An improved moving least squares method for the Material Point Method

Quoc Tran; Martin Berzins; Wojciech Tomasz Sołowski

An improved moving least squares method for the Material Point Method

Quoc Tran, Martin Berzins, Wojciech Tomasz Sołowski

University of Utah

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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Abstract

The paper presents an improved moving least squares reconstruction technique for the Material Point Method. The moving least squares reconstruction (MLS) can improve spatial accuracy in simulations involving large deformations. However, the MLS algorithm relies on computing the inverse of the moment matrix. This is both expensive and potentially unstable when there are not enough material points to reconstruct the high-order least squares function, which leads to a singular or an ill-conditioned matrix. The shown formulation can overcome this limitation while retain the same order of accuracy compared with the conventional moving least squares reconstruction. Numerical experiments demonstrate the improvements in the accuracy and comparison with the original Material Point Method and the Convected Particles Domain Interpolation method.

Original language	English
Title of host publication	Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019)
Editors	Dongfang Liang, Krishna Kumar, Alexander Rohe
Publisher	Ocean Press
Number of pages	8
ISBN (Print)	978-7-5210-0316-1
Publication status	Published - 10 Jan 2019
MoE publication type	A4 Conference publication
Event	International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction - University of Cambridge, Cambridge, United Kingdom Duration: 8 Jan 2019 → 10 Jan 2019 Conference number: 2 http://mpm2019.eu/home

Conference

Conference	International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction
Abbreviated title	MPM
Country/Territory	United Kingdom
City	Cambridge
Period	08/01/2019 → 10/01/2019
Internet address	http://mpm2019.eu/home

Keywords

Material Point Method
Moving least square
CPDI
improved moving least squares

Access to Document

ENG_Tran_et_al_An_improved_moving_least_squares-method_MPM_2019Accepted author manuscript, 464 KBLicence: CC BY-ND

1 Conference presentation

SECOND INTERNATIONAL CONFERENCE ON THE MATERIAL POINT METHOD FOR MODELLING SOIL–WATER–STRUCTURE INTERACTION
Quoc Anh Tran (Speaker)
8 Jan 2019 → 10 Jan 2019
Activity: Talk or presentation types › Conference presentation

1 Conference article in proceedings

Moving least squares reconstruction for B-spline Material Point Method
Tran, Q., Wobbes, E., Sołowski, W. T., Möller, M. & Vuik, C., 2019, Proceedings os the 2nd International Conference on the Material Point Method for Modelling Sil-Water-Structure Interaction. Liang, D., Kumar, K. & Rohe, A. (eds.). Ocean Press, 7 p. mpm2019.07
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

Open Access
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Cite this

@inproceedings{4fc97aa60f044a5a88dfd9d18948b649,

title = "An improved moving least squares method for the Material Point Method",

abstract = "The paper presents an improved moving least squares reconstruction technique for the Material Point Method. The moving least squares reconstruction (MLS) can improve spatial accuracy in simulations involving large deformations. However, the MLS algorithm relies on computing the inverse of the moment matrix. This is both expensive and potentially unstable when there are not enough material points to reconstruct the high-order least squares function, which leads to a singular or an ill-conditioned matrix. The shown formulation can overcome this limitation while retain the same order of accuracy compared with the conventional moving least squares reconstruction. Numerical experiments demonstrate the improvements in the accuracy and comparison with the original Material Point Method and the Convected Particles Domain Interpolation method.",

keywords = "Material Point Method, Moving least square, CPDI, improved moving least squares",

author = "Quoc Tran and Martin Berzins and So{\l}owski, {Wojciech Tomasz}",

year = "2019",

month = jan,

day = "10",

language = "English",

isbn = "978-7-5210-0316-1",

editor = "Dongfang Liang and Krishna Kumar and Alexander Rohe",

booktitle = "Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019)",

publisher = "Ocean Press",

address = "United Kingdom",

note = "International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, MPM ; Conference date: 08-01-2019 Through 10-01-2019",

url = "http://mpm2019.eu/home",

}

Tran, Q, Berzins, M & Sołowski, WT 2019, An improved moving least squares method for the Material Point Method. in D Liang, K Kumar & A Rohe (eds), Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019)., mpm2019.06, Ocean Press, International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, United Kingdom, 08/01/2019.

An improved moving least squares method for the Material Point Method. / Tran, Quoc; Berzins, Martin; Sołowski, Wojciech Tomasz.
Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019). ed. / Dongfang Liang; Krishna Kumar; Alexander Rohe. Ocean Press, 2019. mpm2019.06.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - An improved moving least squares method for the Material Point Method

AU - Tran, Quoc

AU - Berzins, Martin

AU - Sołowski, Wojciech Tomasz

N1 - Conference code: 2

PY - 2019/1/10

Y1 - 2019/1/10

N2 - The paper presents an improved moving least squares reconstruction technique for the Material Point Method. The moving least squares reconstruction (MLS) can improve spatial accuracy in simulations involving large deformations. However, the MLS algorithm relies on computing the inverse of the moment matrix. This is both expensive and potentially unstable when there are not enough material points to reconstruct the high-order least squares function, which leads to a singular or an ill-conditioned matrix. The shown formulation can overcome this limitation while retain the same order of accuracy compared with the conventional moving least squares reconstruction. Numerical experiments demonstrate the improvements in the accuracy and comparison with the original Material Point Method and the Convected Particles Domain Interpolation method.

AB - The paper presents an improved moving least squares reconstruction technique for the Material Point Method. The moving least squares reconstruction (MLS) can improve spatial accuracy in simulations involving large deformations. However, the MLS algorithm relies on computing the inverse of the moment matrix. This is both expensive and potentially unstable when there are not enough material points to reconstruct the high-order least squares function, which leads to a singular or an ill-conditioned matrix. The shown formulation can overcome this limitation while retain the same order of accuracy compared with the conventional moving least squares reconstruction. Numerical experiments demonstrate the improvements in the accuracy and comparison with the original Material Point Method and the Convected Particles Domain Interpolation method.

KW - Material Point Method

KW - Moving least square

KW - CPDI

KW - improved moving least squares

M3 - Conference article in proceedings

SN - 978-7-5210-0316-1

BT - Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019)

A2 - Liang, Dongfang

A2 - Kumar, Krishna

A2 - Rohe, Alexander

PB - Ocean Press

T2 - International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction

Y2 - 8 January 2019 through 10 January 2019

ER -

An improved moving least squares method for the Material Point Method

Abstract

Conference

Keywords

Access to Document

Fingerprint

Activities

SECOND INTERNATIONAL CONFERENCE ON THE MATERIAL POINT METHOD FOR MODELLING SOIL–WATER–STRUCTURE INTERACTION

Research output

Moving least squares reconstruction for B-spline Material Point Method

Cite this