Jacobi iteration using OpenMP with parallel do constructs

The code below implements Jacobi iteration for solving the linear system arising from the steady state heat equation with a simple application of parallel do loops using OpenMP.

Compare to:

• Jacobi iteration using OpenMP with coarse-grain parallel block
• Jacobi iteration using MPI

The code:

! $CLASSHG/codes/openmp/jacobi1.f90

program jacobi1
    use omp_lib
    implicit none
    integer :: n, nthreads
    real(kind=8), dimension(:), allocatable :: x,u,uold,f
    real(kind=8) :: alpha, beta, dx, tol, dumax
    real(kind=8), intrinsic :: exp
    integer :: i,iter,maxiter 

   ! Specify number of threads to use:
   nthreads = 2
   !$ call omp_set_num_threads(nthreads)
   !$ print "('Using OpenMP with ',i3,' threads')", nthreads

    print *, "Input n ... "
    read *, n

    ! allocate storage for boundary points too:
    allocate(x(0:n+1), u(0:n+1), uold(0:n+1), f(0:n+1))

    open(unit=20, file="heatsoln.txt", status="unknown")

    ! grid spacing:
    dx = 1.d0 / (n+1.d0)

    ! boundary conditions:
    alpha = 20.d0
    beta = 60.d0

    !$omp parallel do
    do i=0,n+1
        ! grid points:
        x(i) = i*dx
        ! source term:
        f(i) = 100.*exp(x(i))
        ! initial guess:
        u(i) = alpha + x(i)*(beta-alpha)
        enddo

    ! tolerance and max number of iterations:
    tol = 0.1 * dx**2
    print *, "Convergence tolerance: tol = ",tol
    maxiter = 100000
    print *, "Maximum number of iterations: maxiter = ",maxiter

    ! Jacobi iteratation:

    uold = u  ! starting values before updating

    do iter=1,maxiter
        dumax = 0.d0
        !$omp parallel do reduction(max : dumax)
        do i=1,n
            u(i) = 0.5d0*(uold(i-1) + uold(i+1) + dx**2*f(i))
            dumax = max(dumax, abs(u(i)-uold(i)))
            enddo
        if (mod(iter,10000)==0) then
            print *, iter, dumax
            endif
        ! check for convergence:
        if (dumax .lt. tol) exit

        !$omp parallel do 
        do i=1,n
            uold(i) = u(i)   ! for next iteration
            enddo
        enddo

    print *, "Total number of iterations: ",iter

    write(20,*) "          x                  u"
    do i=0,n+1
        write(20,222), x(i), u(i)
        enddo
222 format(2e20.10)

    print *, "Solution is in heatsoln.txt"

    close(20)

end program jacobi1