OpenQ$^\star$D code has been used by the RC$^\star$ collaboration for the generation of fully dynamical QCD+QED gauge configurations with C$^\star$ boundary conditions. In this talk, optimization of solvers provided with the openQ$^\star$D package relevant for porting the code on GPU-accelerated supercomputing platforms is discussed. We present the analysis of the current implementations of the GCR solver preconditioned with Schwarz alternating procedure for ill-conditioned Dirac-operators. With the goal of enabling support for GPUs from various vendors, a novel method of adaptive CPU/GPU-hybrid implementation is proposed.