Inexact Block Diagonal Preconditioners to Mitigate the Effects of Relative Differences in Material Stiffnesses

Abstract

Finite-element analysis of many soil-structure interaction problems involves material zones of widely differing stiffnesses. The large relative differences in material stiffnesses usually result in an ill-conditioned system for which practical preconditioners become ineffective for the iterative solution of such systems. The study suggests that a block diagonal preconditioner can exploit such differences. However, the theoretical preconditioner is expensive for practical use. Less costly block diagonal preconditioners are numerically evaluated for various inexact forms of the blocks in conjunction with conjugate gradient solver. The study includes analysis of two representative soil-structure interaction problems and proposes two simplified block diagonal preconditioners that effectively mitigate such material ill conditionings.