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

0490551 - MÚ 2019 RIV SG eng J - Journal Article
Calvo, Juan Gabriel
On the approximation of a virtual coarse space for domain decomposition methods in two dimensions.
Mathematical Models and Methods in Applied Sciences. Roč. 28, č. 7 (2018), s. 1267-1289. ISSN 0218-2025. E-ISSN 1793-6314
Institutional support: RVO:67985840
Keywords : domain decomposition * irregular subdomain boundaries * nodal elliptic problem * soverlapping Schwarz algorithms
OECD category: Pure mathematics
Impact factor: 3.127, year: 2018
https://www.worldscientific.com/doi/abs/10.1142/S0218202518500343

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.
Permanent Link: http://hdl.handle.net/11104/0284741