A high order solver for the unbounded Poisson equation

Mads Mølholm Hejlesen, Johannes Tophøj Rasmussen, Philippe Chatelain, Jens Honore Walther

Research output: Contribution to journalJournal articleResearchpeer-review


A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field. The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain.
Original languageEnglish
JournalJournal of Computational Physics
Pages (from-to)458-467
Publication statusPublished - 2013


  • Poisson solver
  • Elliptic solver
  • Unbounded domain
  • Infinite domain
  • Isolated system
  • Green’s function solution
  • Numerical integration
  • Vortex methods
  • Particle-mesh methods


Dive into the research topics of 'A high order solver for the unbounded Poisson equation'. Together they form a unique fingerprint.

Cite this