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Analysis of the Parallel Finite Volume Solver for the Anisotropic Allen–Cahn Equation in 3D

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Pavel Strachota

    (Czech Technical University in Prague, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering)

  • Michal Beneš

    (Czech Technical University in Prague, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering)

  • Marco Grottadaurea

    (Czech Technical University in Prague, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering)

  • Jaroslav Tintěra

    (Czech Technical University in Prague, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering)

Abstract

In this contribution, a parallel implementation of the finite volume solver is introduced, designated to numerically solve the initial boundary value problem for the Allen–Cahn equation with anisotropy on large 3D grids. The choice of a suitable numerical scheme is discussed and its convergence properties are investigated by means of evaluation of the experimental order of convergence. Afterwards, the consequent limitations for the theoretical error estimate are pointed out. Furthermore, the results of parallel algorithm efficiency measurements are shown, based on extensive tests performed on high performance computing systems. The final part gives a brief overview of a magnetic resonance tractography (neural tract tracking and visualization) method consisting in the solution of the above problem.

Suggested Citation

  • Pavel Strachota & Michal Beneš & Marco Grottadaurea & Jaroslav Tintěra, 2010. "Analysis of the Parallel Finite Volume Solver for the Anisotropic Allen–Cahn Equation in 3D," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 839-846, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_90
    DOI: 10.1007/978-3-642-11795-4_90
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