Eigenvalue analysis of Eiffel tower
Eigenvalue analysis of Eiffel tower is done using JuliaFEM 0.3.3 and Julia 0.6. Assembly of global matrices and writing results is optimized a bit. Results show that when models are big enough, solution of eigenvalue problem takes about 80 % of time.
Code
using JuliaFEM
using JuliaFEM.Preprocess
using JuliaFEM.Postprocess
#model = "EIFFEL_TOWER_TET10_220271"
model = ARGS[1]
mesh = joinpath("eiffel-tower", "$model.inp")
results = "$model"
@timeit "run performance test" begin
@timeit "parse input data" begin
mesh = abaqus_read_mesh(mesh)
for (nid, ncoords) in mesh.nodes
mesh.nodes[nid] = 304.8 * ncoords
end
info("element sets = ", collect(keys(mesh.element_sets)))
info("surface sets = ", collect(keys(mesh.surface_sets)))
end
@timeit "initialize model" begin
tower = Problem(Elasticity, "tower", 3)
tower.elements = create_elements(mesh, "TOWER")
update!(tower, "youngs modulus", 210.0E3)
update!(tower, "poissons ratio", 0.3)
update!(tower, "density", 7.85E-9)
support = Problem(Dirichlet, "fixed", 3, "displacement")
support.elements = create_surface_elements(mesh, "SUPPORT")
update!(support, "geometry", mesh.nodes)
update!(support, "displacement 1", 0.0)
update!(support, "displacement 2", 0.0)
update!(support, "displacement 3", 0.0)
end
@timeit "solve eigenvalue problem" begin
solver = Solver(Modal, tower, support)
solver.xdmf = Xdmf(results; overwrite=true)
solver.properties.nev = 5
solver.properties.which = :SM
solver()
println("Eigenvalues: ", sqrt.(solver.properties.eigvals) / (2*pi))
end
end
print_timer()
Results
220271 nodes
Eigenvalues: [0.554667, 0.557987, 1.59926, 1.60043, 2.37304]
──────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
Tot / % measured: 18436996367s / 0.00% 46.1GiB / 97.8%
Section ncalls time %tot avg alloc %tot avg
──────────────────────────────────────────────────────────────────────────────
run performance test 1 122s 100% 122s 45.1GiB 100% 45.1GiB
solve eigenvalue... 1 116s 95.2% 116s 44.3GiB 98.1% 44.3GiB
assemble matrices 1 46.0s 37.8% 46.0s 24.6GiB 54.5% 24.6GiB
assemble tow... 1 22.3s 18.3% 22.3s 14.0GiB 31.0% 14.0GiB
assemble tower 1 16.4s 13.5% 16.4s 5.10GiB 11.3% 5.10GiB
assemble fixed 1 334ms 0.27% 334ms 14.6MiB 0.03% 14.6MiB
solve eigenval... 1 37.9s 31.1% 37.9s 8.92GiB 19.8% 8.92GiB
eliminate boun... 1 10.4s 8.50% 10.4s 5.11GiB 11.3% 5.11GiB
save results t... 1 6.39s 5.24% 6.39s 793MiB 1.72% 793MiB
fetch geometry 1 2.94s 2.42% 2.94s 298MiB 0.65% 298MiB
save modes 1 1.55s 1.27% 1.55s 336MiB 0.73% 336MiB
store eige... 5 689ms 0.57% 138ms 287MiB 0.62% 57.4MiB
create m... 5 646ms 0.53% 129ms 260MiB 0.56% 52.1MiB
save topol... 5 261ms 0.21% 52.1ms 28.1MiB 0.06% 5.62MiB
save topol... 5 26.6ms 0.02% 5.32ms 77.7KiB 0.00% 15.5KiB
create topol... 1 1.25s 1.02% 1.25s 108MiB 0.23% 108MiB
create node ... 1 122ms 0.10% 122ms 16.0MiB 0.03% 16.0MiB
create ncoor... 1 106ms 0.09% 106ms 25.7MiB 0.06% 25.7MiB
parse input data 1 4.77s 3.92% 4.77s 689MiB 1.49% 689MiB
