Multiresolution analysis on irregular surface meshes

Scale-separating operators for variational multiscale large eddy simulation of turbulent flows

“…In practice, however, most of the numerical simulations performed in physical space do not rely on a spatial filtering process like (1), unless the so-called ''pre-filtering technique'' is used, see [54]. Rather, the resolution of the underlying numerical discretization is used to define the resolved part of the velocity u h , with the superscript h indicating the characteristic length scale of the discretization.…”

Rate-Distortion Optimized Wavelet-based Irregular Mesh Coding

“…Bonneau describes a generalization of Haar-wavelets in (Bonneau, 1998). Valette et al (Valette et al, 1999;Valette and Prost, 2004a) propose an extension of the work of Lounsbery et al, describing a new subdivision approach which is not restricted to 1-to-4 subdivision, but allows creating one, two, three or four triangles from a single triangle.…”

Freeform surface filtering using the lifting wavelet transform

“…Two major operators were proposed; the smoothing operator to compute the coarse mesh and an error operator to determine the difference between the approximation and the original meshes (Bonneau 1998) [20].…”

“…The introduction of the second generation wavelets and lifting scheme [14][15][16][17] made the extension of wavelets and MRA possible for all types of 3D meshes and a few algorithms have been proposed [13,[18][19][20][21][22]. The main idea behind MRA is to decompose a high resolution mesh into a lower resolution mesh and details that are needed to recover the original mesh, this operation is repeated iteratively starting from the finest mesh M ∞ and ending wish the coarsest base mesh M 0 as shown in Fig.…”