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lulesh.cc
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/*
This is a Version 2.0 MPI + OpenMP implementation of LULESH
Copyright (c) 2010-2013.
Lawrence Livermore National Security, LLC.
Produced at the Lawrence Livermore National Laboratory.
LLNL-CODE-461231
All rights reserved.
This file is part of LULESH, Version 2.0.
Please also read this link -- http://www.opensource.org/licenses/index.php
//////////////
DIFFERENCES BETWEEN THIS VERSION (2.x) AND EARLIER VERSIONS:
* Addition of regions to make work more representative of multi-material codes
* Default size of each domain is 30^3 (27000 elem) instead of 45^3. This is
more representative of our actual working set sizes
* Single source distribution supports pure serial, pure OpenMP, MPI-only,
and MPI+OpenMP
* Addition of ability to visualize the mesh using VisIt
https://wci.llnl.gov/codes/visit/download.html
* Various command line options (see ./lulesh2.0 -h)
-q : quiet mode - suppress stdout
-i <iterations> : number of cycles to run
-s <size> : length of cube mesh along side
-r <numregions> : Number of distinct regions (def: 11)
-b <balance> : Load balance between regions of a domain (def: 1)
-c <cost> : Extra cost of more expensive regions (def: 1)
-f <filepieces> : Number of file parts for viz output (def: np/9)
-p : Print out progress
-v : Output viz file (requires compiling with -DVIZ_MESH
-h : This message
printf("Usage: %s [opts]\n", execname);
printf(" where [opts] is one or more of:\n");
printf(" -q : quiet mode - suppress all stdout\n");
printf(" -i <iterations> : number of cycles to run\n");
printf(" -s <size> : length of cube mesh along side\n");
printf(" -r <numregions> : Number of distinct regions (def: 11)\n");
printf(" -b <balance> : Load balance between regions of a domain (def: 1)\n");
printf(" -c <cost> : Extra cost of more expensive regions (def: 1)\n");
printf(" -f <numfiles> : Number of files to split viz dump into (def: (np+10)/9)\n");
printf(" -p : Print out progress\n");
printf(" -v : Output viz file (requires compiling with -DVIZ_MESH\n");
printf(" -h : This message\n");
printf("\n\n");
*Notable changes in LULESH 2.0
* Split functionality into different files
lulesh.cc - where most (all?) of the timed functionality lies
lulesh-comm.cc - MPI functionality
lulesh-init.cc - Setup code
lulesh-viz.cc - Support for visualization option
lulesh-util.cc - Non-timed functions
*
* The concept of "regions" was added, although every region is the same ideal
* gas material, and the same sedov blast wave problem is still the only
* problem its hardcoded to solve.
* Regions allow two things important to making this proxy app more representative:
* Four of the LULESH routines are now performed on a region-by-region basis,
* making the memory access patterns non-unit stride
* Artificial load imbalances can be easily introduced that could impact
* parallelization strategies.
* The load balance flag changes region assignment. Region number is raised to
* the power entered for assignment probability. Most likely regions changes
* with MPI process id.
* The cost flag raises the cost of ~45% of the regions to evaluate EOS by the
* entered multiple. The cost of 5% is 10x the entered multiple.
* MPI and OpenMP were added, and coalesced into a single version of the source
* that can support serial builds, MPI-only, OpenMP-only, and MPI+OpenMP
* Added support to write plot files using "poor mans parallel I/O" when linked
* with the silo library, which in turn can be read by VisIt.
* Enabled variable timestep calculation by default (courant condition), which
* results in an additional reduction.
* Default domain (mesh) size reduced from 45^3 to 30^3
* Command line options to allow numerous test cases without needing to recompile
* Performance optimizations and code cleanup beyond LULESH 1.0
* Added a "Figure of Merit" calculation (elements solved per microsecond) and
* output in support of using LULESH 2.0 for the 2017 CORAL procurement
*
* Possible Differences in Final Release (other changes possible)
*
* High Level mesh structure to allow data structure transformations
* Different default parameters
* Minor code performance changes and cleanup
TODO in future versions
* Add reader for (truly) unstructured meshes, probably serial only
* CMake based build system
//////////////
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the disclaimer below.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the disclaimer (as noted below)
in the documentation and/or other materials provided with the
distribution.
* Neither the name of the LLNS/LLNL nor the names of its contributors
may be used to endorse or promote products derived from this software
without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL LAWRENCE LIVERMORE NATIONAL SECURITY, LLC,
THE U.S. DEPARTMENT OF ENERGY OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Additional BSD Notice
1. This notice is required to be provided under our contract with the U.S.
Department of Energy (DOE). This work was produced at Lawrence Livermore
National Laboratory under Contract No. DE-AC52-07NA27344 with the DOE.
2. Neither the United States Government nor Lawrence Livermore National
Security, LLC nor any of their employees, makes any warranty, express
or implied, or assumes any liability or responsibility for the accuracy,
completeness, or usefulness of any information, apparatus, product, or
process disclosed, or represents that its use would not infringe
privately-owned rights.
