Preconditioning for diffusion problem with small size high resolution inclusions

摘要

In this paper, we propose and investigate a new preconditioning technique for diffusion problems with multiple small size high contrast inclusions. The inclusions partitioned into two groups. In the first group inclusions the value of diffusion coefficient can be very small, and in the inclusions of the second group it can be very large. The classical P1 finite element discretization is converted in the special algebraic saddle point system. The solution method combines elimination of the DOFs from the first group of inclusions with the Preconditioned Lanczos method with block diagonal preconditioner for the rest of the DOFs. Condition number estimates for the proposed preconditioner are given.