 juin, 11h30
Salle Des Plaines B