3. Also, reference herein to any specific commercial products, process, or
services by trade name, trademark, manufacturer or otherwise does not
necessarily constitute or imply its endorsement, recommendation, or
favoring by the United States Government or Lawrence Livermore National
Security, LLC. The views and opinions of authors expressed herein do not
necessarily state or reflect those of the United States Government or
Lawrence Livermore National Security, LLC, and shall not be used for
advertising or product endorsement purposes.
*/
#include <climits>
#include <vector>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <time.h>
#include <sys/time.h>
#include <iostream>
#include <unistd.h>
#if _OPENMP
# include <omp.h>
#endif
#include "lulesh.h"
/* Work Routines */
static inline
void TimeIncrement(Domain& domain)
{
Real_t targetdt = domain.stoptime() - domain.time() ;
if ((domain.dtfixed() <= Real_t(0.0)) && (domain.cycle() != Int_t(0))) {
Real_t ratio ;
Real_t olddt = domain.deltatime() ;
/* This will require a reduction in parallel */
Real_t gnewdt = Real_t(1.0e+20) ;
Real_t newdt ;
if (domain.dtcourant() < gnewdt) {
gnewdt = domain.dtcourant() / Real_t(2.0) ;
}
if (domain.dthydro() < gnewdt) {
gnewdt = domain.dthydro() * Real_t(2.0) / Real_t(3.0) ;
}
#if USE_MPI
MPI_Allreduce(&gnewdt, &newdt, 1,
((sizeof(Real_t) == 4) ? MPI_FLOAT : MPI_DOUBLE),
MPI_MIN, MPI_COMM_WORLD) ;
#else
newdt = gnewdt;
#endif
ratio = newdt / olddt ;
if (ratio >= Real_t(1.0)) {
if (ratio < domain.deltatimemultlb()) {
newdt = olddt ;
}
else if (ratio > domain.deltatimemultub()) {
newdt = olddt*domain.deltatimemultub() ;
}
}
if (newdt > domain.dtmax()) {
newdt = domain.dtmax() ;
}
domain.deltatime() = newdt ;
}
/* TRY TO PREVENT VERY SMALL SCALING ON THE NEXT CYCLE */
if ((targetdt > domain.deltatime()) &&
(targetdt < (Real_t(4.0) * domain.deltatime() / Real_t(3.0))) ) {
targetdt = Real_t(2.0) * domain.deltatime() / Real_t(3.0) ;
}
if (targetdt < domain.deltatime()) {
domain.deltatime() = targetdt ;
}
domain.time() += domain.deltatime() ;
++domain.cycle() ;
}
/******************************************/
static inline
void CollectDomainNodesToElemNodes(Domain &domain,
const Index_t* elemToNode,
Real_t elemX[8],
Real_t elemY[8],
Real_t elemZ[8])
{
Index_t nd0i = elemToNode[0] ;
Index_t nd1i = elemToNode[1] ;
Index_t nd2i = elemToNode[2] ;
Index_t nd3i = elemToNode[3] ;
Index_t nd4i = elemToNode[4] ;
Index_t nd5i = elemToNode[5] ;
Index_t nd6i = elemToNode[6] ;
Index_t nd7i = elemToNode[7] ;
elemX[0] = domain.x(nd0i);
elemX[1] = domain.x(nd1i);
elemX[2] = domain.x(nd2i);
elemX[3] = domain.x(nd3i);
elemX[4] = domain.x(nd4i);
elemX[5] = domain.x(nd5i);
elemX[6] = domain.x(nd6i);
elemX[7] = domain.x(nd7i);
elemY[0] = domain.y(nd0i);
elemY[1] = domain.y(nd1i);
elemY[2] = domain.y(nd2i);
elemY[3] = domain.y(nd3i);
elemY[4] = domain.y(nd4i);
elemY[5] = domain.y(nd5i);
elemY[6] = domain.y(nd6i);
elemY[7] = domain.y(nd7i);
elemZ[0] = domain.z(nd0i);
elemZ[1] = domain.z(nd1i);
elemZ[2] = domain.z(nd2i);
elemZ[3] = domain.z(nd3i);
elemZ[4] = domain.z(nd4i);
elemZ[5] = domain.z(nd5i);
elemZ[6] = domain.z(nd6i);
elemZ[7] = domain.z(nd7i);
}
/******************************************/
static inline
void InitStressTermsForElems(Domain &domain,
Real_t *sigxx, Real_t *sigyy, Real_t *sigzz,
Index_t numElem)
{
//
// pull in the stresses appropriate to the hydro integration
//
#pragma omp parallel for firstprivate(numElem)
for (Index_t i = 0 ; i < numElem ; ++i){
sigxx[i] = sigyy[i] = sigzz[i] = - domain.p(i) - domain.q(i) ;
}
}
/******************************************/
