2D benchmarks¶

Contents

Benchmark usage
Mass Matrix
Stiffness Matrix
Elastic Stiffness Matrix

Benchmark usage ¶

pyOptFEM.FEM2D.assemblyBench.assemblyBench([assembly=<string>, version=<string>, LN=<array>, meshname=<string>, meshdir=<string>, nbruns=<int>, la=<float>, mu=<float>, Num=<int>, tag=<string>, ...])

Benchmark code for $P_1$ -Lagrange finite element matrices defined in FEM2D.

Parameters:

assembly –
Name of an assembly routine. The string should be :
- ‘MassAssembling2DP1’,
- ‘StiffAssembling2DP1’ (default)
- ‘StiffElasAssembling2DP1’
versions – List of versions. Must be a list of any size whose elements may be {‘base’,’OptV1’,’OptV2’} (default : ['OptV2','OptV1','base'])
meshname – Name of the mesh files. By default it is an empty string ‘’. It means it uses SquareMesh function to generate meshes.
meshdir – Directory location of FreeFEM++ mesh files. Used if meshname is not empty.
LN –
array of integer values. <LN> contains the values of N. Used to generate meshes data via Th=SquareMesh(N) function if meshname is empty or via getMesh class to read FreeFEM++ meshes Th=getMesh(meshdir+’/’+meshname+str(N)+’.msh’)

LN default value is range(50, 90, 10)
nbruns – Number of runs on each mesh (default : 1)
save – For saving benchmark results in a file (see parameters <output>, <outdir> and <tag>)
plot – For plotting computation times (default : True)
output – Name used to set results file name (default : ‘bench2D’)
outdir – Directory location of saved results file name (default : ‘./results’).
tag – Specify a tag string added to filename
la – the first Lame coefficient in Hooke’s law, denoted by $\lambda$ . Used by functions for assembling the elastic stiffness matrix. (default : 2)
mu – the second Lame coefficient in Hooke’s law, denoted by $\mu$ . Used by functions for assembling the elastic stiffness matrix. (default : 0.3)
Num – Numbering choice. Used by functions for assembling the elastic stiffness matrix. (default : 0)

Mass Matrix ¶

Benchmark of MassAssembling2DP1 with base, OptV1 and OptV2 versions (see Mass Matrix)

MassAssembling2DP1 benchmark summary
N	nq	ndof	OptV2	OptV1	base
50	2601	2601	0.0042(s)	0.0816(s)	3.2783(s)
			x1.00	x19.50	x783.85
60	3721	3721	0.0058(s)	0.1162(s)	4.7136(s)
			x1.00	x20.02	x812.43
70	5041	5041	0.0078(s)	0.1584(s)	6.3931(s)
			x1.00	x20.32	x819.97
80	6561	6561	0.0102(s)	0.2075(s)	8.4154(s)
			x1.00	x20.33	x824.26
90	8281	8281	0.0133(s)	0.2622(s)	10.6460(s)
			x1.00	x19.66	x798.28
100	10201	10201	0.0162(s)	0.3228(s)	13.1028(s)
			x1.00	x19.89	x807.38
110	12321	12321	0.0197(s)	0.3912(s)	15.9244(s)
			x1.00	x19.88	x809.23
120	14641	14641	0.0232(s)	0.4685(s)	18.9165(s)
			x1.00	x20.21	x816.09

This tabular was built with the following code :

>>> from pyOptFEM.FEM2D import assemblyBench
>>> assemblyBench(assembly='MassAssembling2DP1',LN=range(50,130,10))
SquareMesh(50):
 -> MassAssembling2DP1OptV2(nq=2601, nme=5000)
  run ( 1/ 1) : cputime=0.004182(s) - matrix 2601-by-2601
...
SquareMesh(120):
 -> MassAssembling2DP1base(nq=14641, nme=28800)
  run ( 1/ 1) : cputime=18.916504(s) - matrix 14641-by-14641
...

