This thesis has demonstrated how GPU-accelerated Domain Decomposition methods efficiently solve the Helmholtz equation. More specifically, I have discussed the subsolvers, and it seems like there are huge benefits from the use of the Restricted Additive Average Schwarz (RAAS) method as a precondition. PyOpenCL implementation of the inner solver Conjugate Gradient method showed huge improvements in computational speed realized through GPU acceleration. The conducted experiments have mainly brought attention to PyOpenCL-CG implementation for multiple right-hand sides in terms of time complexity.

The solvers were also compared with different wave numbers and overlapping layers. The results obtained from solvers in different numbers of overlapping layers were helpful in finding the better values for the properties of the \raas{} method.

This work underlines that, indeed, the remarkable potential is held by advanced GPU programming and domain decomposition in dealing with some of the complex computational challenges, and it opens up the door for numerical simulations to be furthered in this advanced skillset.

Overall, the presented results of this thesis prove the necessity of innovations in preconditioning strategies and the necessity of integration of GPU acceleration in computational science to advance toward more efficient and effective large-scale problem solvers.