P. Letallec et al., A NEUMANN-NEUMANN DOMAIN DECOMPOSITION ALGORITHM FOR SOLVING PLATE AND SHELL PROBLEMS, SIAM journal on numerical analysis, 35(2), 1998, pp. 836-867
We present a new Neumann-Neumann-type preconditioner of large scale li
near systems arising from plate and shell problems. The advantage of t
he new method is a smaller coarse space than those of earlier methods
of the authors; this improves parallel scalability. A new abstract fra
mework for Neumann-Neumann preconditioners is used to prove almost opt
imal convergence properties of the method. The convergence estimates a
re independent of the number of subdomains, coefficient jumps between
subdomains, and depend only polylogarithmically on the number of eleme
nts per subdomain. We formulate and prove an approximate parametric va
riational principle for Reissner-Mindlin elements as the plate thickne
ss approaches zero, which makes the results applicable to a large clas
s of nonlocking elements in everyday engineering use. The theoretical
results are confirmed by computational experiments on model problems a
s well as examples from real world engineering practice.