Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models

  • Authors:

  • Hector Gomez;Alessandro Reali;Giancarlo Sangalli

  • Affiliations:

  • University of A Coruña, Department of Mathematical Methods, Campus de Elviña, s/n, 15192, A Coruña, Spain;University of Pavia, Department of Civil Engineering and Architecture, via Ferrata 3, 27100, Pavia, Italy;University of Pavia, Dipartimento di Matematica "F. Casorati", via Ferrata, 1, 27100, Pavia, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2014

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Abstract

We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.