Mc. Dracopoulos et Ma. Crisfield, A PARTIALLY SEQUENTIAL PRECONDITIONER FOR A PARALLEL AND EFFICIENT FINITE-ELEMENT SOLUTION, Computing systems in engineering, 6(6), 1995, pp. 549-561
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.