Parallel implementation of an iterative solver for atmospheric tomography

Due to atmospheric turbulences the image quality of earthbound Extremely Large Telescopes (ELTs) is heavily degraded. Adaptive Optics (AO) is a technique that compensates for these quickly-varying optical aberrations. Many AO systems require the reconstruction of the turbulence profile in the atmosphere, called atmospheric tomography. The standard way of solving this problem is the so called Matrix Vector Multiplication method, 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 solving the atmospheric tomography problem in real-time become an ambitious and crucial task. 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 decrease significantly. In this paper, we focus on a parallel implementation of FEWHA on real-time hardware used for the control of large AO systems. We evaluate the computational performance of our parallel algorithm via numerical simulations for ELT-sized test configurations.