LU decomposition and forward-backward substitution of recursive bordered block diagonal matrices

Abstract

Tearing methods for large systems have been widely studied and applied over the last decade. Most of the applications used single-level partitioning of a system into subsystems. In the paper, tearing is applied to hierarchically described systems, where each subsystem is itself composed of subsystems, and so on to arbitrary depth. This structure gives rise naturally to ‘recursive’ bordered block diagonal (BBD) matrices, where each diagonal block is itself in the BBD form. Algorithms for LU decomposition and forward and back substitution of such matrices are described.