We also obtain

Figure 31: MassAssembling2DP1 benchmark

Benchmark of MassAssembling2DP1 with OptV2 and OptV1 versions

MassAssembling2DP1 benchmark summary
N	nq	ndof	OptV2	OptV1
100	10201	10201	0.0163(s)	0.3196(s)
			x1.00	x19.61
200	40401	40401	0.0648(s)	1.3025(s)
			x1.00	x20.09
300	90601	90601	0.1583(s)	2.9198(s)
			x1.00	x18.45
400	160801	160801	0.2859(s)	5.1809(s)
			x1.00	x18.12
500	251001	251001	0.4591(s)	8.1059(s)
			x1.00	x17.65
600	361201	361201	0.6595(s)	11.6834(s)
			x1.00	x17.72
700	491401	491401	0.9056(s)	15.8209(s)
			x1.00	x17.47
800	641601	641601	1.1796(s)	20.8883(s)
			x1.00	x17.71
900	811801	811801	1.4933(s)	26.0264(s)
			x1.00	x17.43
1000	1002001	1002001	1.8503(s)	32.5076(s)
			x1.00	x17.57
1100	1212201	1212201	2.2262(s)	39.3237(s)
			x1.00	x17.66
1200	1442401	1442401	2.6616(s)	46.6362(s)
			x1.00	x17.52

This tabular was built with the following code :

>>> from pyOptFEM.FEM2D import assemblyBench
>>> assemblyBench(assembly='MassAssembling2DP1',versions=['OptV2','OptV1'],LN=range(100,1300,100))
SquareMesh(100):
 -> MassAssembling2DP1OptV2(nq=10201, nme=20000)
  run ( 1/ 1) : cputime=0.016294(s) - matrix 10201-by-10201
...
SquareMesh(1200):
 -> MassAssembling2DP1OptV1(nq=1442401, nme=2880000)
  run ( 1/ 1) : cputime=46.636235(s) - matrix 1442401-by-1442401
...

We also obtain

Figure 32: MassAssembling2DP1 benchmark

Stiffness Matrix ¶

Benchmark of StiffAssembling2DP1 with base, OptV1 and OptV2 versions

StiffAssembling2DP1 benchmark summary
N	nq	ndof	OptV2	OptV1	base
50	2601	2601	0.0055(s)	0.2501(s)	3.5504(s)
			x1.00	x45.35	x643.82
60	3721	3721	0.0076(s)	0.3593(s)	5.1301(s)
			x1.00	x47.38	x676.64
70	5041	5041	0.0101(s)	0.4897(s)	6.9854(s)
			x1.00	x48.33	x689.37
80	6561	6561	0.0138(s)	0.6362(s)	9.0807(s)
			x1.00	x46.11	x658.09
90	8281	8281	0.0178(s)	0.8119(s)	11.5354(s)
			x1.00	x45.57	x647.46
100	10201	10201	0.0223(s)	1.0005(s)	14.2190(s)
			x1.00	x44.77	x636.22
110	12321	12321	0.0266(s)	1.2124(s)	17.2704(s)
			x1.00	x45.61	x649.74
120	14641	14641	0.0325(s)	1.4503(s)	20.4368(s)
			x1.00	x44.69	x629.75

This tabular was built with the following code :

>>> from pyOptFEM.FEM2D import assemblyBench
>>> assemblyBench(assembly='StiffAssembling2DP1',LN=range(50,130,10))
SquareMesh(50):
 -> StiffAssembling2DP1OptV2(nq=2601, nme=5000)
  run ( 1/ 1) : cputime=0.005515(s) - matrix 2601-by-2601
...
SquareMesh(120):
 -> StiffAssembling2DP1base(nq=14641, nme=28800)
  run ( 1/ 1) : cputime=20.436779(s) - matrix 14641-by-14641
...

We also obtain

Figure 33: StiffAssembling2DP1 benchmark

Benchmark of StiffAssembling2DP1 with OptV2 and OptV1 versions

StiffAssembling2DP1 benchmark summary
N	nq	ndof	OptV2	OptV1
100	10201	10201	0.0225(s)	1.0104(s)
			x1.00	x44.93
200	40401	40401	0.0945(s)	4.0847(s)
			x1.00	x43.22
300	90601	90601	0.2379(s)	9.1818(s)
			x1.00	x38.59
400	160801	160801	0.4459(s)	16.3333(s)
			x1.00	x36.63
500	251001	251001	0.7169(s)	25.6513(s)
			x1.00	x35.78
600	361201	361201	1.0316(s)	36.8382(s)
			x1.00	x35.71
700	491401	491401	1.4316(s)	49.9507(s)
			x1.00	x34.89
800	641601	641601	1.8965(s)	65.8354(s)
			x1.00	x34.71
900	811801	811801	2.4164(s)	82.7545(s)
			x1.00	x34.25
1000	1002001	1002001	2.9450(s)	102.3931(s)
			x1.00	x34.77
1100	1212201	1212201	3.4908(s)	123.9802(s)
			x1.00	x35.52
1200	1442401	1442401	4.3144(s)	147.2963(s)
			x1.00	x34.14