initialize model 1 1.13s 0.93% 1.13s 180MiB 0.39% 180MiB
──────────────────────────────────────────────────────────────────────────────
376120 nodes
Eigenvalues: [0.548343, 0.548526, 1.56613, 1.56662, 2.32376]
──────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
Tot / % measured: 18436996624s / 0.00% 81.2GiB / 98.7%
Section ncalls time %tot avg alloc %tot avg
──────────────────────────────────────────────────────────────────────────────
run performance test 1 231s 100% 231s 80.2GiB 100% 80.2GiB
solve eigenvalue... 1 221s 96.0% 221s 78.7GiB 98.1% 78.7GiB
assemble matrices 1 87.1s 37.7% 87.1s 43.8GiB 54.6% 43.8GiB
assemble tow... 1 44.0s 19.1% 44.0s 24.5GiB 30.6% 24.5GiB
assemble tower 1 23.1s 10.0% 23.1s 9.59GiB 12.0% 9.59GiB
assemble fixed 1 386ms 0.17% 386ms 44.0MiB 0.05% 44.0MiB
solve eigenval... 1 74.7s 32.4% 74.7s 16.5GiB 20.6% 16.5GiB
eliminate boun... 1 22.9s 9.93% 22.9s 8.78GiB 11.0% 8.78GiB
save results t... 1 13.6s 5.89% 13.6s 1.34GiB 1.67% 1.34GiB
fetch geometry 1 6.69s 2.90% 6.69s 535MiB 0.65% 535MiB
save modes 1 3.68s 1.59% 3.68s 558MiB 0.68% 558MiB
store eige... 5 2.82s 1.22% 565ms 489MiB 0.60% 97.7MiB
create m... 5 2.74s 1.19% 547ms 445MiB 0.54% 88.9MiB
save topol... 5 349ms 0.15% 69.7ms 41.8MiB 0.05% 8.36MiB
save topol... 5 46.3ms 0.02% 9.25ms 164KiB 0.00% 32.7KiB
create topol... 1 2.03s 0.88% 2.03s 190MiB 0.23% 190MiB
create ncoor... 1 489ms 0.21% 489ms 43.5MiB 0.05% 43.5MiB
create node ... 1 150ms 0.07% 150ms 33.0MiB 0.04% 33.0MiB
parse input data 1 7.44s 3.22% 7.44s 1.20GiB 1.50% 1.20GiB
initialize model 1 1.88s 0.82% 1.88s 316MiB 0.38% 316MiB
──────────────────────────────────────────────────────────────────────────────
921317 nodes
Eigenvalues: [0.542289, 0.542386, 1.54818, 1.54852, 2.26661]
──────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
Tot / % measured: 18436997275s / 0.00% 204GiB / 99.5%
Section ncalls time %tot avg alloc %tot avg
──────────────────────────────────────────────────────────────────────────────
run performance test 1 627s 100% 627s 203GiB 100% 203GiB
solve eigenvalue... 1 604s 96.4% 604s 199GiB 98.2% 199GiB
assemble matrices 1 231s 36.8% 231s 108GiB 53.2% 108GiB
assemble tow... 1 126s 20.1% 126s 62.4GiB 30.8% 62.4GiB
assemble tower 1 50.0s 7.97% 50.0s 20.7GiB 10.2% 20.7GiB
assemble fixed 1 518ms 0.08% 518ms 151MiB 0.07% 151MiB
solve eigenval... 1 205s 32.7% 205s 45.6GiB 22.5% 45.6GiB
eliminate boun... 1 80.3s 12.8% 80.3s 21.8GiB 10.8% 21.8GiB
save results t... 1 36.8s 5.86% 36.8s 3.27GiB 1.61% 3.27GiB
save modes 1 13.2s 2.11% 13.2s 1.30GiB 0.64% 1.30GiB
store eige... 5 12.0s 1.91% 2.40s 1.17GiB 0.58% 239MiB
create m... 5 11.7s 1.87% 2.35s 1.06GiB 0.52% 218MiB
save topol... 5 450ms 0.07% 89.9ms 83.5MiB 0.04% 16.7MiB
save topol... 5 116ms 0.02% 23.3ms 496KiB 0.00% 99.2KiB
fetch geometry 1 12.1s 1.93% 12.1s 1.31GiB 0.65% 1.31GiB
create ncoor... 1 3.14s 0.50% 3.14s 106MiB 0.05% 106MiB
create topol... 1 2.66s 0.42% 2.66s 485MiB 0.23% 485MiB
