Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem †

Durkbin Cho

doi:10.3390/axioms12050452

Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem †

Durkbin Cho

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	452
Journal	Axioms
Volume	12
Issue number	5
DOIs	https://doi.org/10.3390/axioms12050452
State	Published - May 2023

Keywords

biharmonic problems
domain decomposition methods
effective preconditioners
finite element method
generalized B-splines
isogeometric analysis
overlapping Schwarz methods

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10.3390/axioms12050452

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title = "Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem †",

abstract = "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.",

keywords = "biharmonic problems, domain decomposition methods, effective preconditioners, finite element method, generalized B-splines, isogeometric analysis, overlapping Schwarz methods",

author = "Durkbin Cho",

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year = "2023",

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doi = "10.3390/axioms12050452",

language = "English",

volume = "12",

journal = "Axioms",

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T1 - Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem †

AU - Cho, Durkbin

PY - 2023/5

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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 - https://www.scopus.com/pages/publications/85160226701

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 -

Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem †

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Keywords

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