An efficient approach for solving the HVDC ion flow field problem using the PDE constrained optimization scheme

In order to have a better performance for solving the ion flow field problem, an efficient numerical approach is proposed. The over specified boundary condition introduced by the Kapzov hypothesis is a leading cause of the performance issue in the study of ion flow field. The inversion algorithm to recover the ion density on the conductor surfaces provides a fresh perspective on solving the ion flow field problem. However, the great computational burden of generating the sensitivity matrix limits the application of the inversion algorithm in the practical problems. In this article, the boundary value problem with over specified boundary condition is formulated into a constrained optimization problem and the all-at-once scheme is utilized to minimized the residual of the partial differential equation (PDE) constraints and the objective function. Numerical experiments show that the PDE constrained optimization based algorithm preserves the accuracy of the inversion algorithm at less than 10% computational cost. As an improvement of the inversion algorithm, the new approach presents an efficient way to handle the ion flow field problem under the variety of complicated scenes.