Coupled Finite and Boundary Element Tearing and Interconnecting solvers for nonlinear potential problems.

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]