Extension operators extend functions defined on the boundary of a domain into its interior. This paper presents explicit extension operators by means of multilevel decompositions on hierarchical grids. It is shown that the norm-preserving property of these operators holds for the 2D as well for the 3D case with constants independent on discretization and domain size. These constants can be further improved by an additional iteration scheme applied to the extension operator. Some implementation of these techniques is presented for a domain decomposition preconditioner and numerical experiments are given.
Keywords: Boundary value problems, trace theory, multilevel methods, domain decomposition, preconditioning, finite ele- ment method.