BDDC Deluxe for Isogeometric Analysis

L. Beirão da Veiga; L. F. Pavarino; S. Scacchi; O. B. Widlund; Stefano Zampini

doi:10.1007/978-3-319-18827-0_2

BDDC Deluxe for Isogeometric Analysis

L. Beirão da Veiga, L. F. Pavarino, S. Scacchi, O. B. Widlund, Stefano Zampini

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

2 Scopus citations

Abstract

The main goal of this paper is to design, analyze, and test a BDDC (Balancing Domain Decomposition by Constraints, see [12, 23]) preconditioner for Isogeometric Analysis (IGA), based on a novel type of interface averaging, which we will denote by deluxe scaling, with either full or reduced set of primal constraints. IGA is an innovative numerical methodology, introduced in [17] and first analyzed in [1], where the geometry description of the PDE domain is adopted from a Computer Aided Design (CAD) parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the same NURBS basis functions are also used as the PDEs discrete basis, following an isoparametric paradigm; see the monograph [10]. Recent works on IGA preconditioners have focused on overlapping Schwarz preconditioners [3, 5, 7, 9], multigrid methods [16], and non-overlapping preconditioners [4, 8, 20].

Original language	English (US)
Title of host publication	Domain Decomposition Methods in Science and Engineering XXII
Publisher	Springer Nature
Pages	15-28
Number of pages	14
ISBN (Print)	978-3-319-18826-3
DOIs	https://doi.org/10.1007/978-3-319-18827-0_2
State	Published - 2016

ASJC Scopus subject areas

General Engineering
Modeling and Simulation
Computational Mathematics
Discrete Mathematics and Combinatorics
Control and Optimization

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10.1007/978-3-319-18827-0_2

https://repository.kaust.edu.sa/bitstream/10754/604999/1/Pavarino-Luca-Beirao_Da_Veiga-Lourenco-Scacchi-Simone-Widlund-Olof-Zampini-Stefano-DD22.pdf

Cite this

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title = "BDDC Deluxe for Isogeometric Analysis",

abstract = "The main goal of this paper is to design, analyze, and test a BDDC (Balancing Domain Decomposition by Constraints, see [12, 23]) preconditioner for Isogeometric Analysis (IGA), based on a novel type of interface averaging, which we will denote by deluxe scaling, with either full or reduced set of primal constraints. IGA is an innovative numerical methodology, introduced in [17] and first analyzed in [1], where the geometry description of the PDE domain is adopted from a Computer Aided Design (CAD) parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the same NURBS basis functions are also used as the PDEs discrete basis, following an isoparametric paradigm; see the monograph [10]. Recent works on IGA preconditioners have focused on overlapping Schwarz preconditioners [3, 5, 7, 9], multigrid methods [16], and non-overlapping preconditioners [4, 8, 20].",

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AU - Scacchi, S.

AU - Widlund, O. B.

AU - Zampini, Stefano

N1 - KAUST Repository Item: Exported on 2020-10-01

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N2 - The main goal of this paper is to design, analyze, and test a BDDC (Balancing Domain Decomposition by Constraints, see [12, 23]) preconditioner for Isogeometric Analysis (IGA), based on a novel type of interface averaging, which we will denote by deluxe scaling, with either full or reduced set of primal constraints. IGA is an innovative numerical methodology, introduced in [17] and first analyzed in [1], where the geometry description of the PDE domain is adopted from a Computer Aided Design (CAD) parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the same NURBS basis functions are also used as the PDEs discrete basis, following an isoparametric paradigm; see the monograph [10]. Recent works on IGA preconditioners have focused on overlapping Schwarz preconditioners [3, 5, 7, 9], multigrid methods [16], and non-overlapping preconditioners [4, 8, 20].

AB - The main goal of this paper is to design, analyze, and test a BDDC (Balancing Domain Decomposition by Constraints, see [12, 23]) preconditioner for Isogeometric Analysis (IGA), based on a novel type of interface averaging, which we will denote by deluxe scaling, with either full or reduced set of primal constraints. IGA is an innovative numerical methodology, introduced in [17] and first analyzed in [1], where the geometry description of the PDE domain is adopted from a Computer Aided Design (CAD) parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the same NURBS basis functions are also used as the PDEs discrete basis, following an isoparametric paradigm; see the monograph [10]. Recent works on IGA preconditioners have focused on overlapping Schwarz preconditioners [3, 5, 7, 9], multigrid methods [16], and non-overlapping preconditioners [4, 8, 20].

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ER -

BDDC Deluxe for Isogeometric Analysis

Abstract

ASJC Scopus subject areas

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