Abstract
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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