  In this work we address the Multiscale Spectral Generalized Finite Element
Method (MS-GFEM) developed in [I. Babu\v{s}ka and R. Lipton, Multiscale
Modeling and Simulation 9 (2011), pp. 373--406]. We outline the numerical
implementation of this method and present simulations that demonstrate contrast
independent exponential convergence of MS-GFEM solutions. We introduce
strategies to reduce the computational cost of generating the optimal
oversampled local approximating spaces used here. These strategies retain
accuracy while reducing the computational work necessary to generate local
bases. Motivated by oversampling we develop a nearly optimal local basis based
on a partition of unity on the boundary and the associated A-harmonic
extensions.
