Moving least squares reconstruction for B-spline Material Point Method

Quoc Tran; Elizaveta  Wobbes; Wojciech Tomasz Sołowski; Matthias  Möller; Cornelis  Vuik

Moving least squares reconstruction for B-spline Material Point Method

Quoc Tran, Elizaveta Wobbes, Wojciech Tomasz Sołowski, Matthias Möller, Cornelis Vuik

Delft University of Technology

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

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Abstract

The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). B-spline MPM have shown to reduce the grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the grid-crossing occurs frequently, the B-spline MPM suffered from the reduction of spatial convergence rate of the numerical solution. In this paper, moving least squares reconstruction is employed to retrieve the expected convergence rate of the numerical solutions. The proposed formulation version is examined in terms of the spatial convergence using the method of manufactured solutions for large deformations.

Original language	English
Title of host publication	Proceedings os the 2nd International Conference on the Material Point Method for Modelling Sil-Water-Structure Interaction
Editors	Dongfang Liang, Krishna Kumar, Alexander Rohe
Publisher	Ocean Press
Number of pages	7
ISBN (Print)	978-7-5210-0316-1
Publication status	Published - 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

moving least squares
function reconstruction
B-spline basis function
Material Point Method

Access to Document

MPM2019_BsplineMPMAccepted author manuscript, 167 KBLicence: CC BY-NC-ND

1 Finished

Progressive failure and post-failure modelling of slopes with Generalized Interpolation Material Point Method
Sołowski, W. (Principal investigator), Tran, Q. A. (Project Member), Lei, X. (Project Member) & Seyedan, S. (Project Member)
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding

1 Conference presentation

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

1 Conference article in proceedings

An improved moving least squares method for the Material Point Method
Tran, Q., Berzins, M. & Sołowski, W. T., 10 Jan 2019, Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019). Liang, D., Kumar, K. & Rohe, A. (eds.). Ocean Press, 8 p. mpm2019.06
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

Open Access
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Cite this

@inproceedings{b97494e7145e4c9daa59a53af222d7b5,

title = "Moving least squares reconstruction for B-spline Material Point Method",

abstract = "The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). B-spline MPM have shown to reduce the grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the grid-crossing occurs frequently, the B-spline MPM suffered from the reduction of spatial convergence rate of the numerical solution. In this paper, moving least squares reconstruction is employed to retrieve the expected convergence rate of the numerical solutions. The proposed formulation version is examined in terms of the spatial convergence using the method of manufactured solutions for large deformations.",

keywords = "moving least squares, function reconstruction, B-spline basis function, Material Point Method",

author = "Quoc Tran and Elizaveta Wobbes and So{\l}owski, {Wojciech Tomasz} and Matthias M{\"o}ller and Cornelis Vuik",

year = "2019",

language = "English",

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

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

booktitle = "Proceedings os the 2nd International Conference on the Material Point Method for Modelling Sil-Water-Structure Interaction",

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, Wobbes, E, Sołowski, WT, Möller, M & Vuik, C 2019, Moving least squares reconstruction for B-spline Material Point Method. in D Liang, K Kumar & A Rohe (eds), Proceedings os the 2nd International Conference on the Material Point Method for Modelling Sil-Water-Structure Interaction., mpm2019.07, Ocean Press, International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, United Kingdom, 08/01/2019.

Moving least squares reconstruction for B-spline Material Point Method. / Tran, Quoc; Wobbes, Elizaveta ; Sołowski, Wojciech Tomasz et al.
Proceedings os the 2nd International Conference on the Material Point Method for Modelling Sil-Water-Structure Interaction. ed. / Dongfang Liang; Krishna Kumar; Alexander Rohe. Ocean Press, 2019. mpm2019.07.

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

TY - GEN

T1 - Moving least squares reconstruction for B-spline Material Point Method

AU - Tran, Quoc

AU - Wobbes, Elizaveta

AU - Sołowski, Wojciech Tomasz

AU - Möller, Matthias

AU - Vuik, Cornelis

N1 - Conference code: 2

PY - 2019

Y1 - 2019

N2 - The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). B-spline MPM have shown to reduce the grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the grid-crossing occurs frequently, the B-spline MPM suffered from the reduction of spatial convergence rate of the numerical solution. In this paper, moving least squares reconstruction is employed to retrieve the expected convergence rate of the numerical solutions. The proposed formulation version is examined in terms of the spatial convergence using the method of manufactured solutions for large deformations.

AB - The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). B-spline MPM have shown to reduce the grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the grid-crossing occurs frequently, the B-spline MPM suffered from the reduction of spatial convergence rate of the numerical solution. In this paper, moving least squares reconstruction is employed to retrieve the expected convergence rate of the numerical solutions. The proposed formulation version is examined in terms of the spatial convergence using the method of manufactured solutions for large deformations.

KW - moving least squares

KW - function reconstruction

KW - B-spline basis function

KW - Material Point Method

M3 - Conference article in proceedings

SN - 978-7-5210-0316-1

BT - Proceedings os the 2nd International Conference on the Material Point Method for Modelling Sil-Water-Structure Interaction

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 -

Moving least squares reconstruction for B-spline Material Point Method

Abstract

Conference

Keywords

Access to Document

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Projects

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

Activities

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

Research output

An improved moving least squares method for the Material Point Method

Cite this