# `FEMSolver`

The `FEMSolver` implements the Finite Element Method for simulating deformable solids on tetrahedral meshes. It supports several constitutive models (linear, stable Neo-Hookean, linear corotated), handles large deformations, and offers an explicit integrator by default with an optional implicit solver for stability at larger time steps. The materials it supports are listed in {doc}`/api_reference/material/fem/index`.

## Usage

The solver activates when the scene contains an FEM entity. Configure it through `FEMOptions`; see {doc}`/api_reference/options/simulator_coupler_and_solver_options/fem_options` for the full option set.

```python
import genesis as gs

gs.init()
scene = gs.Scene(
    fem_options=gs.options.FEMOptions(
        dt=1e-3,
        damping=0.1,
    ),
)

# Add an FEM entity
soft_body = scene.add_entity(
    gs.morphs.Mesh(file="soft_object.obj"),
    material=gs.materials.FEM.Elastic(
        E=1e5,     # Young's modulus, Pa
        nu=0.4,    # Poisson's ratio
        rho=1000,  # density, kg/m^3
    ),
)

scene.build()

for i in range(1000):
    scene.step()
```

## Vertex constraints

Pin vertices to fixed targets or to a rigid link with `set_vertex_constraints`. Under the implicit solver, set `enable_vertex_constraints=True` first.

```python
# Pin the given vertices at their current positions
soft_body.set_vertex_constraints(verts_idx_local=[0, 1, 2])

# Pull vertices toward a target with a soft spring constraint
soft_body.set_vertex_constraints(
    verts_idx_local=[0, 1, 2],
    target_poss=[(0.0, 0.0, 0.5)] * 3,
    is_soft_constraint=True,
    stiffness=1e3,
)
```

## See also

- {doc}`/api_reference/entity/fem_entity`: FEMEntity.
- {doc}`/api_reference/material/fem/index`: FEM materials.
- {doc}`/api_reference/options/simulator_coupler_and_solver_options/fem_options`: full options.