Coarse/fine mesh preconditioners for the iterative solution of finite element problems

A class of preconditioners built around a coarse/fine mesh framework is presented. The proposed method involves the reconstruction of the stiffness equations using a coarse/fine mesh idealization with relative degrees‐of‐freedom derived from the element shape functions. This approach leads naturally to effective preconditioners for iterative solvers 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) techniques. The derivation of the coarse/fine mesh discretization via the use of transformation matrices, allows a straightforward implementation of the proposed techniques (as well as multigrid type procedures) within an existing finite element system.