Multigrid solver for the reference interaction site model of molecular liquids theory

Volodymyr P. Sergiievskyi, Wolfgang Hackbusch, Maxim V. Fedorov

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


In this article, we propose a new multigrid-based algorithm for solving integral equations of the reference interactions site model (RISM). We also investigate the relationship between the parameters of the algorithm and the numerical accuracy of the hydration free energy calculations by RISM. For this purpose, we analyzed the performance of the method for several numerical tests with polar and nonpolar compounds. The results of this analysis provide some guidelines for choosing an optimal set of parameters to minimize computational expenses. We compared the performance of the proposed multigrid-based method with the one-grid Picard iteration and nested Picard iteration methods. We show that the proposed method is over 30 times faster than the one-grid iteration method, and in the high accuracy regime, it is almost seven times faster than the nested Picard iteration method.

Original languageEnglish
Pages (from-to)1982-1992
Number of pages11
JournalJournal of Computational Chemistry
Issue number9
Publication statusPublished - 15 Jul 2011


  • multigrid
  • RISM
  • integral equation theory
  • hydration free energy
  • solving integral equations
  • 3D solvation structure
  • self consistent field
  • free energy
  • iterative subspace
  • numerical solution
  • direct inversion
  • aqueous-solutions
  • water
  • implementation


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