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The ignition of vacuum arcs involves extreme nature and high-complexity physical processes. Phase changes occur in a sub-nanosecond timespan, involving various physical processes that occur at an atomic level and scale up to macroscopic sizes. In order to investigate such complex phenomena, multi-scale and multi-physics simulations that concurrently capture the various processes are necessary. Such highly coupled simulations include molecular dynamics to model the movement of atoms under heating and electromagnetic field stress, concurrently coupled with particle-in-cell plasma simulations and finite element analysis for electrostatics, electron emission, and heat transfer. These simulations capture the processes that occur when a nanoscopic field emitting metal protrusions enter thermal runaway, evaporates, and ignites vacuum arc plasma, with the purpose of understanding the plasma ignition mechanisms, along with their limitations that can be exploited to minimize breakdown occurrence. The coupled simulation technique is assembled in our open-source software "FEMOCS", which is based on the Deal.II library framework for finite element calculations. Here we present an overview of the aforementioned computational techniques and the corresponding software, as well as the main physical results we have obtained.