Leap Frog
[Integrators]

Functions
__global__ void	gpuGetVelOnTime (FLOAT_ARRAY_TYPE dVel, FLOAT_ARRAY_TYPE dVt, FLOAT_ARRAY_TYPE *dForce, int N, float dt)
	Calculates velocities on timestep.
__global__ void	gpuInitialBackstep (FLOAT_ARRAY_TYPE dVel, FLOAT_ARRAY_TYPE dForce, int N, float dt)
	Inital backstep.
__global__ void	gpuIntegratorLeapFrog (FLOAT_ARRAY_TYPE dPos, FLOAT_ARRAY_TYPE dVel, FLOAT_ARRAY_TYPE dForce, int N, float dt, float boxSize, float dmax, float maxDisplacement, bool *needListUpdate)
	Leap Frog integrator.

Detailed Description

The Leap Frog integrator is a variant of the Velocity Verlet integrator.

Function Documentation

__global__ void gpuGetVelOnTime	(	FLOAT_ARRAY_TYPE *	dVel,
		FLOAT_ARRAY_TYPE *	dVt,
		FLOAT_ARRAY_TYPE *	dForce,
		int	N,
		float	dt
	)

When using the Leap Frog integrator, the velocites are calculated only on half-timesteps. For consistent output of positions and velocites this function calculates the mean velocity on time $n$ by averaging the velocites at $n-\frac{1}{2}$ and $n+\frac{1}{2}$ .

Parameters:

`[in]`	dVel	Velocities on half-step
`[out]`	dVt	Velocties on step
`[in]`	dForce	Forces on step
`[in]`	N	Number of particles
`[in]`	dt	time increment

Returns:: Returns CUDA error information

Definition at line 238 of file gpu_tools.cu.

__global__ void gpuInitialBackstep	(	FLOAT_ARRAY_TYPE *	dVel,
		FLOAT_ARRAY_TYPE *	dForce,
		int	N,
		float	dt
	)

This function is called at the beginning of a simulation where the Leap Frog integrator is used. It generates from the forces at the initial time the velocities half a step backwards in time.

Parameters:

`[in,out]`	dVel	Particle velocity array
`[in]`	dForce	Particle force array
`[in]`	N	Number of particles
`[in]`	dt	Time increment

Returns:: Returns CUDA error information.

Definition at line 53 of file gpu_integrator.cu.

__global__ void gpuIntegratorLeapFrog	(	FLOAT_ARRAY_TYPE *	dPos,
		FLOAT_ARRAY_TYPE *	dVel,
		FLOAT_ARRAY_TYPE *	dForce,
		int	N,
		float	dt,
		float	boxSize,
		float *	dmax,
		float	maxDisplacement,
		bool *	needListUpdate
	)

The integration of Newtons equation of motions is done in two steps: First we calculate the velocity at intermediate time $n+\frac{1}{2}$

$\vec{v}(n+\frac{1}{2}) = \vec{v}(n-\frac{1}{2})+\tau\vec{a}(n)\label{verlet1}$

then it is used to calculate the new positions at timte $ n+1 $

$\vec{x}(n+1) = \vec{x}(n) + \tau\vec{v}(n+\frac{1}{2})\label{verlet2}$

Finally, we check the periodic bounds and shift the particles accordingly.

Parameters:

`[in,out]`	dPos	Particle position array
`[in,out]`	dVel	Particle velocity array
`[in]`	dForce	Particle force array
`[in]`	N	Number of particles
`[in]`	dt	Time increment
`[in]`	boxSize	Edge length of the cubic simulation box.
`[in,out]`	dmax	List to store the displacement of each particle
`[in]`	maxDisplacement	Maximum allowed displacement
`[out]`	needListUpdate	Flag which is set when a particle's displacement reached the threshold

Returns:: Returns CUDA error information.

Definition at line 24 of file gpu_integrator.cu.

References checkPBC().

Leap Frog [Integrators]

Functions

Detailed Description

Function Documentation

Leap Frog
[Integrators]