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arXiv · 1703.10796

A linear Uzawa-type solver for nonlinear transmission problems

Thomas Führer·Dirk Praetorius
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Abstract

We propose an Uzawa-type iteration for the Johnson-N\'ed\'elec 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. 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-N\'ed\'elec formulation requires some restrictions on the ellipticity (resp. strong monotonicity constant) in the interior domain, our Uzawa-type solver avoids such assumptions.

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Thomas Führer, Dirk Praetorius. 2017-03-31. A linear Uzawa-type solver for nonlinear transmission problems. https://doi.org/10.1016/j.camwa.2017.12.035

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