The classical finite element method (FEM) has been widely used to simulate diverse problems in engineering. Unlike most engineering problems, geological simulations are dominated by emergence of geometrical structures due to the non-linear processes involved. For the structurally conforming FEM meshes, the large deformations result in distorted meshes, which often require repeated re-meshing in computation. The particle-in-cell (PIC) method allows Lagrangian material particles to move in a background Eulerian mesh. Those particles carry the density, composition, viscosity, etc., while the unknowns are solved at nodes of the mesh.
This is a companion discussion topic for the original entry at https://www.underworldcode.org/articles/stress-recovery-in-underworld/