TY - JOUR
T1 - Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem †
AU - Cho, Durkbin
N1 - Publisher Copyright:
© 2023 by the author.
PY - 2023/5
Y1 - 2023/5
N2 - We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analysis is validated through a set of numerical experiments that illustrate good behavior of the proposed preconditioner with respect to the model parameters.
AB - We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analysis is validated through a set of numerical experiments that illustrate good behavior of the proposed preconditioner with respect to the model parameters.
KW - biharmonic problems
KW - domain decomposition methods
KW - effective preconditioners
KW - finite element method
KW - generalized B-splines
KW - isogeometric analysis
KW - overlapping Schwarz methods
UR - http://www.scopus.com/inward/record.url?scp=85160226701&partnerID=8YFLogxK
U2 - 10.3390/axioms12050452
DO - 10.3390/axioms12050452
M3 - Article
AN - SCOPUS:85160226701
SN - 2075-1680
VL - 12
JO - Axioms
JF - Axioms
IS - 5
M1 - 452
ER -