Premium
Second‐order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces
Author(s) -
Sadeghirad A.,
Bran R.M.,
Guilkey J.E.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4526
Subject(s) - classification of discontinuities , material point method , grid , quadrilateral , interpolation (computer graphics) , domain (mathematical analysis) , hexahedron , particle (ecology) , topology (electrical circuits) , particle swarm optimization , geometry , computer science , mathematics , mathematical analysis , algorithm , finite element method , computer vision , engineering , structural engineering , geology , motion (physics) , oceanography , combinatorics
SUMMARY Convected particle domain interpolation (CPDI) is a recently developed extension of the material point method, in which the shape functions on the overlay grid are replaced with alternative shape functions, which (by coupling with the underlying particle topology) facilitate efficient and algorithmically straightforward evaluation of grid node integrals in the weak formulation of the governing equations. In the original CPDI algorithm, herein called CPDI1, particle domains are tracked as parallelograms in 2‐D (or parallelepipeds in 3‐D). In this paper, the CPDI method is enhanced to more accurately track particle domains as quadrilaterals in 2‐D (hexahedra in 3‐D). This enhancement will be referred to as CPDI2. Not only does this minor revision remove overlaps or gaps between particle domains, it also provides flexibility in choosing particle domain shape in the initial configuration and sets a convenient conceptual framework for enrichment of the fields to accurately solve weak discontinuities in the displacement field across a material interface that passes through the interior of a grid cell. The new CPDI2 method is demonstrated, with and without enrichment, using one‐dimensional and two‐dimensional examples. Copyright © 2013 John Wiley & Sons, Ltd.