Recent observations of protoplanetary disks indicate that planets begin to form during the first million years of their evolution. However, state-of-the-art simulations of disk formation struggle to follow their evolution beyond 100,000 years. Two obstacles are at the root of this limitation. First, the numerical schemes that include the magnetic field are strongly constrained by non-ideal MHD that imposes a quadratic decrease of the timestep with the resolution; this becomes prohibitive once disks are spatially resolved. Second, over such long periods of time, it becomes necessary to model scales that go beyond the prestellar core that constitutes the initial mass reservoir of the disk. We must therefore model the entire molecular clouds, that is to say from the parsec scales down to the astronomical unit, while considering secular times. This is out of reach for commonly used numerical codes. In this thesis, we propose to remove these two technical barriers. We will develop a non-ideal MHD scheme based on the 'heavy ion' method, which is appropriate because dust grains are the main charge carriers during the collapse. Since this approach does not require a diffusion term, it will accelerate the treatment of the magnetic field. Furthermore, it will be implemented in DYABLO, a new code developed at CEA that provides GPU acceleration, unlocking the multi-scale aspect of the project. Building on these developments, we will study the influence of the environment on disks and the formation of planetesimals in order to determine the timing of planet formation.