mirror of
https://github.com/autc04/Retro68.git
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262 lines
6.8 KiB
FortranFixed
262 lines
6.8 KiB
FortranFixed
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* { dg-do run }
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program main
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************************************************************
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* program to solve a finite difference
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* discretization of Helmholtz equation :
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* (d2/dx2)u + (d2/dy2)u - alpha u = f
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* using Jacobi iterative method.
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*
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* Modified: Sanjiv Shah, Kuck and Associates, Inc. (KAI), 1998
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* Author: Joseph Robicheaux, Kuck and Associates, Inc. (KAI), 1998
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*
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* Directives are used in this code to achieve paralleism.
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* All do loops are parallized with default 'static' scheduling.
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*
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* Input : n - grid dimension in x direction
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* m - grid dimension in y direction
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* alpha - Helmholtz constant (always greater than 0.0)
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* tol - error tolerance for iterative solver
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* relax - Successice over relaxation parameter
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* mits - Maximum iterations for iterative solver
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*
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* On output
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* : u(n,m) - Dependent variable (solutions)
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* : f(n,m) - Right hand side function
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*************************************************************
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implicit none
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integer n,m,mits,mtemp
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include "omp_lib.h"
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double precision tol,relax,alpha
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common /idat/ n,m,mits,mtemp
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common /fdat/tol,alpha,relax
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*
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* Read info
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*
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write(*,*) "Input n,m - grid dimension in x,y direction "
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n = 64
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m = 64
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* read(5,*) n,m
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write(*,*) n, m
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write(*,*) "Input alpha - Helmholts constant "
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alpha = 0.5
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* read(5,*) alpha
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write(*,*) alpha
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write(*,*) "Input relax - Successive over-relaxation parameter"
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relax = 0.9
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* read(5,*) relax
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write(*,*) relax
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write(*,*) "Input tol - error tolerance for iterative solver"
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tol = 1.0E-12
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* read(5,*) tol
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write(*,*) tol
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write(*,*) "Input mits - Maximum iterations for solver"
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mits = 100
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* read(5,*) mits
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write(*,*) mits
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call omp_set_num_threads (2)
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*
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* Calls a driver routine
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*
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call driver ()
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stop
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end
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subroutine driver ( )
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*************************************************************
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* Subroutine driver ()
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* This is where the arrays are allocated and initialzed.
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*
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* Working varaibles/arrays
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* dx - grid spacing in x direction
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* dy - grid spacing in y direction
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*************************************************************
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implicit none
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integer n,m,mits,mtemp
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double precision tol,relax,alpha
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common /idat/ n,m,mits,mtemp
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common /fdat/tol,alpha,relax
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double precision u(n,m),f(n,m),dx,dy
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* Initialize data
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call initialize (n,m,alpha,dx,dy,u,f)
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* Solve Helmholtz equation
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call jacobi (n,m,dx,dy,alpha,relax,u,f,tol,mits)
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* Check error between exact solution
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call error_check (n,m,alpha,dx,dy,u,f)
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return
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end
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subroutine initialize (n,m,alpha,dx,dy,u,f)
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******************************************************
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* Initializes data
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* Assumes exact solution is u(x,y) = (1-x^2)*(1-y^2)
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*
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******************************************************
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implicit none
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integer n,m
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double precision u(n,m),f(n,m),dx,dy,alpha
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integer i,j, xx,yy
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double precision PI
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parameter (PI=3.1415926)
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dx = 2.0 / (n-1)
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dy = 2.0 / (m-1)
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* Initilize initial condition and RHS
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!$omp parallel do private(xx,yy)
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do j = 1,m
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do i = 1,n
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xx = -1.0 + dx * dble(i-1) ! -1 < x < 1
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yy = -1.0 + dy * dble(j-1) ! -1 < y < 1
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u(i,j) = 0.0
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f(i,j) = -alpha *(1.0-xx*xx)*(1.0-yy*yy)
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& - 2.0*(1.0-xx*xx)-2.0*(1.0-yy*yy)
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enddo
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enddo
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!$omp end parallel do
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return
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end
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subroutine jacobi (n,m,dx,dy,alpha,omega,u,f,tol,maxit)
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******************************************************************
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* Subroutine HelmholtzJ
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* Solves poisson equation on rectangular grid assuming :
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* (1) Uniform discretization in each direction, and
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* (2) Dirichlect boundary conditions
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*
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* Jacobi method is used in this routine
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*
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* Input : n,m Number of grid points in the X/Y directions
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* dx,dy Grid spacing in the X/Y directions
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* alpha Helmholtz eqn. coefficient
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* omega Relaxation factor
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* f(n,m) Right hand side function
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* u(n,m) Dependent variable/Solution
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* tol Tolerance for iterative solver
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* maxit Maximum number of iterations
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*
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* Output : u(n,m) - Solution
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*****************************************************************
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implicit none
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integer n,m,maxit
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double precision dx,dy,f(n,m),u(n,m),alpha, tol,omega
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*
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* Local variables
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*
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integer i,j,k,k_local
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double precision error,resid,rsum,ax,ay,b
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double precision error_local, uold(n,m)
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real ta,tb,tc,td,te,ta1,ta2,tb1,tb2,tc1,tc2,td1,td2
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real te1,te2
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real second
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external second
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*
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* Initialize coefficients
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ax = 1.0/(dx*dx) ! X-direction coef
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ay = 1.0/(dy*dy) ! Y-direction coef
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b = -2.0/(dx*dx)-2.0/(dy*dy) - alpha ! Central coeff
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error = 10.0 * tol
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k = 1
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do while (k.le.maxit .and. error.gt. tol)
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error = 0.0
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* Copy new solution into old
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!$omp parallel
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!$omp do
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do j=1,m
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do i=1,n
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uold(i,j) = u(i,j)
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enddo
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enddo
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* Compute stencil, residual, & update
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!$omp do private(resid) reduction(+:error)
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do j = 2,m-1
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do i = 2,n-1
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* Evaluate residual
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resid = (ax*(uold(i-1,j) + uold(i+1,j))
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& + ay*(uold(i,j-1) + uold(i,j+1))
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& + b * uold(i,j) - f(i,j))/b
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* Update solution
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u(i,j) = uold(i,j) - omega * resid
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* Accumulate residual error
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error = error + resid*resid
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end do
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enddo
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!$omp enddo nowait
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!$omp end parallel
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* Error check
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k = k + 1
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error = sqrt(error)/dble(n*m)
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*
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enddo ! End iteration loop
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*
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print *, 'Total Number of Iterations ', k
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print *, 'Residual ', error
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return
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end
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subroutine error_check (n,m,alpha,dx,dy,u,f)
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implicit none
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************************************************************
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* Checks error between numerical and exact solution
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*
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************************************************************
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integer n,m
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double precision u(n,m),f(n,m),dx,dy,alpha
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integer i,j
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double precision xx,yy,temp,error
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dx = 2.0 / (n-1)
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dy = 2.0 / (m-1)
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error = 0.0
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!$omp parallel do private(xx,yy,temp) reduction(+:error)
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do j = 1,m
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do i = 1,n
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xx = -1.0d0 + dx * dble(i-1)
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yy = -1.0d0 + dy * dble(j-1)
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temp = u(i,j) - (1.0-xx*xx)*(1.0-yy*yy)
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error = error + temp*temp
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enddo
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enddo
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error = sqrt(error)/dble(n*m)
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print *, 'Solution Error : ',error
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return
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end
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