Interactive FEM CPU deformable simulation: What you should (and shouldn’t) use with Eigen

Abstract

One of the most challenging branches of computer animation is the physic simulation of the behavior of objects in a scene. In particular, deformable objects are complex and challenging to simulate since their behavior is defined by continuum mechanics. The Finite Elements Method is just one way of tackling such a problem. Suppose we also add the requirement of interaction in the simulation. In that case, we need fast linear algebra implementations that entirely use the underlying hardware to reach the desired frame rate.

Usually, such solvers are implemented using C++ together with some linear algebra library such as Eigen. Of course, these libraries are already heavily optimized, with very performant solvers; however, by analyzing the actual problem to solve we can do better than Eigen. What is worth implementing from scratch, and what should you reuse from Eigen?