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This paper describes a novel application of feature preserving mesh simplification to the problem of managing large, multidimensional datasets during scientific visualization. To allow this, we view a scientific dataset as a triangulated mesh of data elements, where the attributes embedded in each element form a set of properties arrayed across the surface of the mesh. Existing simplification techniques were not designed to address the high dimensionality that exists in these types of datasets. As well, vertex operations that relocate, insert, or remove data elements may need to be modified or restricted. Principal component analysis provides an algorithm-independent method for compressing a dataset's dimensionality during simplification. Vertex locking forces certain data elements maintain their spatial locations; this technique is also used to guarantee a minimum density in the simplified dataset. The result is a visualization that significantly reduces the number of data elements to display, while at the same time ensuring that high-variance regions of potential interest remain intact. We apply our techniques to a number of well-known feature preserving algorithms, and demonstrate their applicability in a real-world context by simplifying a multidimensional weather dataset. Our results show a significant improvement in execution time with only a small reduction in accuracy; even when the dataset was simplified to 10% of its original size, average per attribute error was less than 1%.