Terrestrial planet formation in the era of GPU computing

In this chapter, we summarize the underlying numerical methods needed for efficient $N$-body integration of planetary systems. We discuss how symplectic integrators have been developed to tackle the complementary problems of long-term orbital integration and short-term collisional interactions. The public code GENGA, a parallel GPU/CPU planet formation and orbital dynamics simulation code, was developed to unify these methods and take full advantage of the newest available computing hardware. We present state-of-the-art N-body simulations performed with GENGA in a comparative study regarding the basic properties that emerge during the late stages of the terrestrial planet formation process. We show that in modern N-body simulations the commonly used acceleration factor f, used to speed up the collisional growth of planets in simulations, should be avoided since it can lead to distorted chemical composition of the planets. We make a detailed comparison of low to high-resolution simulations, showing that the formation time scale depends on the size of the initial planetesimals. These simulations also show that terrestrial planets can form resonant chains without the need of orbital migration due to gas effects.