We present a new method for constructing multiresolution representations of data sets that contain material interfaces. Material interfaces embedded in the meshes of computational data sets are often a source of error of simplification algorithms because they represent discontinuities in the scalar or vector field over mesh elements. By representing material interfaces explicitly, we are able to provide separate field representations for each material over a single cell. Multiresolution representations utilizing separate field representations can accurately approximate datasets that contain discontinuities without placing a large percentage of cells around the discontinuous regions. Our algorithm uses a multiresolution tetrahedral mesh supporting fast coarsening and refinement capabilities; error bounds for feature preservation; explicit representation of discontinuities within cells; and separate field representations for each material within a cell.
