Forward Euler solver does not support mapped masses

[alxbilger]

The component EulerExplicitSolver does not properly support mapped masses.

When the mass matrix is diagonal (it can be UniformMass or DiagonalMass, or even a lumped MeshMatrixMass), the acceleration can be computed trivially from the force without any linear solver. However, when this diagonal mass is mapped, the acceleration is not $M^{-1} f$, but $(J^T M J)^{-1} f$. This is not considered in the current implementation.

Instead, $M^{-1} f$ is computed, but the resulting acceleration is not transmitted to the main dofs. It results in a null acceleration.

To illustrate this problem, here is a simple scene with a 2d particle submitted to gravity:

def createScene(root):
    root.addObject("DefaultAnimationLoop")

    root.addObject('RequiredPlugin', pluginName=[
        'Sofa.Component.LinearSolver.Direct',
        'Sofa.Component.Mapping.Linear',
        'Sofa.Component.Mass',
        'Sofa.Component.ODESolver.Forward',
        'Sofa.Component.StateContainer',
        'Sofa.Component.Visual',
        'SofaMatrix',
        'SofaMatrix.imgui',
    ])

    root.addObject("LineAxis", size=2)

    root.addObject("EulerExplicitSolver", symplectic=False)
    root.addObject("SparseLDLSolver", template="CompressedRowSparseMatrix")
    root.addObject("GlobalSystemMatrixImage")

    initial_position = [0.0, 0.0]
    initial_velocity = [1.0, 1.0]
    root.addObject("MechanicalObject", template="Vec2", name="particle",
        position=[initial_position], velocity=[initial_velocity])

    with root.addChild("mapped_mass") as mapped_mass_node:
        mapped_mass_node.addObject("MechanicalObject", template="Vec2", name="mapped_particle")
        mapped_mass_node.addObject("IdentityMapping", input="@../particle", output="@mapped_particle")
        mapped_mass_node.addObject("UniformMass", template="Vec2", name="mass", vertexMass=1.0)

    root.addObject("VisualPointCloud", position="@particle.position", sphereRadius=0.05, drawMode="Sphere", color="navy")
    root.addObject("TrailRenderer", template="Vec2", position="@particle.position")

    return root

In this scene, the mapping is trivial: the identity. So its presence should not change the behavior. What we observe with the current implementation:

A trajectory compatible with a zero acceleration.

What we should observe: