Mc. Dracopoulos et Ma. Crisfield, COARSE FINE MESH PRECONDITIONERS FOR THE ITERATIVE SOLUTION OF FINITE-ELEMENT PROBLEMS, International journal for numerical methods in engineering, 38(19), 1995, pp. 3297-3313
A class of preconditioners built around a coarse/fine mesh framework i
s presented. The proposed method involves the reconstruction of the st
iffness equations using a coarse/fine mesh idealization with relative
degrees-of-freedom derived from the element shape functions. This appr
oach leads naturally to effective preconditioners for iterative solver
s which only require a factorization involving coarse mesh variables.
A further extension is the application of the proposed method to super
-elements In conjunction with substructuring (domain decomposition) te
chniques. The derivation of the coarse/fine mesh discretization via th
e use of transformation matrices, allows a straightforward implementat
ion of the proposed techniques (as well as multigrid type procedures)
within an existing finite element system.