A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.
FRANCOMANO E, TORTORICI A, TOSCANO E, ALA G (2007). Multiscale Particle Method in Solving Partial Differential Equations. In Analysis and Applied Mathematics" - Subseries: Mathematical and Statistical Physics (pp.230-232). NEW YORK : American Institute of Physics [10.1063/1.2790115].
Multiscale Particle Method in Solving Partial Differential Equations
FRANCOMANO, Elisa;TORTORICI, Adele;TOSCANO, Elena;ALA, Guido
2007-01-01
Abstract
A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.
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