Summary
This paper presents fast iterative solvers for coupled non-linear Finite Element and Boundary Element problems using a damped inexact Newton method á la Axellson and Kaporin. This method converges globally even if the second Gateaux-dervitative does not exist. The used solvers for the linear saddle point problems occuring in the modified Newton algorithm are optimal in the sense, that they are independent of the number of unknowns. These linear solvers are based either on preconditioned conjugate residual like methods, where no Schur Complement construction is required, or on an inner-outer iteration of Axelsson and Vassilevski. Both methods use multigrid of seperate positive semi-definite and negative definite parts of the coupled operator.
The efficiency of the solvers is shown by numerical experiments yielding fast convergence.
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© 1997 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Funken, S.A., Stephan, E.P. (1997). Fast Solvers for Non-Linear Fem-Bem Equations. In: Helmig, R., Jäger, W., Kinzelbach, W., Knabner, P., Wittum, G. (eds) Modeling and Computation in Environmental Sciences. Notes on Numerical Fluid Mechanics (NNFM), vol 59. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89565-3_16
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DOI: https://doi.org/10.1007/978-3-322-89565-3_16
Publisher Name: Vieweg+Teubner Verlag
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