Abstract
For complex model problems with coefficient or material distributions with large jumps along or across the domain decomposition interface, the convergence rate of classic domain decomposition methods for scalar elliptic problems usually deteriorates. In particular, the classic condition number bounds [1, 12] will depend on the contrast of the coefficient function. As a remedy, different adaptive coarse spaces, e.g. [4, 13], have been developed which are obtained by solving certain generalized eigenvalue problems on local parts of the interface, i.e., edges and/or faces.
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Heinlein, A., Klawonn, A., Lanser, M., Weber, J. (2022). Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning. In: Brenner, S.C., Chung, E., Klawonn, A., Kwok, F., Xu, J., Zou, J. (eds) Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol 145. Springer, Cham. https://doi.org/10.1007/978-3-030-95025-5_32
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DOI: https://doi.org/10.1007/978-3-030-95025-5_32
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