This paper describes a fast and reliable method for redistributing a computational mesh in three dimensions which can generate a complex three dimensional mesh without any problems due to mesh tangling. The method relies on a three dimensional implementation of the parabolic Monge-Ampère (PMA) technique, for finding an optimally transported mesh. The method for implementing PMA is described in detail and applied to both static and dynamic mesh redistribution problems, studying both the convergence and the computational cost of the algorithm. The algorithm is applied to a series of problems of increasing complexity. In particular very regular meshes are generated to resolve real meteorological features (derived from a weather forecasting model covering the UK area) in grids with over 2 × 107 degrees of freedom. The PMA method computes these grids in times commensurate with those required for operational weather forecasting.

Original languageEnglish
Pages (from-to)174-196
Number of pages23
JournalJournal of Computational Physics
Publication statusPublished - 15 Oct 2014


  • Adaptive mesh redistribution
  • Monge-Ampere
  • Optimal transport
  • R-Adaptivity

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


Dive into the research topics of 'Fast three dimensional r-adaptive mesh redistribution'. Together they form a unique fingerprint.

Cite this