Domain Decomposition Algorithms for PDEproblems with Large Scale

We consider a Schur complement BPS-like domain decomposition algorithm for the 2D drift-diiusion equations arising from semiconductor modeling. In particular, we focus on two problems: anisotropic phenomena and large changes in the PDE coeecients as one moves spatial within the domain. The preconditioners that we discuss are essentially BPS preconditioners 2] where the interface coupling is approximated using band matrices generated by the probing technique 3]. To cope with anisotropic phenomena, we introduce additional band matrices (in the context of the probe preconditioner) to approximate the coupling between neighboring interfaces. To address coeecient variations over the domain, we make use of the close connection between domain decomposition and multigrid and introduce specialized interpolation, projection, and averaging techniques to develop an accurate coarse grid approximation. We demonstrate the beneets of the new approach using computational experiments.