Seventh Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 17 (2009), pp. 133-148.
Title: A multilevel adaptive mesh generation scheme using Kd-trees
Authors: Alfonso Limon (Claremont Graduate Univ., CA, USA)
Hedley Morris (Claremont Graduate Univ., CA, USA)
Abstract:
We introduce a mesh refinement strategy for PDE based simulations
that benefits from a multilevel decomposition. Using Harten's MRA
in terms of Schroder-Pander linear multiresolution analysis
[20], we are able to bound discontinuities in
$\mathbb{R}$. This MRA is extended to $\mathbb{R}^n$ in terms
of n-orthogonal linear transforms and utilized to identify cells
that contain a codimension-one discontinuity. These refinement
cells become leaf nodes in a balanced Kd-tree such that a
local dyadic MRA is produced in $\mathbb{R}^n$, while maintaining
a minimal computational footprint. The nodes in the tree form an
adaptive mesh whose density increases in the vicinity of a discontinuity.
Published April 15, 2009.
Math Subject Classifications: 35R05, 65N50.
Key Words: Adaptive grid refinement; Wavelet refined mesh; quadtree grids;
multilevel decomposition; codimension-one discontinuities.