• Corpus ID: 232478544

Nonlinear optimized Schwarz preconditioner for elliptic optimal control problems

@article{Ciaramella2021NonlinearOS,
  title={Nonlinear optimized Schwarz preconditioner for elliptic optimal control problems},
  author={Gabriele Ciaramella and Felix Kwok and Georg M{\"u}ller},
  journal={ArXiv},
  year={2021},
  volume={abs/2104.00274}
}
where ‖·‖Lr denotes the usual norm for L (Ω) with 1 ≤ r ≤ ∞, the functions yd, f ∈ L (Ω) are given, and the scalar parameters b, c, β ≥ 0 and ν, β ≥ 0 are known. Our model includes problems such as the simplified GinzburgLandau superconductivity equation as well as inverse problems where Lregularization is used to enhance sparsity of the control function u. For simplicity, the domain Ω ⊂ R is assumed to be a rectangle (0, L̃)× (0, L̂). The function φ : R → R is assumed to be of class C, with… 
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