Space decomposition preconditioners and their application in geomechanics

This paper addresses the use of space decomposition preconditioners for the numerical solution of boundary value problems. As special cases, it deals with the displacement decomposition (DiD) and overlapping domain decomposition (DD) preconditioners. A special attention is also devoted to inexact solution of sub-problems and the use of non-symmetric preconditioners. In these cases, the generalized preconditioned congugate gradient method is shown to be efficient to use. The considered methods are applied to the solution of selected model problems as well as to a large scale problem arising from assessment of stress changes induced by mining activities