  This paper gives an analysis and an evaluation of linear algebra operations
on Graphics Processing Unit (GPU) with complex number arithmetics with double
precision. Knowing the performance of these operations, iterative Krylov
methods are considered to solve the acoustic problem efficiently. Numerical
experiments carried out on a set of acoustic matrices arising from the
modelisation of acoustic phenomena within a cylinder and a car compartment are
exposed, exhibiting the performance, robustness and efficiency of our
algorithms, with a ratio up to 27x for dot product, 10x for sparse
matrix-vector product and solvers in complex double precision arithmetics.
