An element-based displacement preconditioner for linear elasticity problems
Computers and Structures
| Hi-index | 0.00 |
Preconditioning methods are widely used in conjunction with the conjugate gradient method for solving large sparse symmetric linear systems arising from the discretisation of selfadjoint linear elliptic partial differential equations. Many different preconditioners have been proposed, and they are generally analysed and compared using model problems: simple discretisations of Laplacian operators on regular computational grids, generally in two space dimensions. For such model problems there are highly competitive multigrid methods, and it is principally for geometrically irregular (nonmodel) problems that the applicability and economy of preconditioned conjugate gradient methods are most useful. This is particularly true for problems on irregular unstructured three-dimensional grids. This paper is concerned with the comparison of preconditioners for finite element discretisations of three-dimensional selfadjoint elliptic problems on irregular and unstructured computational grids. It is argued that simple preconditioners, which are inferior for regular grid problems in two dimensions, are competitive for irregular grid problems in three dimensions.