  Today's scientific simulations require a significant reduction of data volume
because of extremely large amounts of data they produce and the limited I/O
bandwidth and storage space. Error-bounded lossy compression has been
considered one of the most effective solutions to the above problem. However,
little work has been done to improve error-bounded lossy compression for
Adaptive Mesh Refinement (AMR) simulation data. Unlike the previous work that
only leverages 1D compression, in this work, we propose to leverage
high-dimensional (e.g., 3D) compression for each refinement level of AMR data.
To remove the data redundancy across different levels, we propose three
pre-process strategies and adaptively use them based on the data
characteristics. Experiments on seven AMR datasets from a real-world
large-scale AMR simulation demonstrate that our proposed approach can improve
the compression ratio by up to 3.3X under the same data distortion, compared to
the state-of-the-art method. In addition, we leverage the flexibility of our
approach to tune the error bound for each level, which achieves much lower data
distortion on two application-specific metrics.