static inline
void CalcElemShapeFunctionDerivatives( Real_t const x[],
Real_t const y[],
Real_t const z[],
Real_t b[][8],
Real_t* const volume )
{
const Real_t x0 = x[0] ; const Real_t x1 = x[1] ;
const Real_t x2 = x[2] ; const Real_t x3 = x[3] ;
const Real_t x4 = x[4] ; const Real_t x5 = x[5] ;
const Real_t x6 = x[6] ; const Real_t x7 = x[7] ;
const Real_t y0 = y[0] ; const Real_t y1 = y[1] ;
const Real_t y2 = y[2] ; const Real_t y3 = y[3] ;
const Real_t y4 = y[4] ; const Real_t y5 = y[5] ;
const Real_t y6 = y[6] ; const Real_t y7 = y[7] ;
const Real_t z0 = z[0] ; const Real_t z1 = z[1] ;
const Real_t z2 = z[2] ; const Real_t z3 = z[3] ;
const Real_t z4 = z[4] ; const Real_t z5 = z[5] ;
const Real_t z6 = z[6] ; const Real_t z7 = z[7] ;
Real_t fjxxi, fjxet, fjxze;
Real_t fjyxi, fjyet, fjyze;
Real_t fjzxi, fjzet, fjzze;
Real_t cjxxi, cjxet, cjxze;
Real_t cjyxi, cjyet, cjyze;
Real_t cjzxi, cjzet, cjzze;
fjxxi = Real_t(.125) * ( (x6-x0) + (x5-x3) - (x7-x1) - (x4-x2) );
fjxet = Real_t(.125) * ( (x6-x0) - (x5-x3) + (x7-x1) - (x4-x2) );
fjxze = Real_t(.125) * ( (x6-x0) + (x5-x3) + (x7-x1) + (x4-x2) );
fjyxi = Real_t(.125) * ( (y6-y0) + (y5-y3) - (y7-y1) - (y4-y2) );
fjyet = Real_t(.125) * ( (y6-y0) - (y5-y3) + (y7-y1) - (y4-y2) );
fjyze = Real_t(.125) * ( (y6-y0) + (y5-y3) + (y7-y1) + (y4-y2) );
fjzxi = Real_t(.125) * ( (z6-z0) + (z5-z3) - (z7-z1) - (z4-z2) );
fjzet = Real_t(.125) * ( (z6-z0) - (z5-z3) + (z7-z1) - (z4-z2) );
fjzze = Real_t(.125) * ( (z6-z0) + (z5-z3) + (z7-z1) + (z4-z2) );
/* compute cofactors */
cjxxi = (fjyet * fjzze) - (fjzet * fjyze);
cjxet = - (fjyxi * fjzze) + (fjzxi * fjyze);
cjxze = (fjyxi * fjzet) - (fjzxi * fjyet);
cjyxi = - (fjxet * fjzze) + (fjzet * fjxze);
cjyet = (fjxxi * fjzze) - (fjzxi * fjxze);
cjyze = - (fjxxi * fjzet) + (fjzxi * fjxet);
cjzxi = (fjxet * fjyze) - (fjyet * fjxze);
cjzet = - (fjxxi * fjyze) + (fjyxi * fjxze);
cjzze = (fjxxi * fjyet) - (fjyxi * fjxet);
/* calculate partials :
this need only be done for l = 0,1,2,3 since , by symmetry ,
(6,7,4,5) = - (0,1,2,3) .
*/
b[0][0] = - cjxxi - cjxet - cjxze;
b[0][1] = cjxxi - cjxet - cjxze;
b[0][2] = cjxxi + cjxet - cjxze;
b[0][3] = - cjxxi + cjxet - cjxze;
b[0][4] = -b[0][2];
b[0][5] = -b[0][3];
b[0][6] = -b[0][0];
b[0][7] = -b[0][1];
b[1][0] = - cjyxi - cjyet - cjyze;
b[1][1] = cjyxi - cjyet - cjyze;
b[1][2] = cjyxi + cjyet - cjyze;
b[1][3] = - cjyxi + cjyet - cjyze;
b[1][4] = -b[1][2];
b[1][5] = -b[1][3];
b[1][6] = -b[1][0];
b[1][7] = -b[1][1];
b[2][0] = - cjzxi - cjzet - cjzze;
b[2][1] = cjzxi - cjzet - cjzze;
b[2][2] = cjzxi + cjzet - cjzze;
b[2][3] = - cjzxi + cjzet - cjzze;
b[2][4] = -b[2][2];
b[2][5] = -b[2][3];
b[2][6] = -b[2][0];
b[2][7] = -b[2][1];
/* calculate jacobian determinant (volume) */
*volume = Real_t(8.) * ( fjxet * cjxet + fjyet * cjyet + fjzet * cjzet);
}
/******************************************/
static inline
void SumElemFaceNormal(Real_t *normalX0, Real_t *normalY0, Real_t *normalZ0,
Real_t *normalX1, Real_t *normalY1, Real_t *normalZ1,
Real_t *normalX2, Real_t *normalY2, Real_t *normalZ2,
Real_t *normalX3, Real_t *normalY3, Real_t *normalZ3,
const Real_t x0, const Real_t y0, const Real_t z0,
const Real_t x1, const Real_t y1, const Real_t z1,
const Real_t x2, const Real_t y2, const Real_t z2,
const Real_t x3, const Real_t y3, const Real_t z3)
{
Real_t bisectX0 = Real_t(0.5) * (x3 + x2 - x1 - x0);
Real_t bisectY0 = Real_t(0.5) * (y3 + y2 - y1 - y0);
Real_t bisectZ0 = Real_t(0.5) * (z3 + z2 - z1 - z0);
Real_t bisectX1 = Real_t(0.5) * (x2 + x1 - x3 - x0);
Real_t bisectY1 = Real_t(0.5) * (y2 + y1 - y3 - y0);
