A PARTIALLY SEQUENTIAL PRECONDITIONER FOR A PARALLEL AND EFFICIENT FINITE-ELEMENT SOLUTION

A coarse/fine mesh preconditioner is presented which can be successful ly applied in a parallel finite element context. The proposed method i nvolves the reconstruction of the stiffness equations using a coarse/f ine mesh idealisation with relative degrees-of-freedom derived directl y from the element shape functions. This approach leads naturally to a n effective preconditioner which only requires a direct solution on co arse mesh variables and which is implemented sequentially. On the othe r hand, the preconditioning of the fine mesh variables involves a perf ectly parallelizable diagonal scaling. The proposed derivation of the coarse/fine mesh discretization via the use of transformation matrices can be very efficient and is directly applicable to existing finite e lememt solution procedures.