Journal of Numerical Mathematics
Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri
Managing Editor: Olshanskii, Maxim
Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold
IMPACT FACTOR 2018: 3.107
CiteScore 2018: 2.43
SCImago Journal Rank (SJR) 2018: 1.252
Source Normalized Impact per Paper (SNIP) 2018: 1.618
Mathematical Citation Quotient (MCQ) 2017: 1.68
A full multigrid solution of control-constrained Cauchy–Riemann optimal control problems
The formulation as well as full-multigrid solution of control-constrained Cauchy–Riemann optimal control problems are presented. A constrained distributed control mechanism through divergence and curl sources is considered with mixed boundary conditions. The corresponding optimal solutions are obtained solving a Cauchy–Riemann optimality system consisting of four first-order partial differential equations and two inequality constraints. For the solution of the optimality system, staggered grids and a full-multigrid scheme are considered. The proposed full-multigrid method is based on a coarsening strategy by a factor of three that results in a nested hierarchy of staggered grids. The smoothing procedure consists of a distributed-Gauss–Seidel scheme for the state and adjoint equations and a projected gradient step for the controls. Numerical results validate the effectiveness of the proposed approach.
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