Real_t bisectZ1 = Real_t(0.5) * (z2 + z1 - z3 - z0);
Real_t areaX = Real_t(0.25) * (bisectY0 * bisectZ1 - bisectZ0 * bisectY1);
Real_t areaY = Real_t(0.25) * (bisectZ0 * bisectX1 - bisectX0 * bisectZ1);
Real_t areaZ = Real_t(0.25) * (bisectX0 * bisectY1 - bisectY0 * bisectX1);
*normalX0 += areaX;
*normalX1 += areaX;
*normalX2 += areaX;
*normalX3 += areaX;
*normalY0 += areaY;
*normalY1 += areaY;
*normalY2 += areaY;
*normalY3 += areaY;
*normalZ0 += areaZ;
*normalZ1 += areaZ;
*normalZ2 += areaZ;
*normalZ3 += areaZ;
}
/******************************************/
static inline
void CalcElemNodeNormals(Real_t pfx[8],
Real_t pfy[8],
Real_t pfz[8],
const Real_t x[8],
const Real_t y[8],
const Real_t z[8])
{
for (Index_t i = 0 ; i < 8 ; ++i) {
pfx[i] = Real_t(0.0);
pfy[i] = Real_t(0.0);
pfz[i] = Real_t(0.0);
}
/* evaluate face one: nodes 0, 1, 2, 3 */
SumElemFaceNormal(&pfx[0], &pfy[0], &pfz[0],
&pfx[1], &pfy[1], &pfz[1],
&pfx[2], &pfy[2], &pfz[2],
&pfx[3], &pfy[3], &pfz[3],
x[0], y[0], z[0], x[1], y[1], z[1],
x[2], y[2], z[2], x[3], y[3], z[3]);
/* evaluate face two: nodes 0, 4, 5, 1 */
SumElemFaceNormal(&pfx[0], &pfy[0], &pfz[0],
&pfx[4], &pfy[4], &pfz[4],
&pfx[5], &pfy[5], &pfz[5],
&pfx[1], &pfy[1], &pfz[1],
x[0], y[0], z[0], x[4], y[4], z[4],
x[5], y[5], z[5], x[1], y[1], z[1]);
/* evaluate face three: nodes 1, 5, 6, 2 */
SumElemFaceNormal(&pfx[1], &pfy[1], &pfz[1],
&pfx[5], &pfy[5], &pfz[5],
&pfx[6], &pfy[6], &pfz[6],
&pfx[2], &pfy[2], &pfz[2],
x[1], y[1], z[1], x[5], y[5], z[5],
x[6], y[6], z[6], x[2], y[2], z[2]);
/* evaluate face four: nodes 2, 6, 7, 3 */
SumElemFaceNormal(&pfx[2], &pfy[2], &pfz[2],
&pfx[6], &pfy[6], &pfz[6],
&pfx[7], &pfy[7], &pfz[7],
&pfx[3], &pfy[3], &pfz[3],
x[2], y[2], z[2], x[6], y[6], z[6],
x[7], y[7], z[7], x[3], y[3], z[3]);
/* evaluate face five: nodes 3, 7, 4, 0 */
SumElemFaceNormal(&pfx[3], &pfy[3], &pfz[3],
&pfx[7], &pfy[7], &pfz[7],
&pfx[4], &pfy[4], &pfz[4],
&pfx[0], &pfy[0], &pfz[0],
x[3], y[3], z[3], x[7], y[7], z[7],
x[4], y[4], z[4], x[0], y[0], z[0]);
/* evaluate face six: nodes 4, 7, 6, 5 */
SumElemFaceNormal(&pfx[4], &pfy[4], &pfz[4],
&pfx[7], &pfy[7], &pfz[7],
&pfx[6], &pfy[6], &pfz[6],
&pfx[5], &pfy[5], &pfz[5],
x[4], y[4], z[4], x[7], y[7], z[7],
x[6], y[6], z[6], x[5], y[5], z[5]);
}
/******************************************/
static inline
void SumElemStressesToNodeForces( const Real_t B[][8],
const Real_t stress_xx,
const Real_t stress_yy,
const Real_t stress_zz,
Real_t fx[], Real_t fy[], Real_t fz[] )
{
for(Index_t i = 0; i < 8; i++) {
fx[i] = -( stress_xx * B[0][i] );
fy[i] = -( stress_yy * B[1][i] );
fz[i] = -( stress_zz * B[2][i] );
}
}
/******************************************/
static inline
void IntegrateStressForElems( Domain &domain,
Real_t *sigxx, Real_t *sigyy, Real_t *sigzz,
Real_t *determ, Index_t numElem, Index_t numNode)
{
#if _OPENMP
Index_t numthreads = omp_get_max_threads();
#else
Index_t numthreads = 1;
#endif
Index_t numElem8 = numElem * 8 ;
Real_t *fx_elem;
Real_t *fy_elem;
Real_t *fz_elem;
Real_t fx_local[8] ;
Real_t fy_local[8] ;
Real_t fz_local[8] ;
if (numthreads > 1) {
fx_elem = Allocate<Real_t>(numElem8) ;
fy_elem = Allocate<Real_t>(numElem8) ;
fz_elem = Allocate<Real_t>(numElem8) ;
}
// loop over all elements
#pragma omp parallel for firstprivate(numElem)
for( Index_t k=0 ; k<numElem ; ++k )
{
const Index_t* const elemToNode = domain.nodelist(k);
Real_t B[3][8] ;// shape function derivatives
Real_t x_local[8] ;
Real_t y_local[8] ;
Real_t z_local[8] ;
// get nodal coordinates from global arrays and copy into local arrays.
CollectDomainNodesToElemNodes(domain, elemToNode, x_local, y_local, z_local);
// Volume calculation involves extra work for numerical consistency
CalcElemShapeFunctionDerivatives(x_local, y_local, z_local,
B, &determ[k]);
CalcElemNodeNormals( B[0] , B[1], B[2],
x_local, y_local, z_local );
if (numthreads > 1) {
// Eliminate thread writing conflicts at the nodes by giving
// each element its own copy to write to
SumElemStressesToNodeForces( B, sigxx[k], sigyy[k], sigzz[k],
&fx_elem[k*8],
&fy_elem[k*8],
&fz_elem[k*8] ) ;
}
else {
SumElemStressesToNodeForces( B, sigxx[k], sigyy[k], sigzz[k],
fx_local, fy_local, fz_local ) ;
// copy nodal force contributions to global force arrray.
for( Index_t lnode=0 ; lnode<8 ; ++lnode ) {
Index_t gnode = elemToNode[lnode];
domain.fx(gnode) += fx_local[lnode];
domain.fy(gnode) += fy_local[lnode];
domain.fz(gnode) += fz_local[lnode];
}
}
}
if (numthreads > 1) {
// If threaded, then we need to copy the data out of the temporary
// arrays used above into the final forces field
#pragma omp parallel for firstprivate(numNode)
for( Index_t gnode=0 ; gnode<numNode ; ++gnode )
{
Index_t count = domain.nodeElemCount(gnode) ;
Index_t *cornerList = domain.nodeElemCornerList(gnode) ;
Real_t fx_tmp = Real_t(0.0) ;
Real_t fy_tmp = Real_t(0.0) ;
Real_t fz_tmp = Real_t(0.0) ;
for (Index_t i=0 ; i < count ; ++i) {
Index_t ielem = cornerList[i] ;
fx_tmp += fx_elem[ielem] ;
fy_tmp += fy_elem[ielem] ;
fz_tmp += fz_elem[ielem] ;
}
domain.fx(gnode) = fx_tmp ;
domain.fy(gnode) = fy_tmp ;
domain.fz(gnode) = fz_tmp ;
}
Release(&fz_elem) ;
Release(&fy_elem) ;
Release(&fx_elem) ;
}
}
/******************************************/
static inline
void VoluDer(const Real_t x0, const Real_t x1, const Real_t x2,
const Real_t x3, const Real_t x4, const Real_t x5,
const Real_t y0, const Real_t y1, const Real_t y2,
const Real_t y3, const Real_t y4, const Real_t y5,
const Real_t z0, const Real_t z1, const Real_t z2,
const Real_t z3, const Real_t z4, const Real_t z5,
Real_t* dvdx, Real_t* dvdy, Real_t* dvdz)
{
const Real_t twelfth = Real_t(1.0) / Real_t(12.0) ;
*dvdx =
(y1 + y2) * (z0 + z1) - (y0 + y1) * (z1 + z2) +
(y0 + y4) * (z3 + z4) - (y3 + y4) * (z0 + z4) -
(y2 + y5) * (z3 + z5) + (y3 + y5) * (z2 + z5);
*dvdy =
- (x1 + x2) * (z0 + z1) + (x0 + x1) * (z1 + z2) -
(x0 + x4) * (z3 + z4) + (x3 + x4) * (z0 + z4) +
(x2 + x5) * (z3 + z5) - (x3 + x5) * (z2 + z5);
*dvdz =
- (y1 + y2) * (x0 + x1) + (y0 + y1) * (x1 + x2) -
(y0 + y4) * (x3 + x4) + (y3 + y4) * (x0 + x4) +
(y2 + y5) * (x3 + x5) - (y3 + y5) * (x2 + x5);
*dvdx *= twelfth;
*dvdy *= twelfth;
*dvdz *= twelfth;
}
/******************************************/
static inline
void CalcElemVolumeDerivative(Real_t dvdx[8],
Real_t dvdy[8],
Real_t dvdz[8],
const Real_t x[8],
const Real_t y[8],
const Real_t z[8])
{
VoluDer(x[1], x[2], x[3], x[4], x[5], x[7],
y[1], y[2], y[3], y[4], y[5], y[7],
z[1], z[2], z[3], z[4], z[5], z[7],
&dvdx[0], &dvdy[0], &dvdz[0]);
