de Valerio, M.; Schäfer, M. Domain decomposition methods for the numerical solution of elliptic partial differential equations on array processors. (English) Zbl 0801.65117 Evans, D. J. (ed.) et al., Parallel computing ’91. Proceedings of the international conference, held in London, GB, 3-6 September 1991. Amsterdam etc.: North-Holland. Adv. Parallel Comput. 4, 167-173 (1992). Summary: We consider a domain decomposition technique due to J. H. Bramble, J. E. Pasciak and A. H. Schatz [Math. Comput. 47, 103-134 (1986; Zbl 0615.65112)] for the numerical solution of elliptic partial differential equations that is well adapted for array processors. The solution is performed by a preconditioned conjugate gradient method, in which the domain decomposition technique is embedded as the preconditioner. The domain is decomposed into boxes which for the most part can be handled independently from each other. Numerical experiments confirm the theoretical considerations and illustrate the capabilities of the algorithm.For the entire collection see [Zbl 0762.00005]. MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 65Y05 Parallel numerical computation 65F35 Numerical computation of matrix norms, conditioning, scaling 35J25 Boundary value problems for second-order elliptic equations Keywords:numerical experiments; finite element; domain decomposition; array processors; preconditioned conjugate gradient method Citations:Zbl 0615.65112 PDFBibTeX XMLCite \textit{M. de Valerio} and \textit{M. Schäfer}, Adv. Parallel Comput. 4, 167--173 (1992; Zbl 0801.65117)