Some modifications of Sobolev spaces and non-linear boundary value problems
Given a fibered manifold , a 2-connection on means a section . The authors determine all first order natural operators transforming a 2-connection on and a classical linear connection on into a connection on . (The proof implies that there is no first order natural operator transforming 2-connections on into connections on .) Using this result, the authors deduce several properties of characterizable connections on .
We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may...