Simple numerical quadrature rules for Gaussian chain polymer density functional calculations in 3D and implementation on parallel platforms

N.M Maurits, J.G E M Fraaije, P. Altevogt, O.A. Evers

Research output: Contribution to journalArticleAcademicpeer-review


We present new quadrature rules (stencil operators) for the efficient integration of Gaussian chain polymer density functionals on a uniform 3D grid for different ratios between the Gaussian bond-strength parameter and the mesh width. The algorithm is in essence off-lattice. The quadrature rules are such that the isotropy on the grid is maximal. Also, the long length scaling of the numerical functionals is guaranteed to be identical to analytical results. Furthermore, we achieve a good accuracy in the entire frequency domain. A comparison with existing lattice models is included. It is shown that the traditional cubic lattice chain model may lead to unphysical singularities in copolymer melt inverse structure factors. Finally, we briefly discuss the implementation of stencil operations on parallel platforms.

Original languageEnglish
Pages (from-to)1 - 8
Number of pages8
JournalComputational & Theoretical Polymer Science
Issue number1-2
Publication statusPublished - 1996


  • quadrature rules
  • polymer density functionals
  • Gaussian chain
  • lattice models
  • parallelization

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