A new parallel domain decomposition method for the adaptive finite elementsolution of elliptic partial differential equations

We present a new domain decomposition algorithm for the parallel finite ele ment solution of elliptic partial differential equations, As with most para llel domain decomposition methods each processor is assigned one or more su bdomains and an iteration is devised which allows the processors to solve t heir own subproblem(s) concurrently. The novel feature of this algorithm ho wever is that each of these subproblems is defined over the entire domain-a lthough the vast majority of the degrees of freedom for each subproblem are associated with a single subdomain (owned by the corresponding processor). This ensures that a global mechanism is contained within each of the subpr oblems tackled and so no separate coarse grid solve is required in order to achieve rapid convergence of the overall iteration, Furthermore, by follow ing the paradigm introduced in [15], it is demonstrated that this domain de composition solver may be coupled easily with a conventional mesh refinemen t code, thus allowing the accuracy, reliability and efficiency of mesh adap tivity to be utilized in a well load-balanced manner, Finally, numerical ev idence is presented which suggests that this technique has significant pote ntial, both in terms of the rapid convergence properties and the efficiency of the parallel implementation, Copyright (C) 2001 John Wiley & Sons, Ltd.