Temporal and Null-space filter for the Material Point Method

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2019-10-19
Major/Subject
Mcode
Degree programme
Language
en
Pages
328-360
Series
International Journal for Numerical Methods in Engineering, Volume 120, issue 3
Abstract
This paper presents algorithm improvements that reduce the numerical noise and increase the numerical stability of the material point method formulation. Because of the linear mapping required in each time step of the material point method algorithm, a possible mismatch between the number of material points and grid nodes leads to a loss of information. These null‐space related errors may accumulate and affect the numerical solution. To remove the null‐space errors, the presented algorithm utilizes a null‐space filter. The null‐space filter shown removes the null‐space errors, resulting from the rank deficient mapping and the difference between the number of material points and the number of nodes. The presented algorithm enhancements also include the use of the explicit generalized‐α integration method, which helps optimizing the numerical algorithmic dissipation. This paper demonstrates the performance of the improved algorithms in several numerical examples.
Description
Keywords
Material Point Method, hydro-coupling, dual domain material point method, null-space, material point method, generalized interpolation material point method
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Citation
Tran , Q A & Sołowski , W T 2019 , ' Temporal and Null-space filter for the Material Point Method ' , International Journal for Numerical Methods in Engineering , vol. 120 , no. 3 , pp. 328-360 . https://doi.org/10.1002/nme.6138