ImpactX
Functions
impactx::integrators Namespace Reference

Functions

template<typename T_Element >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp2_integrate (RefPart &refpart, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
 
template<typename T_Element >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp2_integrate_split3 (RefPart &refpart, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
 
template<typename T_Element >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp4_integrate (RefPart &refpart, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
 

Function Documentation

◆ symp2_integrate()

template<typename T_Element >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void impactx::integrators::symp2_integrate ( RefPart refpart,
amrex::ParticleReal const  zin,
amrex::ParticleReal const  zout,
int const  nsteps,
T_Element const &  element 
)

A second-order symplectic integrator based on a Hamiltonian splitting H = H_1 + H_2. This is a generalization of the second- order leapfrog algorithm. For a detailed overview:

E. Hairer et al, Geometric Numerical Integration: Structure- Preserving Algorithms for Ordinary Differential Equations, 2nd ed, Springer, Berlin, 2006.

Parameters
refpartReference particle data
zinInitial value of independent variable (z-location)
zoutFinal value of independent variable (z-location)
nstepsNumber of integration steps
elementElement defining the two maps associated with H_1 and H_2

◆ symp2_integrate_split3()

template<typename T_Element >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void impactx::integrators::symp2_integrate_split3 ( RefPart refpart,
amrex::ParticleReal const  zin,
amrex::ParticleReal const  zout,
int const  nsteps,
T_Element const &  element 
)

A second-order symplectic integrator based on a Hamiltonian splitting H = H_1 + H_2 + H_3. This is the result of applying the two-terms splitting of symp2_integrate twice in succession. The form shown here appears, for example, in:

R. D. Ryne, Computational Methods in Accelerator Physics, USPAS lecture notes, 2009.

Parameters
refpartReference particle data
zinInitial value of independent variable (z-location)
zoutFinal value of independent variable (z-location)
nstepsNumber of integration steps
elementElement defining the two maps associated with H_1 and H_2

◆ symp4_integrate()

template<typename T_Element >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void impactx::integrators::symp4_integrate ( RefPart refpart,
amrex::ParticleReal const  zin,
amrex::ParticleReal const  zout,
int const  nsteps,
T_Element const &  element 
)

A fourth-order symplectic integrator based on a Hamiltonian splitting H = H_1 + H_2. This is the result of applying the two-terms splitting of symp2_integrate together with the method of Yoshida.

H. Yoshida, Phys. Lett. A 150, 292-268 (1990).

The form shown here appears, for example, in:

E. Forest and R. D. Ruth, Physica D 43, 105-117 (1990).

Parameters
refpartReference particle data
zinInitial value of independent variable (z-location)
zoutFinal value of independent variable (z-location)
nstepsNumber of integration steps
elementElement defining the two maps associated with H_1 and H_2