  Geometry Independent Field approximaTion (GIFT) was proposed as a
generalization of Isogeometric analysis (IGA), where different types of splines
are used for the parameterization of the computational domain and approximation
of the unknown solution. GIFT with Non-Uniform Rational B-Splines (NUBRS) for
the geometry and PHT-splines for the solution approximation were successfully
applied to problems of time-harmonic acoustics, where it was shown that in some
cases, adaptive PHT-spline mesh yields highly accurate solutions at lower
computational cost than methods with uniform refinement. Therefore, it is of
interest to investigate performance of GIFT for shape optimization problems,
where NURBS are used to model the boundary with their control points being the
design variables and PHT-splines are used to approximate the solution
adaptively to the boundary changes during the optimization process.
  In this work we demonstrate the application of GIFT for 2D acoustic shape
optimization problems and, using three benchmark examples, we show that the
method yields accurate solutions with significant computational savings in
terms of the number of degrees of freedom and computational time.
