A Convected Particle Least Square Interpolation Material Point Method

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@article{697e6ec1a5d74f7e886b8c08f21cb32f,
title = "A Convected Particle Least Square Interpolation Material Point Method",
abstract = "Applying the Convected Particle Domain Interpolation (CPDI) to the Material Point Method has many advantages over the original Material Point Method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The Convected Particle Least Square Interpolation (CPLS) Material Point Method assumes the velocity field inside the material point domain as non‐constant. This velocity field in the material point domain is mapped to the background grid nodes with a Moving Least Squares reconstruction. In this paper, we apply the Improved Moving Least Squares method to avoid the instability of the conventional Moving Least Squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the Method of Manufactured Solutions.",
keywords = "convected particle domain interpolation, improved moving least squares, material point method, methods of manufactured solution, moving least squares, numerical convergence",
author = "Tran, {Quoc Anh} and Sołowski, {Wojciech Tomasz} and Martin Berzins and James Guilkey",
year = "2019",
month = "10",
day = "23",
doi = "10.1002/nme.6257",
language = "English",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",

}

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TY - JOUR

T1 - A Convected Particle Least Square Interpolation Material Point Method

AU - Tran, Quoc Anh

AU - Sołowski, Wojciech Tomasz

AU - Berzins, Martin

AU - Guilkey, James

PY - 2019/10/23

Y1 - 2019/10/23

N2 - Applying the Convected Particle Domain Interpolation (CPDI) to the Material Point Method has many advantages over the original Material Point Method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The Convected Particle Least Square Interpolation (CPLS) Material Point Method assumes the velocity field inside the material point domain as non‐constant. This velocity field in the material point domain is mapped to the background grid nodes with a Moving Least Squares reconstruction. In this paper, we apply the Improved Moving Least Squares method to avoid the instability of the conventional Moving Least Squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the Method of Manufactured Solutions.

AB - Applying the Convected Particle Domain Interpolation (CPDI) to the Material Point Method has many advantages over the original Material Point Method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The Convected Particle Least Square Interpolation (CPLS) Material Point Method assumes the velocity field inside the material point domain as non‐constant. This velocity field in the material point domain is mapped to the background grid nodes with a Moving Least Squares reconstruction. In this paper, we apply the Improved Moving Least Squares method to avoid the instability of the conventional Moving Least Squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the Method of Manufactured Solutions.

KW - convected particle domain interpolation

KW - improved moving least squares

KW - material point method

KW - methods of manufactured solution

KW - moving least squares

KW - numerical convergence

UR - http://www.scopus.com/inward/record.url?scp=85075746103&partnerID=8YFLogxK

U2 - 10.1002/nme.6257

DO - 10.1002/nme.6257

M3 - Article

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

ER -

ID: 38195312