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Published in:
Initial Attempts on CAD/CAE Integration Read chapter Read first chapter

2019 | OriginalPaper | Chapter

13. Domain Decomposition and Other Advanced Issues

Author : Christopher G. Provatidis

Published in: Precursors of Isogeometric Analysis

Publisher: Springer International Publishing

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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).

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previous chapter The Boundary Element Method Using CAD-Based Macroelements
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Metadata
Title
Domain Decomposition and Other Advanced Issues
Author
Christopher G. Provatidis
Copyright Year
2019
Book
Precursors of Isogeometric Analysis

Print ISBN: 978-3-030-03888-5

Electronic ISBN: 978-3-030-03889-2

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-03889-2_13

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