  The image quality of the new generation of earthbound Extremely Large
Telescopes (ELTs) is heavily influenced by atmospheric turbulences. To
compensate these optical distortions a technique called adaptive optics (AO) is
used. Many AO systems require the reconstruction of the refractive index
fluctuations in the atmosphere, called atmospheric tomography. The standard way
of solving this problem is the Matrix Vector Multiplication, i.e., the direct
application of a (regularized) generalized inverse of the system operator.
However, over the last years the telescope sizes have increased significantly
and the computational efficiency become an issue. Promising alternatives are
iterative methods such as the Finite Element Wavelet Hybrid Algorithm (FEWHA),
which is based on wavelets. Due to its efficient matrix-free representation of
the underlying operators, the number of floating point operations and memory
usage decreases significantly. In this paper, we focus on performance
optimization techniques, such as parallel programming models, for the
implementation of this iterative method on CPUs and GPUs. We evaluate the
computational performance of our optimized, parallel version of FEWHA for
ELT-sized test configurations.
