A convected particle least square interpolation material point method

• Published in: International journal for numerical methods in engineering Vol. 121; no. 6; pp. 1068 - 1100
• Main Authors: Tran, Quoc Anh, Sołowski, Wojciech, Berzins, Martin, Guilkey, James
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.03.2020; Wiley Subscription Services, Inc
• Subjects: Algorithms; convected particle domain interpolation; Convergence; Domains; Goal programming; improved moving least squares; Interpolation; Least squares method; material point method; methods of manufactured solution; moving least squares; numerical convergence; Reconstruction; Velocity distribution
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6257

Summary 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 nonconstant. 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.