Local adaptive q-enrichments and generalized finite elements for transient heat diffusion problems

Muhammad Iqbal; David Stark; Heiko Gimperlein; M. Shadi Mohamed; Omar Laghrouche

doi:10.1016/j.cma.2020.113359

Local adaptive q-enrichments and generalized finite elements for transient heat diffusion problems

Muhammad Iqbal, David Stark, Heiko Gimperlein, M. Shadi Mohamed, Omar Laghrouche

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

4 Citations (Scopus)

44 Downloads (Pure)

Abstract

A residual a-posteriori error estimate is used in conjunction with a q-adaptive procedure for selecting enrichment functions in the modelling of transient heat diffusion problems with the Generalized Finite Element Method (GFEM). The error estimate allows to assess local as well as global errors of the GFEM solutions and provides a tool to adaptively enrich the approximation space. With the proposed adaptive algorithm, the total number of degrees of freedom (DOFs) is significantly reduced in comparison to uniform enrichment. For a comparable accuracy, a reduction of up to 80% in DOFs is achieved. Moreover, the error estimate captures the deterioration of the conditioning of the system matrix typically encountered in enrichment based methods and enables the possibility of keeping the condition number within an acceptable limit.

Original language	English
Article number	113359
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	372
Early online date	22 Aug 2020
DOIs	https://doi.org/10.1016/j.cma.2020.113359
Publication status	Published - 1 Dec 2020

Access to Document

10.1016/j.cma.2020.113359

Download pdf
© 2020 Elsevier B.V.
Accepted author manuscript, 2.29 MBLicence: CC BY-NC-ND

Cite this

@article{2204ae5ece004b5fbeeb12053539119c,

title = "Local adaptive q-enrichments and generalized finite elements for transient heat diffusion problems",

abstract = "A residual a-posteriori error estimate is used in conjunction with a q-adaptive procedure for selecting enrichment functions in the modelling of transient heat diffusion problems with the Generalized Finite Element Method (GFEM). The error estimate allows to assess local as well as global errors of the GFEM solutions and provides a tool to adaptively enrich the approximation space. With the proposed adaptive algorithm, the total number of degrees of freedom (DOFs) is significantly reduced in comparison to uniform enrichment. For a comparable accuracy, a reduction of up to 80% in DOFs is achieved. Moreover, the error estimate captures the deterioration of the conditioning of the system matrix typically encountered in enrichment based methods and enables the possibility of keeping the condition number within an acceptable limit.",

author = "Muhammad Iqbal and David Stark and Heiko Gimperlein and Mohamed, {M. Shadi} and Omar Laghrouche",

year = "2020",

month = dec,

day = "1",

doi = "10.1016/j.cma.2020.113359",

language = "English",

volume = "372",

journal = "Computer Methods in Applied Mechanics and Engineering",

issn = "0045-7825",

publisher = "Elsevier",

}

TY - JOUR

T1 - Local adaptive q-enrichments and generalized finite elements for transient heat diffusion problems

AU - Iqbal, Muhammad

AU - Stark, David

AU - Gimperlein, Heiko

AU - Mohamed, M. Shadi

AU - Laghrouche, Omar

PY - 2020/12/1

Y1 - 2020/12/1

N2 - A residual a-posteriori error estimate is used in conjunction with a q-adaptive procedure for selecting enrichment functions in the modelling of transient heat diffusion problems with the Generalized Finite Element Method (GFEM). The error estimate allows to assess local as well as global errors of the GFEM solutions and provides a tool to adaptively enrich the approximation space. With the proposed adaptive algorithm, the total number of degrees of freedom (DOFs) is significantly reduced in comparison to uniform enrichment. For a comparable accuracy, a reduction of up to 80% in DOFs is achieved. Moreover, the error estimate captures the deterioration of the conditioning of the system matrix typically encountered in enrichment based methods and enables the possibility of keeping the condition number within an acceptable limit.

AB - A residual a-posteriori error estimate is used in conjunction with a q-adaptive procedure for selecting enrichment functions in the modelling of transient heat diffusion problems with the Generalized Finite Element Method (GFEM). The error estimate allows to assess local as well as global errors of the GFEM solutions and provides a tool to adaptively enrich the approximation space. With the proposed adaptive algorithm, the total number of degrees of freedom (DOFs) is significantly reduced in comparison to uniform enrichment. For a comparable accuracy, a reduction of up to 80% in DOFs is achieved. Moreover, the error estimate captures the deterioration of the conditioning of the system matrix typically encountered in enrichment based methods and enables the possibility of keeping the condition number within an acceptable limit.

U2 - 10.1016/j.cma.2020.113359

DO - 10.1016/j.cma.2020.113359

M3 - Article

SN - 0045-7825

VL - 372

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 113359

ER -

Local adaptive q-enrichments and generalized finite elements for transient heat diffusion problems

Abstract

Access to Document

Fingerprint

Cite this