Wavelet analysis has been formalized extensively due to the efforts of mathematicians,
physicists and engineers in the last two decades. It has generated a tremendous interest in …

Abstract The Wavelet Adaptive Multiresolution Representation (WAMR) method provides a
robust method for controlling spatial grid adaptation—fine grid spacing in regions where a …

Adaptive strategies in space and time allow considerable speed-up of finite volume
schemes for conservation laws, while controlling the accuracy of the discretization. In this …

We present a detailed comparison between two adaptive numerical approaches to solve
partial differential equations, adaptive multiresolution (MR) and adaptive mesh refinement …

Adaptive representations are increasingly indispensable for reducing the in-memory and on-
disk footprints of large-scale data. Usual solutions are designed broadly along two themes …

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics
used, for instance, for model reduction and extraction of coherent flow features. However, its …

We present a wavelet-based adaptive method for computing 3D multiscale flows in complex,
time-dependent geometries, implemented on massively parallel computers. While our focus …

These lecture notes present adaptive multiresolution schemes for evolutionary PDEs in
Cartesian geometries. The discretization schemes are based either on finite volume or finite …

In this paper, space adaptivity is introduced to control the error in the numerical solution of
hyperbolic systems of conservation laws. The reference numerical scheme is a new version …

We present adaptive multiresolution (MR) computations of the two-dimensional
compressible Euler equations for a classical Riemann problem. The results are then …