VoluDer(x[0], x[1], x[2], x[7], x[4], x[6],
y[0], y[1], y[2], y[7], y[4], y[6],
z[0], z[1], z[2], z[7], z[4], z[6],
&dvdx[3], &dvdy[3], &dvdz[3]);
VoluDer(x[3], x[0], x[1], x[6], x[7], x[5],
y[3], y[0], y[1], y[6], y[7], y[5],
z[3], z[0], z[1], z[6], z[7], z[5],
&dvdx[2], &dvdy[2], &dvdz[2]);
VoluDer(x[2], x[3], x[0], x[5], x[6], x[4],
y[2], y[3], y[0], y[5], y[6], y[4],
z[2], z[3], z[0], z[5], z[6], z[4],
&dvdx[1], &dvdy[1], &dvdz[1]);
VoluDer(x[7], x[6], x[5], x[0], x[3], x[1],
y[7], y[6], y[5], y[0], y[3], y[1],
z[7], z[6], z[5], z[0], z[3], z[1],
&dvdx[4], &dvdy[4], &dvdz[4]);
VoluDer(x[4], x[7], x[6], x[1], x[0], x[2],
y[4], y[7], y[6], y[1], y[0], y[2],
z[4], z[7], z[6], z[1], z[0], z[2],
&dvdx[5], &dvdy[5], &dvdz[5]);
VoluDer(x[5], x[4], x[7], x[2], x[1], x[3],
y[5], y[4], y[7], y[2], y[1], y[3],
z[5], z[4], z[7], z[2], z[1], z[3],
&dvdx[6], &dvdy[6], &dvdz[6]);
VoluDer(x[6], x[5], x[4], x[3], x[2], x[0],
y[6], y[5], y[4], y[3], y[2], y[0],
z[6], z[5], z[4], z[3], z[2], z[0],
&dvdx[7], &dvdy[7], &dvdz[7]);
}
/******************************************/
static inline
void CalcElemFBHourglassForce(Real_t *xd, Real_t *yd, Real_t *zd, Real_t hourgam[][4],
Real_t coefficient,
Real_t *hgfx, Real_t *hgfy, Real_t *hgfz )
{
Real_t hxx[4];
for(Index_t i = 0; i < 4; i++) {
hxx[i] = hourgam[0][i] * xd[0] + hourgam[1][i] * xd[1] +
hourgam[2][i] * xd[2] + hourgam[3][i] * xd[3] +
hourgam[4][i] * xd[4] + hourgam[5][i] * xd[5] +
hourgam[6][i] * xd[6] + hourgam[7][i] * xd[7];
}
for(Index_t i = 0; i < 8; i++) {
hgfx[i] = coefficient *
(hourgam[i][0] * hxx[0] + hourgam[i][1] * hxx[1] +
hourgam[i][2] * hxx[2] + hourgam[i][3] * hxx[3]);
}
for(Index_t i = 0; i < 4; i++) {
hxx[i] = hourgam[0][i] * yd[0] + hourgam[1][i] * yd[1] +
hourgam[2][i] * yd[2] + hourgam[3][i] * yd[3] +
hourgam[4][i] * yd[4] + hourgam[5][i] * yd[5] +
hourgam[6][i] * yd[6] + hourgam[7][i] * yd[7];
}
for(Index_t i = 0; i < 8; i++) {
hgfy[i] = coefficient *
(hourgam[i][0] * hxx[0] + hourgam[i][1] * hxx[1] +
hourgam[i][2] * hxx[2] + hourgam[i][3] * hxx[3]);
}
for(Index_t i = 0; i < 4; i++) {
hxx[i] = hourgam[0][i] * zd[0] + hourgam[1][i] * zd[1] +
hourgam[2][i] * zd[2] + hourgam[3][i] * zd[3] +
hourgam[4][i] * zd[4] + hourgam[5][i] * zd[5] +
hourgam[6][i] * zd[6] + hourgam[7][i] * zd[7];
}
for(Index_t i = 0; i < 8; i++) {
hgfz[i] = coefficient *
(hourgam[i][0] * hxx[0] + hourgam[i][1] * hxx[1] +
hourgam[i][2] * hxx[2] + hourgam[i][3] * hxx[3]);
}
}
/******************************************/
static inline
void CalcFBHourglassForceForElems( Domain &domain,
Real_t *determ,
Real_t *x8n, Real_t *y8n, Real_t *z8n,
Real_t *dvdx, Real_t *dvdy, Real_t *dvdz,
Real_t hourg, Index_t numElem,
Index_t numNode)
{
#if _OPENMP
Index_t numthreads = omp_get_max_threads();
#else
Index_t numthreads = 1;
#endif
/*************************************************
*
* FUNCTION: Calculates the Flanagan-Belytschko anti-hourglass
* force.
