Multi-object adaptive optics (MOAO) is a novel adaptive optics (AO) technique dedicated to the special case of wide-field multiobject spectrographs (MOS). It applies dedicated wavefront corrections to numerous independent tiny patches spread over a large field of view (FOV). The control of each deformable mirror (DM) is done individually using a tomographic reconstruction of the phase based on measurements from a number of wavefront sensors (WFS) pointing at natural and artificial guide stars in the field. The output of this study helps the design of a new instrument called MOSAIC, a multi-object spectrograph proposed for the European Extremely Large Telescope (E-ELT)1. We have developed a novel hybrid pseudo-analytical simulation scheme that allows us to accurately simulate in detail the tomographic problem. The main challenge resides in the computation of the tomographic reconstructor, which involves pseudo-inversion of a large dense symmetric matrix. The pseudo-inverse is computed using an eigenvalue decomposition, based on the divide and conquer algorithm, on multicore systems with multi-GPUs. Thanks to a new symmetric matrix-vector product (SYMV) multi-GPU kernel, our overall implementation scores significant speedups over standard numerical libraries on multicore, like Intel MKL, and up to 60% speedups over the standard MAGMA implementation on 8 Kepler K20c GPUs. At 40,000 unknowns, this appears to be the largest-scale tomographic AO matrix solver submitted to computation, to date, to our knowledge and opens new research directions for extreme scale AO simulations.