In this article, we introduce a new coupling algorithm between the reservoir multiphase Darcy flow simulator and the geomechanical code accounting for the compaction of the porous medium. The coupling is defined on time periods in such a way that the reservoir unknowns are computed for time steps which are small enough subdivisions of the time period whereas the mechanical problem is solved at the end of the period. Our new approach is based on a nonlinear preconditioned conjugate gradient method which is applied to the mechanical displacement variable. This algorithm is compared, on a one dimensional example, to the staggered coupling algorithm with a porous medium compressibility as relaxation parameter. The main conclusion is that the preconditioned conjugate gradient method is much more robust and converge much faster than the staggered algorithm, while the additional cost per iteration should remain in practical situations very small.