create node ... 1 232ms 0.04% 232ms 67.0MiB 0.03% 67.0MiB
parse input data 1 18.7s 2.98% 18.7s 2.94GiB 1.45% 2.94GiB
initialize model 1 3.71s 0.59% 3.71s 802MiB 0.39% 802MiB
──────────────────────────────────────────────────────────────────────────────
1327989 nodes
Eigenvalues: [0.541056, 0.541163, 1.54381, 1.54408, 2.25313]
──────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
Tot / % measured: 18436998213s / 0.00% 307GiB / 100%
Section ncalls time %tot avg alloc %tot avg
──────────────────────────────────────────────────────────────────────────────
run performance test 1 905s 100% 905s 306GiB 100% 306GiB
solve eigenvalue... 1 873s 96.5% 873s 301GiB 98.3% 301GiB
solve eigenval... 1 350s 38.7% 350s 71.8GiB 23.5% 71.8GiB
assemble matrices 1 256s 28.3% 256s 168GiB 54.9% 168GiB
assemble tow... 1 135s 14.9% 135s 94.5GiB 30.9% 94.5GiB
assemble tower 1 73.6s 8.13% 73.6s 36.7GiB 12.0% 36.7GiB
assemble fixed 1 680ms 0.08% 680ms 229MiB 0.07% 229MiB
eliminate boun... 1 115s 12.7% 115s 26.4GiB 8.64% 26.4GiB
save results t... 1 65.9s 7.28% 65.9s 4.71GiB 1.54% 4.71GiB
save modes 1 29.8s 3.29% 29.8s 1.87GiB 0.61% 1.87GiB
store eige... 5 27.9s 3.09% 5.59s 1.68GiB 0.55% 345MiB
create m... 5 27.5s 3.04% 5.51s 1.53GiB 0.50% 314MiB
save topol... 5 830ms 0.09% 166ms 129MiB 0.04% 25.8MiB
save topol... 5 206ms 0.02% 41.1ms 887KiB 0.00% 177KiB
fetch geometry 1 20.6s 2.27% 20.6s 1.89GiB 0.62% 1.89GiB
create topol... 1 8.58s 0.95% 8.58s 724MiB 0.23% 724MiB
create ncoor... 1 4.74s 0.52% 4.74s 152MiB 0.05% 152MiB
create node ... 1 581ms 0.06% 581ms 67.0MiB 0.02% 67.0MiB
parse input data 1 27.0s 2.98% 27.0s 4.19GiB 1.37% 4.19GiB
initialize model 1 4.84s 0.53% 4.84s 1.16GiB 0.38% 1.16GiB
──────────────────────────────────────────────────────────────────────────────
2357071 nodes
──────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
Tot / % measured: 18437001397s / 0.00% 587GiB / 100%
Section ncalls time %tot avg alloc %tot avg
──────────────────────────────────────────────────────────────────────────────
run performance test 1 3158s 100% 3158s 586GiB 100% 586GiB
solve eigenvalue... 1 3112s 98.5% 3112s 576GiB 98.3% 576GiB
solve eigenval... 1 1381s 43.7% 1381s 149GiB 25.5% 149GiB
assemble matrices 1 928s 29.4% 928s 306GiB 52.2% 306GiB
assemble tow... 1 589s 18.6% 589s 174GiB 29.6% 174GiB
assemble tower 1 143s 4.52% 143s 63.5GiB 10.8% 63.5GiB
assemble fixed 1 902ms 0.03% 902ms 401MiB 0.07% 401MiB
eliminate boun... 1 381s 12.1% 381s 58.0GiB 9.90% 58.0GiB
save results t... 1 206s 6.51% 206s 8.66GiB 1.48% 8.66GiB
save modes 1 78.6s 2.49% 78.6s 3.32GiB 0.57% 3.32GiB
store eige... 5 75.1s 2.38% 15.0s 2.99GiB 0.51% 612MiB
create m... 5 73.3s 2.32% 14.7s 2.72GiB 0.46% 557MiB
save topol... 5 2.16s 0.07% 433ms 236MiB 0.04% 47.3MiB
save topol... 5 358ms 0.01% 71.5ms 1.63MiB 0.00% 335KiB
fetch geometry 1 64.6s 2.04% 64.6s 3.58GiB 0.61% 3.58GiB
create ncoor... 1 22.9s 0.72% 22.9s 270MiB 0.05% 270MiB
