Timestepping and Space and Time Errors and Stability in the Material Point Method

Abstract

The choice of the time step for the Material Point Method (MPM) is often addressed by using a simple stability criterion, such as the speed of sound or a CFL condition. Recently there have been several advances in understanding the stability of MPM. These range from non-linear stability analysis, through to Von Neumann type approaches. While in many instances this works well it is important to understand how this relates to the overall errors present in the method. Although it has been observed that spatial errors may dominate temporal onesi at stable time steps, at the same time recent work has made more precise the forms of the different MPM errors. This now makes it possible to understand how the different errors and the stability analysis are connected. At the same time this also requires simple computable estimates of the different errors in the material point method. The use of simple estimates of these errors imakes it possible to connect some of the errors introduced with the stability criteria used. A number of simple computational experiments are used to illustrate the theoretical results.

Abstract

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