The EulerExplicitSolver (or EulerSolver) component belongs to the category of integration schemes or ODE Solver. This scheme allows to solve dynamic systems explicitely: all forces will be computed based on the state information at the current time step .
Looking at continuum mechanics, the linear system arises from the dynamic equation. This dynamic is written as follows but other physics (like heat transfer) result in a similar equation:
where is the degrees of freedom, the mass matrix and a function of (and possibly its derivatives) acting on our system. In the case of the EulerExplicitSolver, this equation can be written:
since forces only depend on known state (at our current time step). These forces are computed by the ForceField in the
addForce() function. The system matrix is only equal to the mass matrix .
In SOFA, the EulerExplicitSolver only handles diagonal mass matrices, thus making the resolution of the linear system trivial. In this case, the system matrix equals a diagonal mass matrix which is diagonal and it can be stored as a vector . Moreover, its inverse can directly be obtained as:
The solution finally corresponds to a division operation of by the mass. This computation is actually performed by the Mass component in the
accFromF() function. Therefore, no LinearSolver is needed to compute directly or iteratively a solution.
The data symplectic allows to modify the scheme to make is symplectic, i.e. velocities are updated before the positions. This option makes the scheme more robust in time.
The EulerExplicitSolver requires a MechanicalObject to store the state vectors. However, as explained above, no LinearSolver is needed and the EulerExplicitSolver is only working using a UniformMass or DiagonalMass, which ensures to have a diagonal system matrix.
This component is used as follows in XML format:
or using Python:
An example scene involving a EulerExplicitSolver is available in examples/Components/solver/EulerExplicitSolver.scn
Last modified: 14 September 2020