The Thermoflow60 Finite-Element. Program
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1 The Thermoflow60 Finite-Element Program Ulrich Wepler,, German Aerospace enter (DLR) Dieter an Mey, enter for omputing and ommunication,, RWTH Alexander Spiegel, enter for omputing and ommunication,, RWTH Thomas Haarmann, Daimlerhrysler Wolfgang Koschel,, Jet Propulsion Laboratory, RWTH 1 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
2 Heat Flow Simulation with Finite Elements - ThermoFlow60 simulation of the heat flow in a rocket combustion chamber 2D sufficient because of rotational symmetrie Finite Element method home-grown code 14 years of development has been vectorized before lines of Fortran ~ 200 OpenMP directives 69 parallel loops 1 main parallel region (orphaning) 200,000 cells 230 MB memory footprint 2 weeks serial runtime 2 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
3 Simulation of the Heat Flow in a Rocket ombustion hamber 3 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
4 The Grid very fine resolution at the boundary to the wall. no adaptation necessary => loop limits remain constant coupled FD- and structural analysis in preparation 4 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
5 First Approach to OpenMP c$omp parallel do private(k1,k2,k3,dtel,q1,q2,q3,dtdrye,viture,ynorme,retur c$omp& rhoe,tuke,epse,xmatl,prode1,prode2,dampqe,cw1e,q11,q12, c$omp& q13,w11,w12,w13,vilaml,viturl,rlamda,rmue2,dudxns, $omp& DUDYNS,DVDXNS,DVDYNS,DTDX,DTDY,dq2dx,dq2dy,PL,UUEL, $omp& VVEL,VISK,VISE,q21,q22,q23,w21,w22,w23) DO I=1,NELM K1 = IELM(I,1) K2 = IELM(I,2) K3 = IELM(I,3) DTEL =.5d+00*DRI*(DTKN(K1)+DTKN(K2)+DTKN(K3)) Q1 = U(K1)*DNDX(I,1)+V(K1)*DNDY(I,1) Q2 = U(K2)*DNDX(I,2)+V(K2)*DNDY(I,2) Q3 = U(K3)*DNDX(I,3)+V(K3)*DNDY(I,3) DTDRYE = DRI/YEL(I) lines omitted --- q21 = tukl(i) * cq1 * cmy*dampqe*prode1*rhol(i)/epsl(i) q22 = tukl(i) * cq1 * prode2 q23 = tukl(i) * cq1 * ( 1.0d+00+sark*xmatl )*epsl(i)/rhol(i) w21 = epsl(i) * cw1e * cmy*prode1*rhol(i)/epsl(i) w22 = epsl(i) * cw1e * cw3*1.5d+00*prode2 w23 = epsl(i) * cw2*epsl(i)/rhol(i) qtukl(i) = q21 + q22 - q23 qepsl(i) = w21 + w22 - w23 loop over all elements END DO c$omp 5 end parallel U.Wepler, do A. Spiegel, D. an Mey, et.al. Thermoflow60 All these arrays reside in g(shared (shared) OMMON blocks enter for omputing and ommunication
6 Here Orphaning simplifies the ode... c$omp do code out of parallelized loops has to be put in single regions or has to be executed redundantly all the local variables are private by default DO I=1,NELM K1 = IELM(I,1) K2 = IELM(I,2) K3 = IELM(I,3) DTEL =.5d+00*DRI*(DTKN(K1)+DTKN(K2)+DTKN(K3)) Q1 = U(K1)*DNDX(I,1)+V(K1)*DNDY(I,1) Q2 = U(K2)*DNDX(I,2)+V(K2)*DNDY(I,2) Q3 = U(K3)*DNDX(I,3)+V(K3)*DNDY(I,3) DTDRYE = DRI/YEL(I) lines omitted --- q21 = tukl(i) * cq1 * cmy*dampqe*prode1*rhol(i)/epsl(i) q22 = tukl(i) * cq1 * prode2 q23 = tukl(i) * cq1 * ( 1.0d+00+sark*xmatl )*epsl(i)/rhol(i) w21 = epsl(i) * cw1e * cmy*prode1*rhol(i)/epsl(i) w22 = epsl(i) * cw1e * cw3*1.5d+00*prode2 w23 = epsl(i) * cw2*epsl(i)/rhol(i) qtukl(i) = q21 + q22 - q23 qepsl(i) = w21 + w22 - w23 END DO c$omp 6 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 All All these arrays in reside OMMON in g(shared blocks OMMON remain shared blocks enter for omputing and ommunication
