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A Lagrangian Approach Based on the Natural Neighbor Interpolation

Facundo del Pin 1
1 SINUS - Numerical Simulation for the Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : A Lagrangian formulation is constructed using the so-called Moving-Particle Semi-Implicit Method. The approximation scheme is then modified to incorporate the natural neighbor interpolation in the definition of the shape functions. In this way, a multi-scale method results. This method is presented as an alternative for solving partial-differential equations (PDE). Second-order convergence is achieved when uniform rectangular (finite-differ­ence-type) grids are used. Laplace and Poisson equations are solved in somewhat more general geometries as examples; the method demonstrates the same second-order accuracy as classical finite-elements (FEM), but allows a different treatment of geometry potentially powerful for local mesh adaptation in particular.
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https://hal.inria.fr/inria-00072542
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Submitted on : Wednesday, May 24, 2006 - 10:14:37 AM
Last modification on : Friday, February 4, 2022 - 3:19:39 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:55:57 PM

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  • HAL Id : inria-00072542, version 1

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Facundo del Pin. A Lagrangian Approach Based on the Natural Neighbor Interpolation. RR-4090, INRIA. 2000. ⟨inria-00072542⟩

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