  We propose an implementation of the Smooth Selection Embedding Method (SSEM)
in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain
/ collocation method which solves boundary value problems in complex domains by
recasting them as constrained optimization problems in a simple encompassing
set. Previously, the SSEM was introduced and implemented using a periodic box
(read a torus) using Fourier series; here, it is implemented on a
(non-periodic) rectangle using Chebyshev polynomial expansions. This
implementation has faster convergence on smaller grids. Numerical experiments
will demonstrate that the method provides a simple, robust, efficient, and high
order fictitious domain method which can solve problems in complex geometries,
with non-constant coefficients, and for general boundary conditions.
