Substepping the Material Point Method

TL;DR

This paper introduces a straightforward substepping algorithm that enables explicit Material Point Method (MPM) implementations to operate efficiently with larger time steps, facilitating coupling, constraints, and multiphysics applications.

Contribution

The authors propose a simple, plug-and-play substepping technique that effectively transforms explicit MPM into a pseudo-implicit method for large time steps.

Findings

Enables larger time steps in explicit MPM implementations.

Maintains stability and accuracy with substepping.

Facilitates coupling with other large-step solvers and multiphysics.

Abstract

Many Material Point Method implementations favor explicit time integration. However large time steps are often desirable for special reasons - for example, for partitioned coupling with another large-step solver, or for imposing constraints, projections, or multiphysics solves. We present a simple, plug-and-play algorithm that advances MPM with a large time step using substeps, effectively wrapping an explicit MPM integrator into a pseudo-implicit one.