A linear Uzawa-type FEM–BEM solver for nonlinear transmission problems. (15th April 2018)

• Record Type: Journal Article
• Authors: Führer, Thomas; Praetorius, Dirk
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 8(2018)
• Page Start: 2678
• Page End: 2697
• Publication Date: 2018-04-15
• Subjects: FEM–BEM coupling -- Adaptivity -- Uzawa algorithm; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.12.035
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We propose a fully discrete Uzawa-type iteration for the Johnson–Nédélec formulation of a Laplace-type transmission problem with possible (strongly monotone) nonlinearity in the interior domain. In each step, we sequentially solve one BEM for the weakly-singular integral equation associated with the Laplace-operator and one FEM for the linear Yukawa equation. In particular, the nonlinearity is only evaluated to build the right-hand side of the Yukawa equation. The algorithm includes the inexact solution of the BEM/FEM part by a preconditioned CG method. We prove that the proposed method leads to linear convergence with respect to the number of Uzawa iterations. Moreover, while the current analysis of a direct FEM–BEM discretization of the Johnson–Nédélec formulation requires some restrictions on the ellipticity (resp. strong monotonicity constant) in the interior domain, our Uzawa-type solver avoids such assumptions.