DDMPM in Picasso

[abisner]

This issue concerns the implementation of the dual domain material point method (DDMPM) in Picasso.
DDMPM scores a few numerical advantages over the classical MPM, namely, improved accuracy and stability, especially in the vicinity of contact discontinuities, by reducing cell crossing noise.

A few sub-steps for a robust implementation are required:

• A distribution coefficient algorithm (DCA) for reducing small node mass instabilities. This requires the definition of nodal transfer coefficients, $C_{li}$. See Eq. (41) in the Zhang et al. paper.
• Modified shape function gradient calculation. This may be represented by a series of two consecutive stencil operations on the nodes.
• Incorporation of modified shape function gradient in the velocity (momentum) update.