## Abstract

In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order of convergence consistent with the moments conserved by the applied smoothing function. In the hybrid particle-mesh method of Hockney and Eastwood (HE) the particles are interpolated onto a

regular mesh where the unbounded Poisson equation is solved by a discrete non-cyclic convolution of the mesh values and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight in the convergence of particle methods.

regular mesh where the unbounded Poisson equation is solved by a discrete non-cyclic convolution of the mesh values and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight in the convergence of particle methods.

Original language | English |
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Publication date | 2013 |

Number of pages | 1 |

Publication status | Published - 2013 |

Event | Workshop on Hybrid Particle-Continuum Methods in Computational Materials Physics - Forschungszentrum Jülich, Institute for Advanced Simulation, Jülich, Germany Duration: 4 Mar 2013 → 7 Mar 2013 |

### Workshop

Workshop | Workshop on Hybrid Particle-Continuum Methods in Computational Materials Physics |
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Location | Forschungszentrum Jülich, Institute for Advanced Simulation |

Country/Territory | Germany |

City | Jülich |

Period | 04/03/2013 → 07/03/2013 |