Finite Element Method

A numerical method that cuts an object into many small elements, solves each approximately, and assembles them into the whole.

The finite element method is a general numerical technique for solving partial differential equations: a continuous object or region is divided into a large number of simple small pieces (elements, commonly triangles or tetrahedra), each approximated with a simple function, then assembled into an overall system of equations to solve. It originated in structural-mechanics research in the 1940s–50s, with foundational work by Courant and others, and later became the standard tool for engineering analysis of structural strength, heat transfer, fluids, and electromagnetics. In embodied AI, FEM is mainly used for soft-body simulation: rigid-body simulation treats an object as one undeformable whole, but tasks like grasping a sponge, squeezing a soft package, or designing a soft gripper require computing how the object deforms and how much internal force it experiences, which needs FEM. The cost is heavy computation — a finer mesh is more accurate but also slower, forcing a trade-off between accuracy and speed.

ExamplePhysX 5 (the physics backend behind Isaac Sim) simulates soft bodies with FEM using two tetrahedral meshes: a coarser one for computing deformation and a surface-fitted one for collision, and it only runs on the GPU; Genesis also has a built-in FEM solver.

Also called

FEM, Finite Element Analysis, FEA

Related

Deformable-Body Simulation · Material Point Method · Position-Based Dynamics · Deformable Object Manipulation · Physics Engine · Genesis

Sources

Finite element method - Wikipedia
PhysX 5 Documentation: Soft Bodies
Genesis Documentation: What is Genesis