create topol... 1 22.1s 0.70% 22.1s 1.32GiB 0.23% 1.32GiB
create node ... 1 14.5s 0.46% 14.5s 135MiB 0.02% 135MiB
parse input data 1 38.2s 1.21% 38.2s 7.75GiB 1.32% 7.75GiB
initialize model 1 7.85s 0.25% 7.85s 2.17GiB 0.37% 2.17GiB
──────────────────────────────────────────────────────────────────────────────
3640549 nodes
──────────────────────────────────────────────────────────────────────────────
Time Allocations
────────────────────── ───────────────────────
Tot / % measured: 18436983005s / 0.00% 805GiB / 100%
Section ncalls time %tot avg alloc %tot avg
──────────────────────────────────────────────────────────────────────────────
run performance test 1 9182s 100% 9182s 804GiB 100% 804GiB
solve eigenvalue... 1 9133s 99.5% 9133s 788GiB 98.0% 788GiB
solve eigenval... 1 7484s 81.5% 7484s 279GiB 34.7% 279GiB
assemble matrices 1 580s 6.32% 580s 318GiB 39.5% 318GiB
assemble tower 1 220s 2.40% 220s 93.2GiB 11.6% 93.2GiB
assemble tow... 1 188s 2.04% 188s 114GiB 14.1% 114GiB
assemble fixed 1 1.17s 0.01% 1.17s 586MiB 0.07% 586MiB
save results t... 1 377s 4.11% 377s 13.8GiB 1.72% 13.8GiB
fetch geometry 1 143s 1.56% 143s 5.90GiB 0.73% 5.90GiB
save modes 1 135s 1.47% 135s 5.08GiB 0.63% 5.08GiB
store eige... 5 129s 1.41% 25.8s 4.61GiB 0.57% 944MiB
create m... 5 127s 1.39% 25.5s 4.20GiB 0.52% 861MiB
save topol... 5 3.34s 0.04% 669ms 326MiB 0.04% 65.1MiB
save topol... 5 582ms 0.01% 116ms 1.79MiB 0.00% 366KiB
create topol... 1 40.7s 0.44% 40.7s 2.13GiB 0.26% 2.13GiB
create ncoor... 1 35.2s 0.38% 35.2s 417MiB 0.05% 417MiB
create node ... 1 18.3s 0.20% 18.3s 271MiB 0.03% 271MiB
eliminate boun... 1 326s 3.55% 326s 91.6GiB 11.4% 91.6GiB
parse input data 1 40.1s 0.44% 40.1s 12.5GiB 1.56% 12.5GiB
initialize model 1 8.80s 0.10% 8.80s 3.51GiB 0.44% 3.51GiB
──────────────────────────────────────────────────────────────────────────────
Further analysis and discussion
Dashed results are calculated using JuliaFEM 0.3.2 and solid lines are for 0.3.3.
Assemly of stiffness and mass matrix is optimized without sacrificing readablity
of code (too much). It can still be optimized more to get even better performance,
or run assembler using threads. The results however shows that vast major of the
time is spend in a single command eigs(K, M). So when model sizes are realistic,
the assembly time is under 10 % of total solution time. The result is totally
different compared to small toy models, where assembly time can be over 50 % of
total solution time. That’s the reason why performance tests must be done using full
size models.
Conclusions are, that we get 80-90 % of performance with 10 % of effort using dynamic language like Julia. The performance penalty, compared to some statically typed languages like FORTRAN or C, is acceptable by taking into account that development time of the software itself is reduced dramatically.
Next steps are to optimize memory usage during the solution of eigenmodes to be able to calculate even bigger models.