LAMMPS (7 Jan 2022) # Numerical difference calculation # of error in forces, virial stress, and Born matrix # adjustable parameters variable nsteps index 500 # length of run variable nthermo index 10 # thermo output interval variable ndump index 500 # dump output interval variable nlat index 3 # size of box variable fdelta index 1.0e-4 # displacement size variable vdelta index 1.0e-6 # strain size for numdiff/virial variable bdelta index 1.0e-8 # strain size for numdiff Born matrix variable temp index 10.0 # temperature variable nugget equal 1.0e-6 # regularization for relerr units metal atom_style atomic atom_modify map yes lattice fcc 5.358000 Lattice spacing in x,y,z = 5.358 5.358 5.358 region box block 0 ${nlat} 0 ${nlat} 0 ${nlat} region box block 0 3 0 ${nlat} 0 ${nlat} region box block 0 3 0 3 0 ${nlat} region box block 0 3 0 3 0 3 create_box 1 box Created orthogonal box = (0 0 0) to (16.074 16.074 16.074) 1 by 1 by 1 MPI processor grid create_atoms 1 box Created 108 atoms using lattice units in orthogonal box = (0 0 0) to (16.074 16.074 16.074) create_atoms CPU = 0.000 seconds mass 1 39.903 velocity all create ${temp} 2357 mom yes dist gaussian velocity all create 10.0 2357 mom yes dist gaussian pair_style lj/cut 5.0 pair_coeff 1 1 0.0102701 3.42 neighbor 0.0 bin neigh_modify every 1 delay 0 check no timestep 0.001 fix nve all nve # define numerical force calculation fix numforce all numdiff ${nthermo} ${fdelta} fix numforce all numdiff 10 ${fdelta} fix numforce all numdiff 10 1.0e-4 variable ferrx atom f_numforce[1]-fx variable ferry atom f_numforce[2]-fy variable ferrz atom f_numforce[3]-fz variable ferrsq atom v_ferrx^2+v_ferry^2+v_ferrz^2 compute faverrsq all reduce ave v_ferrsq variable fsq atom fx^2+fy^2+fz^2 compute favsq all reduce ave v_fsq variable frelerr equal sqrt(c_faverrsq/(c_favsq+${nugget})) variable frelerr equal sqrt(c_faverrsq/(c_favsq+1e-06)) dump errors all custom ${ndump} force_error.dump v_ferrx v_ferry v_ferrz dump errors all custom 500 force_error.dump v_ferrx v_ferry v_ferrz # define numerical virial stress tensor calculation compute myvirial all pressure NULL virial fix numvirial all numdiff/virial ${nthermo} ${vdelta} fix numvirial all numdiff/virial 10 ${vdelta} fix numvirial all numdiff/virial 10 1.0e-6 variable errxx equal f_numvirial[1]-c_myvirial[1] variable erryy equal f_numvirial[2]-c_myvirial[2] variable errzz equal f_numvirial[3]-c_myvirial[3] variable erryz equal f_numvirial[4]-c_myvirial[6] variable errxz equal f_numvirial[5]-c_myvirial[5] variable errxy equal f_numvirial[6]-c_myvirial[4] variable verrsq equal "v_errxx^2 + v_erryy^2 + v_errzz^2 + v_erryz^2 + v_errxz^2 + v_errxy^2" variable vsq equal "c_myvirial[1]^2 + c_myvirial[3]^2 + c_myvirial[3]^2 + c_myvirial[4]^2 + c_myvirial[5]^2 + c_myvirial[6]^2" variable vrelerr equal sqrt(v_verrsq/(v_vsq+${nugget})) variable vrelerr equal sqrt(v_verrsq/(v_vsq+1e-06)) # define numerical Born matrix calculation compute bornnum all born/matrix numdiff ${bdelta} myvirial compute bornnum all born/matrix numdiff 1.0e-8 myvirial compute born all born/matrix variable berr vector c_bornnum-c_born variable berrsq equal "v_berr[1]^2 + v_berr[2]^2 + v_berr[3]^2 + v_berr[4]^2 + v_berr[5]^2 + v_berr[6]^2 + v_berr[7]^2 + v_berr[8]^2 + v_berr[9]^2 + v_berr[10]^2 + v_berr[11]^2 + v_berr[12]^2 + v_berr[13]^2 + v_berr[14]^2 + v_berr[15]^2 + v_berr[16]^2 + v_berr[17]^2 + v_berr[18]^2 + v_berr[19]^2 + v_berr[20]^2 + v_berr[21]^2" variable bsq equal "c_born[1]^2 + c_born[2]^2 + c_born[3]^2 + c_born[4]^2 + c_born[5]^2 + c_born[6]^2 + c_born[7]^2 + c_born[8]^2 + c_born[9]^2 + c_born[10]^2 + c_born[11]^2 + c_born[12]^2 + c_born[13]^2 + c_born[14]^2 + c_born[15]^2 + c_born[16]^2 + c_born[17]^2 + c_born[18]^2 + c_born[19]^2 + c_born[20]^2 + c_born[21]^2" variable brelerr equal sqrt(v_berrsq/(v_bsq+${nugget})) variable brelerr equal sqrt(v_berrsq/(v_bsq+1e-06)) thermo_style custom step temp pe etotal press v_frelerr v_vrelerr v_brelerr thermo ${nthermo} thermo 10 run ${nsteps} run 500 generated 0 of 0 mixed pair_coeff terms from geometric mixing rule Neighbor list info ... update every 1 steps, delay 0 steps, check no max neighbors/atom: 2000, page size: 100000 master list distance cutoff = 5 ghost atom cutoff = 5 binsize = 2.5, bins = 7 7 7 2 neighbor lists, perpetual/occasional/extra = 1 1 0 (1) pair lj/cut, perpetual attributes: half, newton on pair build: half/bin/atomonly/newton stencil: half/bin/3d bin: standard (2) compute born/matrix, occasional, copy from (1) attributes: half, newton on pair build: copy stencil: none bin: none Per MPI rank memory allocation (min/avg/max) = 6.823 | 6.823 | 6.823 Mbytes Step Temp PotEng TotEng Press v_frelerr v_vrelerr v_brelerr 0 10 -6.6101864 -6.471878 947.70558 5.7012262e-09 1.4849734e-08 9.072204e-09 10 9.9357441 -6.6092976 -6.471878 949.3486 1.3828998e-08 1.9248385e-09 3.0140952e-09 20 9.7444561 -6.6066519 -6.4718779 954.23637 1.385204e-08 1.7476399e-09 2.8104946e-09 30 9.4311148 -6.6023181 -6.4718779 962.23331 1.4147226e-08 1.7647816e-09 3.038408e-09 40 9.0043293 -6.5964152 -6.4718778 973.10762 1.4128155e-08 1.6390138e-09 3.1677083e-09 50 8.4762135 -6.5891108 -6.4718777 986.53572 1.4168048e-08 2.3910821e-09 3.2880496e-09 60 7.8621735 -6.5806179 -6.4718775 1002.1092 1.411958e-08 2.0683414e-09 2.650625e-09 70 7.1805874 -6.5711908 -6.4718773 1019.3448 1.4139911e-08 1.6084571e-09 2.7690475e-09 80 6.4523557 -6.5611186 -6.4718771 1037.6974 1.4105096e-08 1.9929271e-09 3.7464396e-09 90 5.7003071 -6.5507169 -6.4718769 1056.5767 1.4084183e-08 1.750579e-09 4.1502319e-09 100 4.9484503 -6.5403179 -6.4718767 1075.3674 1.4063796e-08 1.0250271e-09 3.0940885e-09 110 4.221081 -6.5302576 -6.4718765 1093.4526 1.400901e-08 1.389277e-09 3.3111451e-09 120 3.5417733 -6.520862 -6.4718763 1110.2388 1.4038158e-08 8.6231891e-10 2.6872042e-09 130 2.9323072 -6.5124324 -6.4718762 1125.183 1.4048645e-08 7.0840985e-10 2.5616823e-09 140 2.411607 -6.5052306 -6.471876 1137.8182 1.3968429e-08 1.8508015e-09 3.984183e-09 150 1.9947801 -6.4994654 -6.4718759 1147.7764 1.395965e-08 1.9484728e-09 3.8459442e-09 160 1.6923481 -6.4952825 -6.4718759 1154.8063 1.3948606e-08 1.5275137e-09 3.4566825e-09 170 1.5097515 -6.492757 -6.4718759 1158.7853 1.3845523e-08 1.5455e-09 2.4291888e-09 180 1.4471795 -6.4918916 -6.4718759 1159.7221 1.3788451e-08 1.578099e-09 2.2452653e-09 190 1.4997431 -6.4926187 -6.471876 1157.7529 1.374841e-08 2.142073e-09 2.3614867e-09 200 1.6579637 -6.4948072 -6.4718761 1153.1286 1.3674788e-08 2.111894e-09 3.4774073e-09 210 1.908522 -6.4982727 -6.4718763 1146.1965 1.3639408e-08 1.2386489e-09 2.1550029e-09 220 2.23518 -6.5027908 -6.4718764 1137.3775 1.3524209e-08 1.7016573e-09 3.3806952e-09 230 2.6197892 -6.5081105 -6.4718766 1127.1415 1.3344007e-08 1.5843477e-09 2.9517742e-09 240 3.043298 -6.5139681 -6.4718768 1115.9815 1.3245227e-08 1.5502368e-09 3.7751316e-09 250 3.4866901 -6.5201007 -6.4718769 1104.3906 1.3080142e-08 1.369987e-09 3.1015926e-09 260 3.9318061 -6.5262572 -6.4718771 1092.84 1.2885339e-08 1.0743728e-09 3.2781775e-09 270 4.3620216 -6.5322076 -6.4718772 1081.7617 1.2705966e-08 1.3618619e-09 3.2074528e-09 280 4.7627723 -6.5377504 -6.4718773 1071.5341 1.2480463e-08 1.4346869e-09 2.6014531e-09 290 5.1219322 -6.542718 -6.4718774 1062.4716 1.2434727e-08 2.1935942e-09 2.8738025e-09 300 5.4300557 -6.5469796 -6.4718774 1054.8177 1.2321314e-08 8.2365886e-10 3.0321861e-09 310 5.6804997 -6.5504435 -6.4718774 1048.7409 1.2300884e-08 1.4855741e-09 3.0631008e-09 320 5.8694423 -6.5530567 -6.4718774 1044.3341 1.2483087e-08 1.8711589e-09 3.9505726e-09 330 5.9958115 -6.5548045 -6.4718774 1041.6165 1.2627617e-08 1.9256986e-09 2.0214697e-09 340 6.0611353 -6.555708 -6.4718774 1040.5369 1.2935701e-08 1.6609255e-09 3.0860271e-09 350 6.0693222 -6.5558211 -6.4718773 1040.9803 1.3218179e-08 1.985355e-09 2.8012116e-09 360 6.0263776 -6.5552271 -6.4718773 1042.7755 1.3471701e-08 1.5125203e-09 2.8686484e-09 370 5.9400629 -6.5540332 -6.4718772 1045.7049 1.3676495e-08 1.7364093e-09 2.578312e-09 380 5.8195019 -6.5523657 -6.4718771 1049.515 1.3859995e-08 1.6834835e-09 2.9599336e-09 390 5.6747442 -6.5503635 -6.471877 1053.9288 1.3987553e-08 1.7893896e-09 2.5163687e-09 400 5.5162948 -6.5481719 -6.4718769 1058.6583 1.4091878e-08 1.4468098e-09 2.1565248e-09 410 5.3546269 -6.5459358 -6.4718768 1063.4182 1.4188438e-08 1.7231047e-09 2.8650537e-09 420 5.1996958 -6.5437929 -6.4718768 1067.9384 1.4205207e-08 1.3551982e-09 4.5778887e-09 430 5.0604771 -6.5418673 -6.4718767 1071.9767 1.4267199e-08 1.361845e-09 3.0381078e-09 440 4.9445529 -6.5402639 -6.4718766 1075.3292 1.4253464e-08 1.3945282e-09 2.820632e-09 450 4.8577717 -6.5390637 -6.4718766 1077.8394 1.4240998e-08 1.8767323e-09 3.4379833e-09 460 4.8040023 -6.53832 -6.4718766 1079.4048 1.4242259e-08 1.4785379e-09 4.399133e-09 470 4.7849977 -6.5380571 -6.4718766 1079.9795 1.4227939e-08 1.8623848e-09 3.0102588e-09 480 4.8003794 -6.5382699 -6.4718766 1079.5756 1.4215836e-08 1.2821795e-09 3.0643976e-09 490 4.8477405 -6.538925 -6.4718767 1078.2596 1.4186541e-08 2.47604e-09 3.3809071e-09 500 4.9228588 -6.539964 -6.4718767 1076.1469 1.4099819e-08 1.6653302e-09 3.4324143e-09 Loop time of 0.476785 on 1 procs for 500 steps with 108 atoms Performance: 90.607 ns/day, 0.265 hours/ns, 1048.692 timesteps/s 99.6% CPU use with 1 MPI tasks x no OpenMP threads MPI task timing breakdown: Section | min time | avg time | max time |%varavg| %total --------------------------------------------------------------- Pair | 0.0043699 | 0.0043699 | 0.0043699 | 0.0 | 0.92 Neigh | 0.026529 | 0.026529 | 0.026529 | 0.0 | 5.56 Comm | 0.0026272 | 0.0026272 | 0.0026272 | 0.0 | 0.55 Output | 0.014971 | 0.014971 | 0.014971 | 0.0 | 3.14 Modify | 0.42777 | 0.42777 | 0.42777 | 0.0 | 89.72 Other | | 0.0005208 | | | 0.11 Nlocal: 108 ave 108 max 108 min Histogram: 1 0 0 0 0 0 0 0 0 0 Nghost: 256 ave 256 max 256 min Histogram: 1 0 0 0 0 0 0 0 0 0 Neighs: 648 ave 648 max 648 min Histogram: 1 0 0 0 0 0 0 0 0 0 Total # of neighbors = 648 Ave neighs/atom = 6 Neighbor list builds = 500 Dangerous builds not checked Total wall time: 0:00:00