Temporal and Null-space filter for the Material Point Method

Research output: Contribution to journalArticle

Standard

Harvard

APA

Vancouver

Author

Bibtex - Download

@article{f250e060d05b400d9203361cc5aa66f8,
title = "Temporal and Null-space filter for the Material Point Method",
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.",
keywords = "Material Point Method, hydro-coupling, dual domain material point method, null-space, material point method, generalized interpolation material point method",
author = "Tran, {Quoc Anh} and Sołowski, {Wojciech Tomasz}",
year = "2019",
month = "10",
day = "19",
doi = "10.1002/nme.6138",
language = "English",
volume = "120",
pages = "328--360",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
number = "3",

}

RIS - Download

TY - JOUR

T1 - Temporal and Null-space filter for the Material Point Method

AU - Tran, Quoc Anh

AU - Sołowski, Wojciech Tomasz

PY - 2019/10/19

Y1 - 2019/10/19

N2 - 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.

AB - 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.

KW - Material Point Method

KW - hydro-coupling

KW - dual domain material point method

KW - null-space

KW - material point method

KW - generalized interpolation material point method

UR - http://www.scopus.com/inward/record.url?scp=85067457266&partnerID=8YFLogxK

U2 - 10.1002/nme.6138

DO - 10.1002/nme.6138

M3 - Article

VL - 120

SP - 328

EP - 360

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 3

ER -

ID: 34824987