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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
Part of the Communications in Computer and Information Science book series (CCIS, volume 485)

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 phase-field 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

Isogeometric analysis high-performance computing high-order partial differential equations finite elements phase-field modeling 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Adriano M. A. Côrtes
    • 1
    • 2
  • Philippe Vignal
    • 1
    • 3
  • Adel Sarmiento
    • 1
    • 4
  • Daniel García
    • 1
    • 5
  • Nathan Collier
    • 1
    • 6
  • Lisandro Dalcin
    • 1
    • 7
  • Victor M. Calo
    • 1
    • 2
    • 4
  1. 1.Center for Numerical Porous MediaKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.Earth Sciences & EngineeringKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  3. 3.Material Science & EngineeringKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  4. 4.Applied Mathematics & Computational Science, Earth Science & EngineeringKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  5. 5.Mechanical EngineeringKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  6. 6.Oak Ridge National LaboratoryOak RidgeUSA
  7. 7.Consejo Nacional de Investigaciones Científicas y Técnicas and Universidad Nacional del LitoralSanta FeArgentina

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