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Partitioning meshes is a preprocessing step for parallel scientific simulation. The quality of a partitioning is measured by load balance and communication overhead. The effectiveness of a partitioning significantly influences the performance of parallel computation. In this paper, we propose a quadtree spatial-based domain decomposition method for partitioning unstructured meshes. The background quadtree, which is originally used to represent the density distribution among elements within the computing domain, can be used to obtain an initial partitioning and to do multi-level refinement. As the quadtree implicitly defines hierarchical relationship, which is a natural way to define coarsening and uncoarsening phases, we can repeatedly apply coarsening, partitioning, and uncoarsening multilevel refinement phases, until no improvement can be made. Thus, for most cases, the partitioning results by our method are better than those produced by other graph-based partitioning methods. Experimental studies for the NACA0012 airfoil, the NASA EET wing, and an artillery shell within a shock tube are reported.