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Domain Decomposition and Other Advanced Issues

  • Christopher G. ProvatidisEmail author
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 256)

Abstract

While previous chapters focused on the performance of single macroelements, here we study the case of assembling adjacent CAD-based macroelements in which the computational domain has been decomposed. The discussion starts with Coons–Gordon interpolation using Lagrange polynomials, in which no difficulty appears provided the same nodes are used along an interface being at the same time an entire side in both adjacent patches. Obviously, the aforementioned easiness appears to all tensor-product CAD-based macroelements (Bézier, B-splines). If, however, the interface between two adjacent patches is not an entire edge, then Gordon interpolation has to be extended in a proper way using artificial external nodes. The case of two macroelements that share the same edge but do not have the same number of nodes along it is also studied. A short discussion is devoted to issues such as closed surface patches and local control. Numerical examples refer to potential problems (heat flow and acoustics) and elasticity problems (tension and bending).

Keywords

Domain decomposition Mortar finite element methods Lagrange multiplier Master–slave Mismatching Artificial nodes Degeneration Non-rational Bernstein–Bézier and B-splines Test cases 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringNational Technical University of AthensAthensGreece

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