TABLE OF CONTENTS
- 1. /ADI
- 1.1. ADI/debugADI
- 1.2. ADI/init
- 1.3. ADI/ADI_solve_Douglas
- 1.4. ADI/ADI_Coulomb
- 1.5. ADI/ADI_solve
/ADI [ Modules ]
NAME
module ADI
PURPOSE
This module contains the subroutine ADI_solve for the solution of the matrix equations, which appear when the gradient terms are taken into account in RMF. Can also be applied for the Yukawa or Coulomb potential calculations. Uses the Alternating Direction Implicit (ADI) iterative method, similar to the one from module yukawa. (See S.Teis, PhD thesis, and the book of R.S.Varga, "Matrix Iterative Analysis".)
ADI/debugADI [ Global module-variables ]
[ Top ] [ ADI ] [ Global module-variables ]
SOURCE
logical, parameter :: debugADI=.false.
PURPOSE
ADI/init [ Subroutines ]
[ Top ] [ ADI ] [ Subroutines ]
NAME
subroutine init
PURPOSE
Reads input switches. Initializes fields.
ADI/ADI_solve_Douglas [ Subroutines ]
[ Top ] [ ADI ] [ Subroutines ]
NAME
subroutine ADI_solve_Douglas(U, S, Diag, eta_x, eta_y, CoulombFlag, rconv, niter_out, error_out)
PURPOSE
Solve the linear system
( tildeX + tildeY + tildeZ )* U = S
with respect to the field U(i,j,k), i=2,...,Nx-1, j=2,...,Ny-1, k=2,...,Nz-1, where Nx=2*gridPoints(1)+1, Ny=2*gridPoints(2)+1, Nz=2*gridPoints(3)+1. Here tildeX, tildeY and tildeZ are the linear operators:
[ tildeX * U ](i,j,k) = ( - U(i-1,j,k) + 2.*U(i,j,k) - U(i+1,j,k) )*eta_x + Diag(i,j,k)*U(i,j,k), [ tildeY * U ](i,j,k) = ( - U(i,j-1,k) + 2.*U(i,j,k) - U(i,j+1,k) )*eta_y + Diag(i,j,k)*U(i,j,k), [ tildeZ * U ](i,j,k) = - U(i,j,k-1) + 2.*U(i,j,k) - U(i,j,k+1) + Diag(i,j,k)*U(i,j,k).
with:
- S(i,j,k), i=2,...,Nx-1, j=2,...,Ny-1, k=2,...,Nz-1 --- the source field.
The values of U(i,j,k) at the boundary ( i=1,Nx or j=1,Ny or k=1,Nz ) are fixed.
INPUTS
- real, dimension(:,:,:), intent(inout) :: U ! -- starting value of the field U for iterations,
- real, dimension(:,:,:), intent(in) :: S ! -- the source field,
- real, dimension(:,:,:), intent(in) :: Diag ! -- diagonal coefficient field,
- real, intent(in) :: eta_x ! =(gridSpacing(3)/gridSpacing(1))**2,
- real, intent(in) :: eta_y ! =(gridSpacing(3)/gridSpacing(2))**2
- logical, optional, intent(in) :: CoulombFlag ! please, set .true. when Coulomb field is computed
- real, optional, intent(in) :: rconv ! convergence parameter
- integer, optional, intent(out) :: niter_out ! number of iterations
- real, optional, intent(out) :: error_out ! error
OUTPUT
NOTES
Uses the Douglas Iterative Method (c.f. R.S.Varga, "Matrix Iterative Analysis") The tridiagonal inversion procedure is explained, e.g. in S.E. Koonin, D.C. Meredith, "Computational Physics"
ADI/ADI_Coulomb [ Subroutines ]
[ Top ] [ ADI ] [ Subroutines ]
NAME
subroutine ADI_Coulomb(U, S, eta_x, eta_y, rconv, niter_out, error_out)
PURPOSE
Solve the linear system
( tildeX + tildeY + tildeZ )* U = S
with respect to the field U(i,j,k), i=2,...,Nx-1, j=2,...,Ny-1, k=2,...,Nz-1, where Nx=2*gridPoints(1)+1, Ny=2*gridPoints(2)+1, Nz=2*gridPoints(3)+1. Here tildeX, tildeY and tildeZ are the linear operators:
[ tildeX * U ](i,j,k) = ( - U(i-1,j,k) + 2.*U(i,j,k) - U(i+1,j,k) )*eta_x [ tildeY * U ](i,j,k) = ( - U(i,j-1,k) + 2.*U(i,j,k) - U(i,j+1,k) )*eta_y [ tildeZ * U ](i,j,k) = - U(i,j,k-1) + 2.*U(i,j,k) - U(i,j,k+1)
with:
- S(i,j,k), i=2,...,Nx-1, j=2,...,Ny-1, k=2,...,Nz-1 --- the source field.
