Improved Algebraic Preconditioning for Multiscale Electromagnetic Problems

Abstract

An improved scheme for the algebraic preconditioners is proposed in this letter to accelerate the iterative convergence rate of the multiscale electromagnetic problems, in which the overcrowded leaf boxes of the multilevel fast multipole algorithm are recursively bisected with the application of the multilevel accelerated Cartesian expansion algorithm to maintain the computational efficiency. Due to a lack of some strong couplings measured by the relative distance between the testing/basis functions, the algebraic preconditioners constructed by filtering the near-field interaction matrix of the fast algorithm are consequently ineffective. To alleviate the adverse effect of the multiscale-size boxes, the proposed scheme constructs the preconditioners on higher levels rather than the leaf level of the related fast algorithm, thus speeding up the iterative convergence rate significantly. Moreover, the rank-revealing adaptive cross approximation algorithm is first introduced to compute and store the enlarged computational domain of the preconditioner. As a result, there is only a modest increase in the computational cost. Numerical experiments have been performed to demonstrate the effectiveness and efficiency of the proposed method.