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Software

The GSML package provides implementation of different classes of Spectral methods for the numerical solution of generalized partial differential equation (PDE) systems. The main focus of this library is a recently proposed Fourier continuation method [Bruno2010, Albin2011], the FC(Gram) method. This methodology provides solutions with high-order accuracy and compatibility with SIMD accellerators such as GPUs. Thus GSML is enables blending of the advantageous numerical properties of a Spectral methods with a parallel scalable application of GPU acceleration to the solution of PDEs.

FC Gram Figure: An example of the FC-method for a 1D non-periodic function (black dots) periodically extended (grey dots) for FFT computation; Taken from [Albin2011]

This Python library is hosted currently under active development, an initial development version is available via Launchpad.

References

  • O. Bruno and M. Lyon. "High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements". In: Journal of Computational Physics 229 (2010), pp. 2009-6033.
  • N. Albin and O. Bruno. "A spectral FC solver for the compressible Navier-Stokes equations in general domains I: Explicit time-stepping". In: Journal of Computational Physics 230 (2011), pp. 6248-6270.

    SAIA - Self-Assembly Image Analysis Library

The SAIA library is being developed to address a need amongst the research community studying self-assembled materials to quantitatively characterize the patterns observed in imaging data of these materials. SAIA utilizes imaging processing techniques in conjunction with the theoretical framework of bond-orientational order [Brock1992] for 2D periodic self-assembled domains (see figure).

BOORL1 BOORL2
Figure: (left) Simulation data (background) of a hexagonal self-assembled domain with pattern defects identified using BOORL (points and arrows in foreground); (right) BOORL post-processing output using simulation domain (left) including defects (points and arrows) and local orientation (colored regions); Taken from [Abukhdeir2011].

This (Python) package is currently in its development phase and has not been release. An "alpha" version of the code is available under the GNU Public License, please contact nmabukhdeir at uwaterloo.ca for access to this code.
This code supports non-periodic domains/images and sub-domains but rigorous validation of this new functionality has been completed for periodic domains only.

References

  • J. D. Brock. "Bond-Orientational Order". In: Bond-Orientational Order in Condensed Matter Systems. Ed. by K. J. Strandburg. Springer-Verlag, 1992.
  • N. M. Abukhdeir and D. G. Vlachos. "Nanoscale Surface Pattern Evolution in Heteroepitaxial Bimetallic Films". In: ACS Nano 5.9 (2011), pp. 7168-7175..