WIAS Preprint No. 3080, (2023)

Optimal beam forming for laser materials processing


Authors

  • Arenas, Manuel J.
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Lasarzik, Robert
    ORCID: 0000-0002-1677-6925

2020 Mathematics Subject Classification

  • 35A35 35Q35 49J20 76A15

Keywords

  • Quasi-linear elliptic equation, transport dominated PDE, additive manufacturing, selective laser, melting, finite element method, simulation

DOI

10.20347/WIAS.PREPRINT.3080

Abstract

We investigate an optimal control problem related to laser material treatments such as welding, remelting, hardening, or the 3D printing of metal components. The mathematical model leads to the investigation of a quasilinear elliptic state system with additional non-monotone lower-oder terms. We analyze the state system, derive first order optimality conditions and show first results for beam shaping.

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