A NEUMANN-NEUMANN DOMAIN DECOMPOSITION ALGORITHM FOR SOLVING PLATE AND SHELL PROBLEMS

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.