Extended isogeometric analysis for material interface problems

Yue Jia; Cosmin Anitescu; Seyed Shahram Ghorashi; Timon Rabczuk

doi:10.1093/imamat/hxu004

Extended isogeometric analysis for material interface problems

Yue Jia, Cosmin Anitescu, Seyed Shahram Ghorashi, Timon Rabczuk

College of Engineering

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

32 Citations (Scopus)

Abstract

We propose an approach to extend the isogeometric analysis (IGA) method to solve material interface problems. The development is carried out through incorporating the advantages of the extended finite element method into the standard IGA approach for solving problems with discontinuities. By applying both the XIGA and IGA methods to solve Poisson's equation problem containing weak discontinuities, we demonstrate that the XIGA achieves the optimal convergence rate, whereas the IGA only converges suboptimally. The proposed method is then successfully applied to solve bimaterial and curved material interface problems.

Original language	English
Pages (from-to)	608-633
Number of pages	26
Journal	IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume	80
Issue number	3
DOIs	https://doi.org/10.1093/imamat/hxu004
Publication status	Published - 2015 Sept 1

Keywords

Isogeometric analysis
NURBS
Poissons equation
XIGA
curved triangular element
enrichment functions
inverse mapping

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1093/imamat/hxu004

Cite this

@article{641b0cae059240ab8d49a563af8011d6,

title = "Extended isogeometric analysis for material interface problems",

abstract = "We propose an approach to extend the isogeometric analysis (IGA) method to solve material interface problems. The development is carried out through incorporating the advantages of the extended finite element method into the standard IGA approach for solving problems with discontinuities. By applying both the XIGA and IGA methods to solve Poisson's equation problem containing weak discontinuities, we demonstrate that the XIGA achieves the optimal convergence rate, whereas the IGA only converges suboptimally. The proposed method is then successfully applied to solve bimaterial and curved material interface problems.",

keywords = "Isogeometric analysis, NURBS, Poissons equation, XIGA, curved triangular element, enrichment functions, inverse mapping",

author = "Yue Jia and Cosmin Anitescu and Ghorashi, {Seyed Shahram} and Timon Rabczuk",

note = "Publisher Copyright: {\textcopyright} 2014 The authors.",

year = "2015",

month = sep,

day = "1",

doi = "10.1093/imamat/hxu004",

language = "English",

volume = "80",

pages = "608--633",

journal = "IMA Journal of Applied Mathematics",

issn = "0272-4960",

publisher = "Oxford University Press",

number = "3",

}

TY - JOUR

T1 - Extended isogeometric analysis for material interface problems

AU - Jia, Yue

AU - Anitescu, Cosmin

AU - Ghorashi, Seyed Shahram

AU - Rabczuk, Timon

PY - 2015/9/1

Y1 - 2015/9/1

N2 - We propose an approach to extend the isogeometric analysis (IGA) method to solve material interface problems. The development is carried out through incorporating the advantages of the extended finite element method into the standard IGA approach for solving problems with discontinuities. By applying both the XIGA and IGA methods to solve Poisson's equation problem containing weak discontinuities, we demonstrate that the XIGA achieves the optimal convergence rate, whereas the IGA only converges suboptimally. The proposed method is then successfully applied to solve bimaterial and curved material interface problems.

AB - We propose an approach to extend the isogeometric analysis (IGA) method to solve material interface problems. The development is carried out through incorporating the advantages of the extended finite element method into the standard IGA approach for solving problems with discontinuities. By applying both the XIGA and IGA methods to solve Poisson's equation problem containing weak discontinuities, we demonstrate that the XIGA achieves the optimal convergence rate, whereas the IGA only converges suboptimally. The proposed method is then successfully applied to solve bimaterial and curved material interface problems.

KW - Isogeometric analysis

KW - NURBS

KW - Poissons equation

KW - XIGA

KW - curved triangular element

KW - enrichment functions

KW - inverse mapping

UR - http://www.scopus.com/inward/record.url?scp=84941203843&partnerID=8YFLogxK

U2 - 10.1093/imamat/hxu004

DO - 10.1093/imamat/hxu004

M3 - Article

AN - SCOPUS:84941203843

SN - 0272-4960

VL - 80

SP - 608

EP - 633

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 3

ER -

Extended isogeometric analysis for material interface problems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this