Lifting MGARD: construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order

Abstract

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements ${\mathbb{Q}}_p$, $p\ge 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

References in corpus (3)

• MGARD: A multigrid framework for high-performance, error-controlled data compression and refactoring
• HexaShrink, an exact scalable framework for hexahedral meshes with attributes and discontinuities: multiresolution rendering and storage of geoscience models
• Spatiotemporally adaptive compression for scientific dataset with feature preservation -- a case study on simulation data with extreme climate events analysis

Cited by in corpus (1)

• A framework for compressing unstructured scientific data via serialization