Some results on uniformly high-order accurate essentially nonoscillatory schemes
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Ten lectures on wavelets
Adapted wavelet analysis from theory to software
Adapted wavelet analysis from theory to software
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Multigrid
ENO-Wavelet Transforms for Piecewise Smooth Functions
SIAM Journal on Numerical Analysis
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
Dual Marching Cubes: Primal Contouring of Dual Grids
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Adaptive lifting schemes with perfect reconstruction
IEEE Transactions on Signal Processing
Nonlinear wavelet transforms for image coding via lifting
IEEE Transactions on Image Processing
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Whether tracking the eye of a storm, the leading edge of a wildfire, or the front of a chemical reaction, one finds that significant change occurs at the thin edge of an advancing line. The tracking of such change-fronts comes in myriad forms with a wide variety of applications expressible as PDEs. Expanding on Ami Harten's ideas, we construct an alternative to wavelet-based grid refinement, a multiresolution coarsening method that is capable of capturing sharp gradients across different scales, thus improving PDE-based simulations by concentrating computational resources where the solution varies sharply. We present this alternative grid coarsening method and compare its performance to other multiresolution methods by means of several examples.