# An improved moving least squares method for the Material Point Method

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

### Standard

**An improved moving least squares method for the Material Point Method.** / Tran, Quoc; Berzins, Martin; Sołowski, Wojciech Tomasz.

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

### Harvard

*Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019).*, mpm2019.06, International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, United Kingdom, 08/01/2019.

### APA

*Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019)*[mpm2019.06]

### Vancouver

### Author

### Bibtex - Download

}

### RIS - Download

TY - GEN

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

AU - Tran, Quoc

AU - Berzins, Martin

AU - Sołowski, Wojciech Tomasz

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 contribution

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

ER -

ID: 31265321