  Data management is becoming increasingly important in dealing with the large
amounts of data produced by large-scale scientific simulations and instruments.
Existing multilevel compression algorithms offer a promising way to manage
scientific data at scale, but may suffer from relatively low performance and
reduction quality. In this paper, we propose MGARD+, a multilevel data
reduction and refactoring framework drawing on previous multilevel methods, to
achieve high-performance data decomposition and high-quality error-bounded
lossy compression. Our contributions are four-fold: 1) We propose a level-wise
coefficient quantization method, which uses different error tolerances to
quantize the multilevel coefficients. 2) We propose an adaptive decomposition
method which treats the multilevel decomposition as a preconditioner and
terminates the decomposition process at an appropriate level. 3) We leverage a
set of algorithmic optimization strategies to significantly improve the
performance of multilevel decomposition/recomposition. 4) We evaluate our
proposed method using four real-world scientific datasets and compare with
several state-of-the-art lossy compressors. Experiments demonstrate that our
optimizations improve the decomposition/recomposition performance of the
existing multilevel method by up to 70X, and the proposed compression method
can improve compression ratio by up to 2X compared with other state-of-the-art
error-bounded lossy compressors under the same level of data distortion.
