An overlapping Schwarz method for virtual element discretizations in two dimensions

 

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Detalles Bibliográficos
Autor: Calvo Alpízar, Juan Gabriel
Formato: artículo original
Fecha de Publicación:2019
Descripción:A new coarse space for domain decomposition methods is presented for nodal ellipticproblems in two dimensions. The coarse space is derived from the novel virtual elementmethods and therefore can accommodate quite irregular polygonal subdomains. It hasthe advantage with respect to previous studies that no discrete harmonic extensionsare required. The virtual element method allows us to handle polygonal meshes andthe algorithm can then be used as a preconditioner for linear systems that arise froma discretization with such triangulations. A bound is obtained for the condition numberof the preconditioned system by using a two-level overlapping Schwarz algorithm, butthe coarse space can also be used for different substructuring methods. This bound isindependent of jumps in the coefficient across the interface between the subdomains.Numerical experiments that verify the result are shown, including some with triangular,square, hexagonal and irregular elements and with irregular subdomains obtained by a mesh partitioner
País:Kérwá
Institución:Universidad de Costa Rica
Repositorio:Kérwá
OAI Identifier:oai:kerwa.ucr.ac.cr:10669/77379
Acceso en línea:https://www.sciencedirect.com/science/article/pii/S0898122118306400?via%3Dihub
https://hdl.handle.net/10669/77379
Palabra clave:Overlapping Schwarz algorithms
Nodal elliptic problems
Domain Decomposition
Irregular subdomain boundaries
Virtual element methods