An Efficient Preconditioner Based on Adaptive Grouping Technique for Multiscale Problems

It is well known that the matrix condition number of discretized formulation for analyzing multiscale objects is very large, because the multiscale objects include the interaction between discrete unknowns in different sizes. The traditional efficient preconditioners for analysis of homogeneous objects are not efficient anymore or cannot be directly extended for the solution of multiscale objects. A good quality compressed block decomposition preconditioner is constructed to speed up the convergence rate of Krylov iterations in this communication by using the adaptive grouping technique. Meanwhile, the multilevel mymargin QR algorithm is utilized to accelerate the matrix-vector product operations. A series of numerical results show that this novel preconditioner is very effective in electromagnetic scattering calculation and can reduce simulation time significantly.