  A design optimization framework for process parameters of additive
manufacturing based on finite element simulation is proposed. The finite
element method uses a coupled thermomechanical model developed for fused
deposition modeling from the authors' previous work. Both gradient-based and
gradient-free optimization methods are proposed. The gradient-based approach,
which solves a PDE-constrained optimization problem, requires sensitivities
computed from the fully discretized finite element model. We show the
derivation of the sensitivities and apply them in a projected gradient descent
algorithm. For the gradient-free approach, we propose two distinct algorithms:
a local search algorithm called the method of local variations and a Bayesian
optimization algorithm using Gaussian processes. To illustrate the
effectiveness and differences of the methods, we provide two-dimensional design
optimization examples using all three proposed algorithms.
