jaxdem.integrators.direct_euler

Direct (semi-implicit / symplectic Euler) Integrator.

Classes

DirectEuler()

Semi-implicit (symplectic) Euler integration method.

class jaxdem.integrators.direct_euler.DirectEuler

Bases: LinearIntegrator

Semi-implicit (symplectic) Euler integration method.

The method updates the velocity first. The position update then uses the new velocity. This makes the scheme symplectic: first-order accurate with bounded energy error, unlike a true forward Euler step.

static step_after_force(state: State, system: System) → tuple[State, System]

Advance the simulation state by one time step after the force calculation with the semi-implicit (symplectic) Euler method.

The update equations are (the position update uses the updated velocity):

\[\begin{split}& v(t + \Delta t) &= v(t) + \Delta t a(t) \\ & r(t + \Delta t) &= r(t) + \Delta t v(t + \Delta t)\end{split}\]

where:

• \(r\) is the particle position (jaxdem.State.pos)

• \(v\) is the particle velocity (jaxdem.State.vel)

• \(a\) is the particle acceleration computed from forces (jaxdem.State.force)

• \(\Delta t\) is the time step (jaxdem.System.dt)

Parameters:

• state (State) – Current state of the simulation.

• system (System) – Simulation system configuration.

Returns:

The updated state and system after one time step.

Return type:

Tuple[State, System]