*
*************************************************/
Index_t numElem8 = numElem * 8 ;
Real_t *fx_elem;
Real_t *fy_elem;
Real_t *fz_elem;
if(numthreads > 1) {
fx_elem = Allocate<Real_t>(numElem8) ;
fy_elem = Allocate<Real_t>(numElem8) ;
fz_elem = Allocate<Real_t>(numElem8) ;
}
Real_t gamma[4][8];
gamma[0][0] = Real_t( 1.);
gamma[0][1] = Real_t( 1.);
gamma[0][2] = Real_t(-1.);
gamma[0][3] = Real_t(-1.);
gamma[0][4] = Real_t(-1.);
gamma[0][5] = Real_t(-1.);
gamma[0][6] = Real_t( 1.);
gamma[0][7] = Real_t( 1.);
gamma[1][0] = Real_t( 1.);
gamma[1][1] = Real_t(-1.);
gamma[1][2] = Real_t(-1.);
gamma[1][3] = Real_t( 1.);
gamma[1][4] = Real_t(-1.);
gamma[1][5] = Real_t( 1.);
gamma[1][6] = Real_t( 1.);
gamma[1][7] = Real_t(-1.);
gamma[2][0] = Real_t( 1.);
gamma[2][1] = Real_t(-1.);
gamma[2][2] = Real_t( 1.);
gamma[2][3] = Real_t(-1.);
gamma[2][4] = Real_t( 1.);
gamma[2][5] = Real_t(-1.);
gamma[2][6] = Real_t( 1.);
gamma[2][7] = Real_t(-1.);
gamma[3][0] = Real_t(-1.);
gamma[3][1] = Real_t( 1.);
gamma[3][2] = Real_t(-1.);
gamma[3][3] = Real_t( 1.);
gamma[3][4] = Real_t( 1.);
gamma[3][5] = Real_t(-1.);
gamma[3][6] = Real_t( 1.);
gamma[3][7] = Real_t(-1.);
/*************************************************/
/* compute the hourglass modes */
#pragma omp parallel for firstprivate(numElem, hourg)
for(Index_t i2=0;i2<numElem;++i2){
Real_t *fx_local, *fy_local, *fz_local ;
Real_t hgfx[8], hgfy[8], hgfz[8] ;
Real_t coefficient;
Real_t hourgam[8][4];
Real_t xd1[8], yd1[8], zd1[8] ;
const Index_t *elemToNode = domain.nodelist(i2);
Index_t i3=8*i2;
Real_t volinv=Real_t(1.0)/determ[i2];
Real_t ss1, mass1, volume13 ;
for(Index_t i1=0;i1<4;++i1){
Real_t hourmodx =
x8n[i3] * gamma[i1][0] + x8n[i3+1] * gamma[i1][1] +
x8n[i3+2] * gamma[i1][2] + x8n[i3+3] * gamma[i1][3] +
x8n[i3+4] * gamma[i1][4] + x8n[i3+5] * gamma[i1][5] +
x8n[i3+6] * gamma[i1][6] + x8n[i3+7] * gamma[i1][7];
Real_t hourmody =
y8n[i3] * gamma[i1][0] + y8n[i3+1] * gamma[i1][1] +
y8n[i3+2] * gamma[i1][2] + y8n[i3+3] * gamma[i1][3] +
y8n[i3+4] * gamma[i1][4] + y8n[i3+5] * gamma[i1][5] +
y8n[i3+6] * gamma[i1][6] + y8n[i3+7] * gamma[i1][7];
Real_t hourmodz =
z8n[i3] * gamma[i1][0] + z8n[i3+1] * gamma[i1][1] +
z8n[i3+2] * gamma[i1][2] + z8n[i3+3] * gamma[i1][3] +
z8n[i3+4] * gamma[i1][4] + z8n[i3+5] * gamma[i1][5] +
z8n[i3+6] * gamma[i1][6] + z8n[i3+7] * gamma[i1][7];
hourgam[0][i1] = gamma[i1][0] - volinv*(dvdx[i3 ] * hourmodx +
dvdy[i3 ] * hourmody +
dvdz[i3 ] * hourmodz );
hourgam[1][i1] = gamma[i1][1] - volinv*(dvdx[i3+1] * hourmodx +
dvdy[i3+1] * hourmody +
dvdz[i3+1] * hourmodz );
hourgam[2][i1] = gamma[i1][2] - volinv*(dvdx[i3+2] * hourmodx +
dvdy[i3+2] * hourmody +
dvdz[i3+2] * hourmodz );
hourgam[3][i1] = gamma[i1][3] - volinv*(dvdx[i3+3] * hourmodx +
dvdy[i3+3] * hourmody +
dvdz[i3+3] * hourmodz );
hourgam[4][i1] = gamma[i1][4] - volinv*(dvdx[i3+4] * hourmodx +
dvdy[i3+4] * hourmody +
dvdz[i3+4] * hourmodz );
hourgam[5][i1] = gamma[i1][5] - volinv*(dvdx[i3+5] * hourmodx +
dvdy[i3+5] * hourmody +
dvdz[i3+5] * hourmodz );
hourgam[6][i1] = gamma[i1][6] - volinv*(dvdx[i3+6] * hourmodx +
dvdy[i3+6] * hourmody +
dvdz[i3+6] * hourmodz );
hourgam[7][i1] = gamma[i1][7] - volinv*(dvdx[i3+7] * hourmodx +
dvdy[i3+7] * hourmody +
dvdz[i3+7] * hourmodz );
}
/* compute forces */
/* store forces into h arrays (force arrays) */
ss1=domain.ss(i2);
mass1=domain.elemMass(i2);
volume13=CBRT(determ[i2]);
