An efficient AMG based composite solver for the fully coupled solution of the large scale ion flow field problem

Abstract

• The authors provide more details for the mathematical description of the ion flow field problem and explain the irregularity introduced by the Kapzov hypothesis. • The comparison of the iteration costs under the unipolar and the bipolar cases are present to verify the efficiency of the present method. • The misleading statement about the scalability is rephrased. • The capitalization problems and other typos are revised according to the reviewers’ comments. As the configuration of the HVDC transmission line model becomes more complex, the size of the discretized ion flow field problem grows up to an extremely large degree and the computational time needed for solving the linear system is unacceptable. The algebraic multigrid method(AMG) is a well-known preconditioner for its theoretically optimal performance in solving the elliptic equation. In the present work, the Poisson equation is pre-processed by the classical AMG method and the transport part is preconditioned by the Petrov-Galerkin AMG. These two preconditioners are applied to approximate the ideal preconditioner of the Poisson-Continuity coupled system derived from the block LU factorization. The composite preconditioner significantly improves the convergence of the Krylov iterative solver and the ion flow field problem with million degrees of freedom is solved in less than 20 min. The present work brings a novel and general scheme to improve the efficiency of the traditional algorithm for the multi-physics problems.