The values of U(i,j,k) at the boundary ( i=1,Nx or j=1,Ny or k=1,Nz ) are fixed.
INPUTS
- real, dimension(:,:,:), intent(inout) :: U ! -- starting value of the field U for iterations,
- real, dimension(:,:,:), intent(in) :: S ! -- the source field,
- real, intent(in) :: eta_x ! =(gridSpacing(3)/gridSpacing(1))**2,
- real, intent(in) :: eta_y ! =(gridSpacing(3)/gridSpacing(2))**2
- real, optional, intent(in) :: rconv ! convergence parameter
- integer, optional, intent(out) :: niter_out ! number of iterations
- real, optional, intent(out) :: error_out ! error
OUTPUT
NOTES
Uses the Douglas Iterative Method (c.f. R.S. Varga "Matrix Iterative Analysis") The tridiagonal inversion procedure is explained, e.g. in S.E. Koonin, D.C. Meredith, "Computational Physics". This subroutine is the same as ADI_solve_Douglas, but without diagonal coefficients.
ADI/ADI_solve [ Subroutines ]
[ Top ] [ ADI ] [ Subroutines ]
NAME
subroutine ADI_solve(U, S, Diag, eta_x, eta_y, CoulombFlag, rconv, niter_out, error_out)
PURPOSE
Solve the linear system
( tildeX + tildeY + tildeZ )* U = S
with respect to the field U(i,j,k), i=2,...,Nx-1, j=2,...,Ny-1, k=2,...,Nz-1, where Nx=2*gridPoints(1)+1, Ny=2*gridPoints(2)+1, Nz=2*gridPoints(3)+1. Here tildeX, tildeY and tildeZ are the linear operators:
[ tildeX * U ](i,j,k) = ( - U(i-1,j,k) + 2.*U(i,j,k) - U(i+1,j,k) )*eta_x + Diag(i,j,k)*U(i,j,k), [ tildeY * U ](i,j,k) = ( - U(i,j-1,k) + 2.*U(i,j,k) - U(i,j+1,k) )*eta_y + Diag(i,j,k)*U(i,j,k), [ tildeZ * U ](i,j,k) = - U(i,j,k-1) + 2.*U(i,j,k) - U(i,j,k+1) + Diag(i,j,k)*U(i,j,k).
with:
- S(i,j,k), i=2,...,Nx-1, j=2,...,Ny-1, k=2,...,Nz-1 --- the source field.
The values of U(i,j,k) at the boundary ( i=1,Nx or j=1,Ny or k=1,Nz ) are fixed.
INPUTS
- real, dimension(:,:,:), intent(inout) :: U ! -- starting value of the field U for iterations,
- real, dimension(:,:,:), intent(in) :: S ! -- the source field,
- real, dimension(:,:,:), intent(in) :: Diag ! -- diagonal coefficient field,
- real, intent(in) :: Diag_min, Diag_max ! -- min and max values of Diag,
- real, intent(in) :: eta_x ! =(gridSpacing(3)/gridSpacing(1))**2,
- real, intent(in) :: eta_y ! =(gridSpacing(3)/gridSpacing(2))**2
- logical, optional, intent(in) :: CoulombFlag ! please, set .true. when Coulomb field is computed
- real, optional, intent(in) :: rconv ! convergence parameter
- integer, optional, intent(out) :: niter_out ! number of iterations
- real, optional, intent(out) :: error_out ! error
OUTPUT
- real, dimension(:,:,:), intent(inout) :: U ! -- final iterated value of the field U,
- real, intent(out) :: funMax ! =max(abs(( tildeX + tildeY + tildeZ )* U - S))
NOTES
Uses the Peaceman-Rachford Iterative Method (c.f. R.S. Varga "Matrix Iterative Analysis") The tridiagonal inversion procedure is explained, e.g. in S.E. Koonin, D.C. Meredith, "Computational Physics"