Domain Decomposition Methods for Problems in H(curl)

 

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Detalles Bibliográficos
Autor: Calvo Alpízar, Juan Gabriel
Formato: tesis doctoral
Fecha de Publicación:2015
Descripción:Two domain decomposition methods for solving vector field problems posed in H(curl) and discretized with Nedelec finite elements are considered. These finite elements are conforming in H(curl). A two-level overlapping Schwarz algorithm in two dimensions is analyzed, where the subdomains are only assumed to be uniform in the sense of Peter Jones. The coarse space is based on energy minimization and its dimension equals the number of interior subdomain edges. Local direct solvers are based on the overlapping subdomains. The bound for the condition number depends only on a few geometric parameters of the decomposition. This bound is independent of jumps in the coefficients across the interface between the subdomains for most of the different cases considered. A bound is also obtained for the condition number of a balancing domain decomposition by constraints (BDDC) algorithm in two dimensions, with Jones subdomains. For the primal variable space, a continuity constraint for the tangential average over each interior subdomain edge is imposed. For the averaging operator, a new technique named deluxe scaling is used. The optimal bound is independent of jumps in the coefficients across the interface between the subdomains. Furthermore, a new coarse function for problems in three dimensions is introduced, with only one degree of freedom per subdomain edge. In all the cases, it is established that the algorithms are scalable. Numerical results that verify the results are provided, including some with subdomains with fractal edges and others obtained by a mesh partitioner.
País:Kérwá
Institución:Universidad de Costa Rica
Repositorio:Kérwá
OAI Identifier:oai:https://www.kerwa.ucr.ac.cr:10669/75137
Acceso en línea:https://cs.nyu.edu/media/publications/TR2015-974.pdf
https://search.proquest.com/docview/1754416536/fulltextPDF/88A086563B514623PQ/1?accountid=28692
https://hdl.handle.net/10669/75137
Access Level:acceso abierto
Palabra clave:Pure sciences
Applied sciences
BDDC
Domain Decomposition
Preconditioners
Maxwell's equations
Overlapping Schwarz
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