Fast Corotated FEM using Operator Splitting

How to read this

Category

Method: an operator-splitting solver for corotated FEM

Contributions

• Splits the corotated linear deformation energy into a stretching term and a volume-preservation term
• Shows the stretching term is rotation invariant so it is solved accurately with a precomputed Cholesky factorization, while volume is handled via compliant constraints and Gauss-Seidel
• Yields a fast, stable solver for elastic solids and shells that supports large time steps

Context

Sits in the corotated linear FEM and constraint-based simulation lineage, relating to efficient character-skinning elasticity such as McAdams et al. 2011 (Efficient Elasticity for Character Skinning with Contact and Collisions).Builds on: Efficient Elasticity for Character Skinning with Contact and Collisions

Correctness

Relies on the corotated linear energy model and a precomputed factorization, so accuracy depends on that linearization holding and on the Gauss-Seidel volume iterations; demonstrated on elastic solids and shells, but it is an approximation, not a fully nonlinear hyperelastic solve.

Clarity

Moderately technical; a first pass conveys the splitting intuition, and a second pass is needed to follow the backward-Euler-as-optimization derivation and the rotation-invariance argument.

How to read it

Read for the energy-splitting idea and why the stretching term reuses one Cholesky factorization; do a second pass on the optimization formulation if you implement implicit integration.