We present a performance analysis of a parallel implementation for both preconditioned conjugate gradient and preconditioned bi-conjugate gradient solvers running on graphic processing units (GPUs) with CUDA programming model. The solvers were mainly optimized for the solution of sparse systems of algebraic equations at complex entries, arising from the three-dimensional edge-finite element analysis of the electromagnetic phenomena involved in the open-bound earth diffusion of currents under time-harmonic excitation. We used a shifted incomplete Cholesky (IC) factorization as preconditioner. Results show a significant speedup by using either a single-GPU or a multi-GPU device, compared to a serial central processing unit (CPU) implementation, thereby allowing the simulations of large-scale problems in low-cost personal computers. Additional experiments of the optimized solvers show that its use can be extended successfully to other complex systems of equations arising in electrical engineering, such as those obtained in power–system analysis.