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Abstract: Finite element tearing and interconnecting (FETI) methods and boundary element tearing and interconnecting (BETI) methods are special iterative substructuring methods with Lagrange multipliers. For elliptic boundary value problems on bounded domains, the condition number of these methods can be rigorously bounded by , where H is the subdomain diameter and h the mesh size. The constant C is independent of H, h and possible jumps in the coefficients of the partial differential equation. In certain situations, e.g., in electromagnetic field computations, instead of imposing artificial boundary conditions one may be interested in modelling the real physical behaviour in an exterior domain with a radiation condition. In this work we analyze one-level BETI methods for such unbounded domains and show explicit condition number estimates similar to the one above. Our theoretical results are confirmed in numerical experiments. [Copyright &y& Elsevier]

The present paper deals with the numerical solution of boundary value problems for nonlinear potential equations of the form –∇· [ν(|∇ u|) ∇ u] = f arising e. g. in 2D magnetic field computations. We apply Newton's method to the nonlinear variational formulation and solve the linearized problems with coupled Finite and Boundary Element Tearing and Interconnecting (FETI/BETI) methods. The spectrum of the subdomain Jacobi matrices may show high variation due to the nonlinear behavior of the reluctivity on ferromagnetic subdomains. A special preconditioner is proposed to overcome these problems. In order to get a good initial guess for the Newton iteration, we use the nested iteration strategy based on a hierarchy of nested grids. Finally, we discuss our first numerical results obtained from the numerical solution of some 2D magnetostatic model problems. [ABSTRACT FROM AUTHOR]