COARSE FINE MESH PRECONDITIONERS FOR THE ITERATIVE SOLUTION OF FINITE-ELEMENT PROBLEMS

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.