Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains

S.K. Tomar; P. Dutt; B.V. Ratish Kumar

Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains

S.K. Tomar, P. Dutt, B.V. Ratish Kumar

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Spectral element methods (SEM) exhibit exponential convergence only when the solution of the problem is sufficiently regular. However, the solution develops a singularity when the boundary of the domain is non-smooth. The accuracy of the SEM is then deteriorated and they offer no advantage over low order methods. Such problems frequently occur in many important physical applications, for example in structural mechanics. A new h-p spectral element method is presented which resolves this form of singularity and gives asymptotically faster results than conventional methods, while retaining the same order of convergence. Moreover, the computational algorithm is devised to harness the potential of widely available parallel computers.

Original language	English
Title of host publication	NMCM 2002
Subtitle of host publication	an Euro Conference on Numerical Mathematics and Computational Mechanics, July 15-19, 2002, University of Miskolc, Miskolc, Hungary
Place of Publication	Miskolc, Hungary
Publisher	University of Miskolc
Number of pages	12
Publication status	Published - 15 Jul 2002
Event	Euro Conference on Numerical Mathematics and Computational Mechanics, NMCM 2002 - University of Miskolc, Miskolc, Hungary Duration: 15 Jul 2002 → 19 Jul 2002

Conference

Conference	Euro Conference on Numerical Mathematics and Computational Mechanics, NMCM 2002
Abbreviated title	NMCM
Country	Hungary
City	Miskolc
Period	15/07/02 → 19/07/02

Keywords

METIS-207964
EWI-16262
IR-74769

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Tomar-02-NMCM
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title = "Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains",

abstract = "Spectral element methods (SEM) exhibit exponential convergence only when the solution of the problem is sufficiently regular. However, the solution develops a singularity when the boundary of the domain is non-smooth. The accuracy of the SEM is then deteriorated and they offer no advantage over low order methods. Such problems frequently occur in many important physical applications, for example in structural mechanics. A new h-p spectral element method is presented which resolves this form of singularity and gives asymptotically faster results than conventional methods, while retaining the same order of convergence. Moreover, the computational algorithm is devised to harness the potential of widely available parallel computers.",

keywords = "METIS-207964, EWI-16262, IR-74769",

author = "S.K. Tomar and P. Dutt and {Ratish Kumar}, B.V.",

note = "The financial support provided by the CSIR-India (Project no. 9/92(123)/95-EMR-I) and ARDB-India (Project no. 95255) for this work is gratefully acknowledged.; Euro Conference on Numerical Mathematics and Computational Mechanics, NMCM 2002, NMCM ; Conference date: 15-07-2002 Through 19-07-2002",

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publisher = "University of Miskolc",

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Tomar, SK, Dutt, P & Ratish Kumar, BV 2002, Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains. in NMCM 2002: an Euro Conference on Numerical Mathematics and Computational Mechanics, July 15-19, 2002, University of Miskolc, Miskolc, Hungary . University of Miskolc, Miskolc, Hungary, Euro Conference on Numerical Mathematics and Computational Mechanics, NMCM 2002, Miskolc, Hungary, 15/07/02.

Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains. / Tomar, S.K.; Dutt, P.; Ratish Kumar, B.V.

NMCM 2002: an Euro Conference on Numerical Mathematics and Computational Mechanics, July 15-19, 2002, University of Miskolc, Miskolc, Hungary . Miskolc, Hungary : University of Miskolc, 2002.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains

AU - Tomar, S.K.

AU - Dutt, P.

AU - Ratish Kumar, B.V.

N1 - The financial support provided by the CSIR-India (Project no. 9/92(123)/95-EMR-I) and ARDB-India (Project no. 95255) for this work is gratefully acknowledged.

PY - 2002/7/15

Y1 - 2002/7/15

N2 - Spectral element methods (SEM) exhibit exponential convergence only when the solution of the problem is sufficiently regular. However, the solution develops a singularity when the boundary of the domain is non-smooth. The accuracy of the SEM is then deteriorated and they offer no advantage over low order methods. Such problems frequently occur in many important physical applications, for example in structural mechanics. A new h-p spectral element method is presented which resolves this form of singularity and gives asymptotically faster results than conventional methods, while retaining the same order of convergence. Moreover, the computational algorithm is devised to harness the potential of widely available parallel computers.

AB - Spectral element methods (SEM) exhibit exponential convergence only when the solution of the problem is sufficiently regular. However, the solution develops a singularity when the boundary of the domain is non-smooth. The accuracy of the SEM is then deteriorated and they offer no advantage over low order methods. Such problems frequently occur in many important physical applications, for example in structural mechanics. A new h-p spectral element method is presented which resolves this form of singularity and gives asymptotically faster results than conventional methods, while retaining the same order of convergence. Moreover, the computational algorithm is devised to harness the potential of widely available parallel computers.

KW - METIS-207964

KW - EWI-16262

KW - IR-74769

M3 - Conference contribution

BT - NMCM 2002

PB - University of Miskolc

CY - Miskolc, Hungary

T2 - Euro Conference on Numerical Mathematics and Computational Mechanics, NMCM 2002

Y2 - 15 July 2002 through 19 July 2002

ER -