jaxdem.integrators.direct_euler

Direct (forward) Euler integrator.

Classes

DirectEuler()

Implements the explicit (forward) Euler integration method.

class jaxdem.integrators.direct_euler.DirectEuler

Bases: Integrator

Implements the explicit (forward) Euler integration method.

static step(state: State, system: System) → Tuple['State', 'System']

Advances the simulation state by one time step using the Direct Euler method.

The update equations are:

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

where:

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

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

• \(a\) is the particle acceleration (jaxdem.State.accel)

• \(\Delta t\) 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]

static initialize(state: State, system: System) → Tuple['State', 'System']

The Direct Euler integrator does not require a specific initialization step.

Parameters:

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

• system (System) – Simulation system configuration.

Returns:

The original State and System objects.

Return type:

Tuple[State, System]

classmethod registry_name() → str

property type_name: str