Index_t n0si2 = elemToNode[0];
Index_t n1si2 = elemToNode[1];
Index_t n2si2 = elemToNode[2];
Index_t n3si2 = elemToNode[3];
Index_t n4si2 = elemToNode[4];
Index_t n5si2 = elemToNode[5];
Index_t n6si2 = elemToNode[6];
Index_t n7si2 = elemToNode[7];
xd1[0] = domain.xd(n0si2);
xd1[1] = domain.xd(n1si2);
xd1[2] = domain.xd(n2si2);
xd1[3] = domain.xd(n3si2);
xd1[4] = domain.xd(n4si2);
xd1[5] = domain.xd(n5si2);
xd1[6] = domain.xd(n6si2);
xd1[7] = domain.xd(n7si2);
yd1[0] = domain.yd(n0si2);
yd1[1] = domain.yd(n1si2);
yd1[2] = domain.yd(n2si2);
yd1[3] = domain.yd(n3si2);
yd1[4] = domain.yd(n4si2);
yd1[5] = domain.yd(n5si2);
yd1[6] = domain.yd(n6si2);
yd1[7] = domain.yd(n7si2);
zd1[0] = domain.zd(n0si2);
zd1[1] = domain.zd(n1si2);
zd1[2] = domain.zd(n2si2);
zd1[3] = domain.zd(n3si2);
zd1[4] = domain.zd(n4si2);
zd1[5] = domain.zd(n5si2);
zd1[6] = domain.zd(n6si2);
zd1[7] = domain.zd(n7si2);
coefficient = - hourg * Real_t(0.01) * ss1 * mass1 / volume13;
CalcElemFBHourglassForce(xd1,yd1,zd1,
hourgam,
coefficient, hgfx, hgfy, hgfz);
// With the threaded version, we write into local arrays per elem
// so we don't have to worry about race conditions
if (numthreads > 1) {
fx_local = &fx_elem[i3] ;
fx_local[0] = hgfx[0];
fx_local[1] = hgfx[1];
fx_local[2] = hgfx[2];
fx_local[3] = hgfx[3];
fx_local[4] = hgfx[4];
fx_local[5] = hgfx[5];
fx_local[6] = hgfx[6];
fx_local[7] = hgfx[7];
fy_local = &fy_elem[i3] ;
fy_local[0] = hgfy[0];
fy_local[1] = hgfy[1];
fy_local[2] = hgfy[2];
fy_local[3] = hgfy[3];
fy_local[4] = hgfy[4];
fy_local[5] = hgfy[5];
fy_local[6] = hgfy[6];
fy_local[7] = hgfy[7];
fz_local = &fz_elem[i3] ;
fz_local[0] = hgfz[0];
fz_local[1] = hgfz[1];
fz_local[2] = hgfz[2];
fz_local[3] = hgfz[3];
fz_local[4] = hgfz[4];
fz_local[5] = hgfz[5];
fz_local[6] = hgfz[6];
fz_local[7] = hgfz[7];
}
else {
domain.fx(n0si2) += hgfx[0];
domain.fy(n0si2) += hgfy[0];
domain.fz(n0si2) += hgfz[0];
domain.fx(n1si2) += hgfx[1];
domain.fy(n1si2) += hgfy[1];
domain.fz(n1si2) += hgfz[1];
domain.fx(n2si2) += hgfx[2];
domain.fy(n2si2) += hgfy[2];
domain.fz(n2si2) += hgfz[2];
domain.fx(n3si2) += hgfx[3];
domain.fy(n3si2) += hgfy[3];
domain.fz(n3si2) += hgfz[3];
domain.fx(n4si2) += hgfx[4];
domain.fy(n4si2) += hgfy[4];
domain.fz(n4si2) += hgfz[4];
domain.fx(n5si2) += hgfx[5];
domain.fy(n5si2) += hgfy[5];
domain.fz(n5si2) += hgfz[5];
domain.fx(n6si2) += hgfx[6];
domain.fy(n6si2) += hgfy[6];
domain.fz(n6si2) += hgfz[6];
domain.fx(n7si2) += hgfx[7];
domain.fy(n7si2) += hgfy[7];
domain.fz(n7si2) += hgfz[7];
}
}
if (numthreads > 1) {
// Collect the data from the local arrays into the final force arrays
#pragma omp parallel for firstprivate(numNode)
for( Index_t gnode=0 ; gnode<numNode ; ++gnode )
{
Index_t count = domain.nodeElemCount(gnode) ;
Index_t *cornerList = domain.nodeElemCornerList(gnode) ;
Real_t fx_tmp = Real_t(0.0) ;
Real_t fy_tmp = Real_t(0.0) ;
Real_t fz_tmp = Real_t(0.0) ;
for (Index_t i=0 ; i < count ; ++i) {
Index_t ielem = cornerList[i] ;
fx_tmp += fx_elem[ielem] ;
fy_tmp += fy_elem[ielem] ;
fz_tmp += fz_elem[ielem] ;
}
domain.fx(gnode) += fx_tmp ;
domain.fy(gnode) += fy_tmp ;
domain.fz(gnode) += fz_tmp ;
}
Release(&fz_elem) ;
Release(&fy_elem) ;
Release(&fx_elem) ;
}
}
/******************************************/
static inline
void CalcHourglassControlForElems(Domain& domain,
Real_t determ[], Real_t hgcoef)
{
Index_t numElem = domain.numElem() ;
Index_t numElem8 = numElem * 8 ;