Multidip
1.0
Multi-photon matrix elements
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Romberg quadrature for numerical integration. More...
Functions/Subroutines | |
subroutine | nested_cgreen_correct_romberg (Z, a, b, c, N, sa, sb, m, l, k, v) |
Numerically correct asymptotic approximation of the Coulomb-Green integral (Romberg integration) More... | |
complex(wp) function | nested_cgreen_eval (Z, c, N, sa, sb, m, l, k, rs, asy) |
Evaluate the Coulomb-Green's integrand. More... | |
Romberg quadrature for numerical integration.
subroutine multidip_romberg::nested_cgreen_correct_romberg | ( | real(wp), intent(in) | Z, |
real(wp), intent(in) | a, | ||
real(wp), intent(in) | b, | ||
real(wp), intent(in) | c, | ||
integer, intent(in) | N, | ||
integer, intent(in) | sa, | ||
integer, intent(in) | sb, | ||
integer, dimension(:), intent(in) | m, | ||
integer, dimension(:), intent(in) | l, | ||
complex(wp), dimension(:), intent(in) | k, | ||
complex(wp), intent(inout) | v | ||
) |
Numerically correct asymptotic approximation of the Coulomb-Green integral (Romberg integration)
This function computes the integral of the Coulomb-Green's integrand over Q = (a,+∞)^N \ (b,+∞)^N numerically. Currently, Romberg integration based on the trapezoidal rule is used.
Z | Residual ion charge |
a | Lower bound |
b | Upper bound |
c | Damping factor (additional exp(-c*r) added to all r^m functions) |
N | Dimension (number of integration variables) |
sa | Sign of the right-most Coulomb-Hankel function |
sb | Sign of the left-most Coulomb-Hankel function |
m | Array of integer powers of length N |
l | Array of angular momenta of length N + 1 |
k | Array of linear momenta of length N + 1 |
v | Value of the asymptotic integral to correct (updated on exit from this subroutine) |
Definition at line 58 of file multidip_romberg.f90.
complex(wp) function multidip_romberg::nested_cgreen_eval | ( | real(wp), intent(in) | Z, |
real(wp), intent(in) | c, | ||
integer, intent(in) | N, | ||
integer, intent(in) | sa, | ||
integer, intent(in) | sb, | ||
integer, dimension(:), intent(in) | m, | ||
integer, dimension(:), intent(in) | l, | ||
complex(wp), dimension(:), intent(in) | k, | ||
real(wp), dimension(:), intent(in) | rs, | ||
logical, intent(in) | asy | ||
) |
Evaluate the Coulomb-Green's integrand.
Z | Residual ion charge |
c | Damping factor (additional exp(-c*r) added to all r^m functions) |
N | Dimension (number of integration variables) |
sa | Sign of the right-most Coulomb-Hankel function |
sb | Sign of the left-most Coulomb-Hankel function |
m | Array of integer powers of length N |
l | Array of angular momenta of length N + 1 |
k | Array of linear momenta of length N + 1 |
rs | Single point in the multidimensional position space where the evaluate the integrand |
asy | Use the asymptotic form of the Coulomb-Green's functions. |
Definition at line 142 of file multidip_romberg.f90.