  The direct numerical simulation of metal additive manufacturing processes
such as laser powder bed fusion is challenging due to the vast differences in
spatial and temporal scales. Classical approaches based on locally refined
finite elements combined with time-stepping schemes can only address the
spatial multi-scale nature and provide only limited scaling potential for
massively parallel computations. We address these shortcomings in a space-time
Galerkin framework where the finite element interpolation also includes the
temporal direction. In this setting, we construct four-dimensional meshes that
are locally refined towards the laser spot and allow for varying temporal
accuracy depending on the position in space. By splitting the mesh into
conforming time slabs, we recover a stepwise solution to solve the space-time
problem locally in time at this slab; additionally, we can choose time-slab
sizes significantly larger than classical time-stepping schemes. As a result,
we believe this setting to be well suited for large-scale parallelization. In
our work, we use a continuous Galerkin-Petrov formulation of the nonlinear heat
equation with an apparent heat capacity model to account for the phase change.
We validate our approach by computing the AMB2018-02 benchmark, where we obtain
an excellent agreement with the measured melt pool shape. Using the same setup,
we demonstrate the performance potential of our approach by hatching a square
area with a laser path length of about one meter.
