Today's scientific simulations generate exceptionally large volumes of data, challenging the capacities of available I/O bandwidth and storage space. This necessitates a substantial reduction in data volume, for which error-bounded lossy compression has emerged as a highly effective strategy. A crucial metric for assessing the efficacy of lossy compression is visualization. Despite extensive research on the impact of compression on visualization, there is a notable gap in the literature concerning the effects of compression on the visualization of Adaptive Mesh Refinement (AMR) data. AMR has proven to be a potent solution for addressing the rising computational intensity and the explosive growth in data volume that requires storage and transmission. However, the hierarchical and multi-resolution characteristics of AMR data introduce unique challenges to its visualization, and these challenges are further compounded when data compression comes into play. This article delves into the intricacies of how data compression influences and introduces novel challenges to the visualization of AMR data.

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