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Overlapping domain decomposition methods

These methods have been developed in order to gain more flexibility whenever subdomains are of particular interest to the problem and especially if these subdomains are not fixed within the whole problem domain. Examples for such cases are "hot areas" where most of the effects to be approximated take place or where additional effects, i.e. additional governing equations, have to be taken into consideration.
There is a wide range of applications, starting with a better resolution of the areas in question by using a smaller mesh size on the subdomain and not ending with the use of different model equations or new approaches to avoid remeshing when the geometry of the domain changes.
Our attention is mainly focused on methods using mortar techniques for the coupling between the domain and the subdomain.

Introduction to overlapping domain decomposition methods (PDF in German)