  Finding fast yet accurate numerical solutions to the Helmholtz equation
remains a challenging task. The pollution error (i.e. the discrepancy between
the numerical and analytical wave number k) requires the mesh resolution to be
kept fine enough to obtain accurate solutions. A recent study showed that the
use of Isogeometric Analysis (IgA) for the spatial discretization significantly
reduces the pollution error.
  However, solving the resulting linear systems by means of a direct solver
remains computationally expensive when large wave numbers or multiple
dimensions are considered. An alternative lies in the use of (preconditioned)
Krylov subspace methods. Recently, the use of the exact Complex Shifted
Laplacian Preconditioner (CSLP) with a small complex shift has shown to lead to
wave number independent convergence while obtaining more accurate numerical
solutions using IgA.
  In this paper, we propose the use of deflation techniques combined with an
approximated inverse of the CSLP using a geometric multigrid method. Numerical
results obtained for both one- and two-dimensional model problems, including
constant and non-constant wave numbers, show scalable convergence with respect
to the wave number and approximation order p of the spatial discretization.
Furthermore, when kh is kept constant, the proposed approach leads to a
significant reduction of the computational time compared to the use of the
exact inverse of the CSLP with a small shift.
