Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

Adriano M.A. Côrtes; Philippe Vignal; Adel Sarmiento; Daniel García; Nathan Collier; Lisandro Dalcin; Victor M. Calo

doi:10.1007/978-3-662-45483-1_17

Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

Adriano M.A. Côrtes, Philippe Vignal, Adel Sarmiento, Daniel García, Nathan Collier, Lisandro Dalcin, Victor M. Calo

Computational Earth Sciences Group

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

6 Scopus citations

Abstract

In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phasefield models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

Original language	English
Title of host publication	High Performance Computing - First HPCLATAM - CLCAR - Latin American Joint Conference, CARLA 2014, Proceedings
Editors	Gonzalo Hernández, Carlos Jaime Barrios Hernández, Gilberto Díaz, Carlos García Garino, Sergio Nesmachnow, Tomás Pérez-Acle, Mario Storti, Mariano Vázquez
Publisher	Springer Verlag
Pages	236-247
Number of pages	12
ISBN (Electronic)	9783662454824
DOIs	https://doi.org/10.1007/978-3-662-45483-1_17
State	Published - 2014
Event	1st High-Performance Computing Latin America Community, HPCLATAM-CLCAR 2014 and Latin American Joint Conference, CARLA 2014 - Valparaiso, Chile Duration: Oct 20 2014 → Oct 22 2014

Publication series

Name	Communications in Computer and Information Science
Volume	485
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	1st High-Performance Computing Latin America Community, HPCLATAM-CLCAR 2014 and Latin American Joint Conference, CARLA 2014
Country/Territory	Chile
City	Valparaiso
Period	10/20/14 → 10/22/14

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2014.

Keywords

Finite elements
High-performance computing
Highorder partial differential equations
Isogeometric analysis
Phase-field modeling

Access to Document

10.1007/978-3-662-45483-1_17

Cite this

Côrtes, A. M. A., Vignal, P., Sarmiento, A., García, D., Collier, N., Dalcin, L., & Calo, V. M. (2014). Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework. In G. Hernández, C. J. B. Hernández, G. Díaz, C. G. Garino, S. Nesmachnow, T. Pérez-Acle, M. Storti, & M. Vázquez (Eds.), High Performance Computing - First HPCLATAM - CLCAR - Latin American Joint Conference, CARLA 2014, Proceedings (pp. 236-247). (Communications in Computer and Information Science; Vol. 485). Springer Verlag. https://doi.org/10.1007/978-3-662-45483-1_17

Côrtes, Adriano M.A. ; Vignal, Philippe ; Sarmiento, Adel et al. / Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework. High Performance Computing - First HPCLATAM - CLCAR - Latin American Joint Conference, CARLA 2014, Proceedings. editor / Gonzalo Hernández ; Carlos Jaime Barrios Hernández ; Gilberto Díaz ; Carlos García Garino ; Sergio Nesmachnow ; Tomás Pérez-Acle ; Mario Storti ; Mariano Vázquez. Springer Verlag, 2014. pp. 236-247 (Communications in Computer and Information Science).

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abstract = "In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phasefield models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.",

keywords = "Finite elements, High-performance computing, Highorder partial differential equations, Isogeometric analysis, Phase-field modeling",

author = "C{\^o}rtes, {Adriano M.A.} and Philippe Vignal and Adel Sarmiento and Daniel Garc{\'i}a and Nathan Collier and Lisandro Dalcin and Calo, {Victor M.}",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2014.; 1st High-Performance Computing Latin America Community, HPCLATAM-CLCAR 2014 and Latin American Joint Conference, CARLA 2014 ; Conference date: 20-10-2014 Through 22-10-2014",

year = "2014",

doi = "10.1007/978-3-662-45483-1_17",

language = "English",

series = "Communications in Computer and Information Science",

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editor = "Gonzalo Hern{\'a}ndez and Hern{\'a}ndez, {Carlos Jaime Barrios} and Gilberto D{\'i}az and Garino, {Carlos Garc{\'i}a} and Sergio Nesmachnow and Tom{\'a}s P{\'e}rez-Acle and Mario Storti and Mariano V{\'a}zquez",

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Côrtes, AMA, Vignal, P, Sarmiento, A, García, D, Collier, N, Dalcin, L & Calo, VM 2014, Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework. in G Hernández, CJB Hernández, G Díaz, CG Garino, S Nesmachnow, T Pérez-Acle, M Storti & M Vázquez (eds), High Performance Computing - First HPCLATAM - CLCAR - Latin American Joint Conference, CARLA 2014, Proceedings. Communications in Computer and Information Science, vol. 485, Springer Verlag, pp. 236-247, 1st High-Performance Computing Latin America Community, HPCLATAM-CLCAR 2014 and Latin American Joint Conference, CARLA 2014, Valparaiso, Chile, 10/20/14. https://doi.org/10.1007/978-3-662-45483-1_17

Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework. / Côrtes, Adriano M.A.; Vignal, Philippe; Sarmiento, Adel et al.
High Performance Computing - First HPCLATAM - CLCAR - Latin American Joint Conference, CARLA 2014, Proceedings. ed. / Gonzalo Hernández; Carlos Jaime Barrios Hernández; Gilberto Díaz; Carlos García Garino; Sergio Nesmachnow; Tomás Pérez-Acle; Mario Storti; Mariano Vázquez. Springer Verlag, 2014. p. 236-247 (Communications in Computer and Information Science; Vol. 485).

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

TY - GEN

T1 - Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

AU - Côrtes, Adriano M.A.

AU - Vignal, Philippe

AU - Sarmiento, Adel

AU - García, Daniel

AU - Collier, Nathan

AU - Dalcin, Lisandro

AU - Calo, Victor M.

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2014.

PY - 2014

Y1 - 2014

N2 - In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phasefield models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

AB - In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phasefield models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

KW - Finite elements

KW - High-performance computing

KW - Highorder partial differential equations

KW - Isogeometric analysis

KW - Phase-field modeling

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BT - High Performance Computing - First HPCLATAM - CLCAR - Latin American Joint Conference, CARLA 2014, Proceedings

A2 - Hernández, Gonzalo

A2 - Hernández, Carlos Jaime Barrios

A2 - Díaz, Gilberto

A2 - Garino, Carlos García

A2 - Nesmachnow, Sergio

A2 - Pérez-Acle, Tomás

A2 - Storti, Mario

A2 - Vázquez, Mariano

PB - Springer Verlag

T2 - 1st High-Performance Computing Latin America Community, HPCLATAM-CLCAR 2014 and Latin American Joint Conference, CARLA 2014

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Côrtes AMA, Vignal P, Sarmiento A, García D, Collier N, Dalcin L et al. Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework. In Hernández G, Hernández CJB, Díaz G, Garino CG, Nesmachnow S, Pérez-Acle T, Storti M, Vázquez M, editors, High Performance Computing - First HPCLATAM - CLCAR - Latin American Joint Conference, CARLA 2014, Proceedings. Springer Verlag. 2014. p. 236-247. (Communications in Computer and Information Science). doi: 10.1007/978-3-662-45483-1_17

Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

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Keywords

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