scholarly journals A Discontinuous Galerkin like Coarse Space correction for Domain Decomposition Methods with continuous local spaces: the DCS-DGLC Algorithm

2014 ◽  
Vol 45 ◽  
pp. 275-284 ◽  
Author(s):  
Kévin Santugini
Keyword(s):  
Domain Decomposition ◽  
Discontinuous Galerkin ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Coarse Space

On the approximation of a virtual coarse space for domain decomposition methods in two dimensions

2018 ◽  
Vol 28 (07) ◽  
pp. 1267-1289 ◽  
Author(s):  
Juan G. Calvo
Keyword(s):  
Domain Decomposition ◽  
Numerical Experiments ◽  
Decomposition Methods ◽  
Extension Operator ◽  
Two Dimensions ◽  
Computational Time ◽  
Domain Decomposition Methods ◽  
Polygonal Elements ◽  
Schwarz Algorithm ◽  
Coarse Space

A new extension operator for a virtual coarse space is presented which can be used in domain decomposition methods for nodal elliptic problems in two dimensions. In particular, a two-level overlapping Schwarz algorithm is considered and a bound for the condition number of the preconditioned system is obtained. This bound is independent of discontinuities across the interface. The extension operator saves computational time compared to previous studies where discrete harmonic extensions are required and it is suitable for general polygonal meshes and irregular subdomains. Numerical experiments that verify the result are shown, including some with regular and irregular polygonal elements and with subdomains obtained by a mesh partitioner.

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