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Nonlinear stability and time step selection for the MPM method

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Abstract

The Material Point Method (MPM) has been developed from the Particle in Cell (PIC) method over the last 25 years and has proved its worth in solving many challenging problems involving large deformations. Nevertheless there are many open questions regarding the theoretical properties of MPM. For example in while Fourier methods, as applied to PIC may provide useful insight, the non-linear nature of MPM makes it necessary to use a full non-linear stability analysis to determine a stable time step for MPM. In order to begin to address this the stability analysis of Spigler and Vianello is adapted to MPM and used to derive a stable time step bound for a model problem. This bound is contrasted against traditional Speed of sound and CFL bounds and shown to be a realistic stability bound for a model problem.

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Acknowledgements

Chris Gritton is thanked for the use of his code for the model problem used to obtain the results shown in Sect. 6. This research was partially sponsored by the Army Research Laboratory under Cooperative Agreement Number W911NF-12-2-0023. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government.

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  1. SCI Institute, University of Utah, Salt Lake City, UT, USA

    Martin Berzins

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  1. Martin Berzins
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Correspondence to Martin Berzins.

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Berzins, M. Nonlinear stability and time step selection for the MPM method. Comp. Part. Mech. 5, 455–466 (2018). https://doi.org/10.1007/s40571-018-0182-y

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