Lifting MGARD: construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909425683398656 |
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| author | Reshniak, Viktor Ferguson, Evan Gong, Qian Vidal, Nicolas Archibald, Rick Klasky, Scott |
| author_facet | Reshniak, Viktor Ferguson, Evan Gong, Qian Vidal, Nicolas Archibald, Rick Klasky, Scott |
| contents | 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 $\mathbb{Q}_p$, $p \geq 0$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lifting MGARD: construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order Reshniak, Viktor Ferguson, Evan Gong, Qian Vidal, Nicolas Archibald, Rick Klasky, Scott Numerical Analysis Functional Analysis 65T60 (Primary), 42C40 (Secondary) 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 $\mathbb{Q}_p$, $p \geq 0$, 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. |
| title | Lifting MGARD: construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order |
| topic | Numerical Analysis Functional Analysis 65T60 (Primary), 42C40 (Secondary) |
| url | https://arxiv.org/abs/2408.07212 |