Alfonso Limon, Hedley Morris
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
.
This MRA is extended to
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
,
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:
Key Words: Adaptive grid refinement; Wavelet refined mesh; quadtree grids;
multilevel decomposition; codimension-one discontinuities.
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Alfonso Limon School of Mathematical Sciences Claremont Graduate University, CA 91711, USA email: alfonso.limon@cgu.edu | |
Hedley Morris School of Mathematical Sciences Claremont Graduate University, CA 91711, USA email: hedley.morris@cgu.edu |
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