7 Frequently used Loop onstructs! Loop type 1, loop over (~100,000) FE nodes...!$omp! Loop type 2, loop over (~200,000) FE cells do i = 1, nelm...!$omp! Loop (nest) type 3, loop over nodes and neighbours do j = 1, nknot(i)! varies between 3 and 6...!$omp 7 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
8 Eliminating unnecessary Barriers! Barriers between loops of the same type! can in many cases be eliminated:...!$omp nowait...!$omp 8 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
9 Avoiding the Overhead of Worksharing onstructs! Loop type 1, loop over (~100,000) FE nodes do i = ilo_poin, ihi_poin >...!$omp!$omp barrier! Loop type 2, loop over (~200,000) FE cells do i = 1, nelm do i = ilo_elm, ihi_elm >...!$omp!$omp barrier! Loop (nest) type 3, loop over nodes and neighbours do i = ilo_knot, ihi_knot do j = 1, nknot(i) do j = 1, nknot(i) >...!$omp!$omp barrier 9 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
10 Precalculating the Loop Limits (1 of 2)! Loop type 1, loop over (~100,000) FE nodes integer ilo_poin,ihi_poin,ilo_elm,ihi_elm,ilo_knot,ihi_knot common /omp_com/ilo_poin,ihi_poin,ilo_elm,ihi_elm,ilo_knot,...!$omp threadprivate(/omp_com/) nrem_poin = mod ( npoin, nthreads )! remaining nodes nchunk_poin = ( npoin - nrem_poin ) / nthreads! chunk size!$omp parallel private(myid) myid = omp_get_thread_num() Even work distribution if ( myid < nrem_poin ) then ilo_poin = 1 + myid * ( nchunk_poin + 1 ) ihi_poin = ilo_poin + nchunk_poin else ilo_poin = 1 + myid * nchunk_poin + nrem_poin ihi_poin = ilo_poin + nchunk_poin - 1 end if!$omp end parallel! Loop type 2, loop over (~200,000) FE cells --- similar to loop type U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
11 Precalculating the Loop Limits (2 of 2)! Loop (nest) type 3, loop over nodes and neighbours itotal = 0 itotal = itotal + nknot(i) nchunk_knot = itotal / nthreads itotal = 0 ithread = 0 ilo_temp(0) = 1 itotal = itotal + nknot(i) if ( itotal.ge. (ithread+1)*nchunk_knot ) then ihi_temp(ithread) = i ithread = ithread + 1 if ( ithread.ge. nthreads ) exit ilo_temp(ithread) = i + 1 end if ihi_temp(nthreads-1) = npoin!$omp parallel private(myid) myid = omp_get_thread_num() ilo_knot = ilo_temp(myid) ihi_knot = ihi_temp(myid)!$omp end parallel 11 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
12 Loop Nest with Precalculated Optimal Schedule do i = ilo_knot, ihi_knot do j = 1,nknot(i) ii = iknot(i,j)! Element number kk = iknel(i,j)! local node number (1-3) lines omitted --- c$omp barrier 12 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
13 Timings on Sun Fire 15K 13 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
14 OMPlab Scalability on Sun and IBM Analysis (Sun Analyzer, IBM Memory Placement Tuning, IBM xprofiler, Paraver...) 14 U.Wepler, A. Spiegel, D. an Mey, et.al. Thermoflow60 enter for omputing and ommunication
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