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.

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discontinuities local dyadic mra mathbbr^n pde based simulations codimensionone mesh refinement strategy balanced kdtree discontinuity computational footprint northogonal linear transforms schroderpander linear multiresolution analysis multilevel decomposition

Alfonso Limon,Hedley Morris,.A multilevel adaptive mesh generation scheme using Kd-trees. 2009 (17),.

Alfonso Limon,Hedley Morris,"A multilevel adaptive mesh generation scheme using Kd-trees" 2009

Alfonso Limon,Hedley Morris,"A multilevel adaptive mesh generation scheme using Kd-trees"