TY - JOUR
T1 - Overlapping Schwarz methods for isogeometric analysis based on generalized B-splines
AU - Cho, Durkbin
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Generalized B-splines (GB-splines) are a special class of Tchebycheff B-splines that are smooth piecewise function with sections in more general spaces. GB-splines allow for an exact representation of conic sections as well as transcendental curves and thus they become very attractive for geometrical modeling and numerical simulation. In this paper, we present overlapping Schwarz preconditioners for elliptic problems discretized with isogeometric analysis based on GB-splines. An h-analysis of the proposed preconditioners shows an optimal convergence rate bound that is scalable in the number of subdomains and that is linear in the ratio between subdomain and overlap sizes. Numerical results in two- and three-dimensional tests confirm this analysis and also illustrate the good convergence properties of the preconditioner with respect to the discretization parameters, the domain deformation and the jumping coefficients.
AB - Generalized B-splines (GB-splines) are a special class of Tchebycheff B-splines that are smooth piecewise function with sections in more general spaces. GB-splines allow for an exact representation of conic sections as well as transcendental curves and thus they become very attractive for geometrical modeling and numerical simulation. In this paper, we present overlapping Schwarz preconditioners for elliptic problems discretized with isogeometric analysis based on GB-splines. An h-analysis of the proposed preconditioners shows an optimal convergence rate bound that is scalable in the number of subdomains and that is linear in the ratio between subdomain and overlap sizes. Numerical results in two- and three-dimensional tests confirm this analysis and also illustrate the good convergence properties of the preconditioner with respect to the discretization parameters, the domain deformation and the jumping coefficients.
KW - Domain decomposition methods
KW - Generalized B-splines
KW - Isogeometric analysis
KW - Overlapping Schwarz
KW - Scalable preconditioners
UR - http://www.scopus.com/inward/record.url?scp=85091798297&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2020.113430
DO - 10.1016/j.cma.2020.113430
M3 - Article
AN - SCOPUS:85091798297
SN - 0045-7825
VL - 372
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 113430
ER -