High Performance Scientific Computing   AMath 483/583 Class Notes   Spring Quarter, 2013

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Jacobi iteration using OpenMP with parallel do constructs

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Jacobi iteration using MPI

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 ! $UWHPSC/codes/openmp/jacobi1d_omp2.f90 ! ! Domain decomposition version of Jacobi iteration illustrating ! coarse grain parallelism with OpenMP. ! ! The grid points are split up into nthreads disjoint sets and each thread ! is assigned one set that it updates for all iterations. program jacobi1d_omp2 use omp_lib implicit none real(kind=8), dimension(:), allocatable :: x,u,uold,f real(kind=8) :: alpha, beta, dx, tol, dumax, dumax_thread real(kind=8), intrinsic :: exp real(kind=8) :: t1,t2 integer :: n, nthreads, points_per_thread,thread_num integer :: i,iter,maxiter,istart,iend,nprint ! Specify number of threads to use: nthreads = 1 ! need this value in serial mode !$ nthreads = 2 !$call omp_set_num_threads(nthreads) !$ print "('Using OpenMP with ',i3,' threads')", nthreads nprint = 10000 ! print dumax every nprint iterations 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") call cpu_time(t1) ! grid spacing: dx = 1.d0 / (n+1.d0) ! boundary conditions: alpha = 20.d0 beta = 60.d0 ! 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 ! Determine how many points to handle with each thread. ! Note that dividing two integers and assigning to an integer will ! round down if the result is not an integer. ! This, together with the min(...) in the definition of iend below, ! insures that all points will get distributed to some thread. points_per_thread = (n + nthreads - 1) / nthreads print *, "points_per_thread = ",points_per_thread ! Start of the parallel block... ! ------------------------------ ! This is the only time threads are forked in this program: !$omp parallel private(thread_num, iter, istart, iend, i, dumax_thread) thread_num = 0 ! needed in serial mode !$ thread_num = omp_get_thread_num() ! unique for each thread ! Determine start and end index for the set of points to be ! handled by this thread: istart = thread_num * points_per_thread + 1 iend = min((thread_num+1) * points_per_thread, n) !$omp critical print '("Thread ",i2," will take i = ",i6," through i = ",i6)', & thread_num, istart, iend !$omp end critical ! Initialize: ! ----------- ! each thread sets part of these arrays: do i=istart, iend ! grid points: x(i) = i*dx ! source term: f(i) = 100.*exp(x(i)) ! initial guess: u(i) = alpha + x(i)*(beta-alpha) enddo ! boundary conditions need to be added: u(0) = alpha u(n+1) = beta uold = u ! initialize, including boundary values ! Jacobi iteratation: ! ------------------- do iter=1,maxiter ! initialize uold to u (note each thread does part!) uold(istart:iend) = u(istart:iend) !$omp single dumax = 0.d0 ! global max initialized by one thread !$omp end single ! Make sure all of uold is initialized before iterating !$omp barrier ! Make sure uold is consitent in memory: !$omp flush dumax_thread = 0.d0 ! max seen by this thread do i=istart,iend u(i) = 0.5d0*(uold(i-1) + uold(i+1) + dx**2*f(i)) dumax_thread = max(dumax_thread, abs(u(i)-uold(i))) enddo !$omp critical ! update global dumax using value from this thread: dumax = max(dumax, dumax_thread) !$omp end critical ! make sure all threads are done with dumax: !$omp barrier !$omp single ! only one thread will do this print statement: if (mod(iter,nprint)==0) then print '("After ",i8," iterations, dumax = ",d16.6,/)', iter, dumax endif !$omp end single ! check for convergence: ! note that all threads have same value of dumax ! at this point, so they will all exit on the same iteration. if (dumax .lt. tol) exit ! need to synchronize here so no thread resets dumax = 0 ! at start of next iteration before all have done the test above. !$omp barrier enddo print '("Thread number ",i2," finished after ",i9, & " iterations, dumax = ", e16.6)', & thread_num,iter,dumax !\$omp end parallel call cpu_time(t2) print '("CPU time = ",f12.8, " seconds")', t2-t1 ! Write solution to heatsoln.txt: write(20,*) " x u" do i=0,n+1 write(20,'(2e20.10)'), x(i), u(i) enddo print *, "Solution is in heatsoln.txt" close(20) end program jacobi1d_omp2