Temporal and Null-space filter for the Material Point Method

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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.
Original languageEnglish
Pages (from-to)328-360
JournalInternational Journal for Numerical Methods in Engineering
Issue number3
Early online date5 Jun 2019
Publication statusPublished - 19 Oct 2019
MoE publication typeA1 Journal article-refereed


  • Material Point Method
  • hydro-coupling
  • dual domain material point method
  • null-space
  • material point method
  • generalized interpolation material point method

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    Progressive failure and post-failure modelling of slopes with Generalized Interpolation Material Point Method

    Sołowski, W., Lei, X., Tran, Q. A. & Seyedan, S.


    Project: Academy of Finland: Other research funding

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