This tabular was built with the following code :

>>> from pyOptFEM.FEM2D import assemblyBench
>>> assemblyBench(assembly='StiffAssembling2DP1',versions=['OptV2','OptV1'],LN=range(100,1300,100))
SquareMesh(100):
 -> StiffAssembling2DP1OptV2(nq=10201, nme=20000)
  run ( 1/ 1) : cputime=0.022488(s) - matrix 10201-by-10201
...
SquareMesh(1200):
 -> StiffAssembling2DP1OptV1(nq=1442401, nme=2880000)
  run ( 1/ 1) : cputime=147.296321(s) - matrix 1442401-by-1442401
...

We also obtain

Figure 34: StiffAssembling2DP1 benchmark

Elastic Stiffness Matrix ¶

Benchmark of StiffElasAssembling2DP1 with base, OptV1 and OptV2 versions

StiffElasAssembling2DP1 benchmark summary
N	nq	ndof	OptV2	OptV1	base
30	961	1922	0.0107(s)	0.2809(s)	1.8485(s)
			x1.00	x26.29	x173.04
35	1296	2592	0.0134(s)	0.3807(s)	2.5109(s)
			x1.00	x28.37	x187.11
40	1681	3362	0.0172(s)	0.4986(s)	3.2952(s)
			x1.00	x28.92	x191.13
45	2116	4232	0.0216(s)	0.6306(s)	4.1589(s)
			x1.00	x29.26	x192.97
50	2601	5202	0.0269(s)	0.7800(s)	5.1323(s)
			x1.00	x29.04	x191.07
55	3136	6272	0.0322(s)	0.9453(s)	6.2180(s)
			x1.00	x29.39	x193.35
60	3721	7442	0.0386(s)	1.1282(s)	7.4995(s)
			x1.00	x29.21	x194.14

This tabular was built with the following code :

>>> from pyOptFEM.FEM2D import assemblyBench
>>> assemblyBench(assembly='StiffElasAssembling2DP1',LN=range(30,65,5))
SquareMesh(30):
 -> StiffElasAssembling2DP1OptV2(nq=961, nme=1800)
  run ( 1/ 1) : cputime=0.010683(s) - matrix 1922-by-1922
...
SquareMesh(30):
 -> StiffElasAssembling2DP1OptV2(nq=961, nme=1800)
  run ( 1/ 1) : cputime=0.010683(s) - matrix 1922-by-1922
...

We also obtain

Figure 35: StiffElasAssembling2DP1 benchmark

Benchmark of StiffElasAssembling2DP1 with OptV2 and OptV1 versions

StiffElasAssembling2DP1 benchmark summary
N	nq	ndof	OptV2	OptV1
100	10201	20402	0.1110(s)	3.1286(s)
			x1.00	x28.18
200	40401	80802	0.5036(s)	12.5861(s)
			x1.00	x24.99
300	90601	181202	1.2058(s)	28.2232(s)
			x1.00	x23.41
400	160801	321602	2.1346(s)	50.2407(s)
			x1.00	x23.54
500	251001	502002	3.5360(s)	78.4291(s)
			x1.00	x22.18
600	361201	722402	5.3290(s)	113.4194(s)
			x1.00	x21.28
700	491401	982802	7.4691(s)	153.6793(s)
			x1.00	x20.58
800	641601	1283202	9.8943(s)	201.4319(s)
			x1.00	x20.36

This tabular was built with the following code :

>>> from pyOptFEM.FEM2D import assemblyBench
>>> assemblyBench(assembly='StiffElasAssembling2DP1',versions=['OptV2','OptV1'],LN=range(100,900,100))
SquareMesh(100):
 -> StiffElasAssembling2DP1OptV2(nq=10201, nme=20000)
  run ( 1/ 1) : cputime=0.111037(s) - matrix 20402-by-20402
...
SquareMesh(800):
 -> StiffElasAssembling2DP1OptV1(nq=641601, nme=1280000)
  run ( 1/ 1) : cputime=201.431866(s) - matrix 1283202-by-1283202
...

We also obtain

Figure 36: StiffElasAssembling2DP1 benchmark

2D benchmarks¶

Benchmark usage ¶

Mass Matrix ¶

Stiffness Matrix ¶

Elastic Stiffness Matrix ¶

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2D benchmarks¶

Benchmark usage¶

Mass Matrix¶

Stiffness Matrix¶

Elastic Stiffness Matrix¶

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Benchmark usage ¶

Mass Matrix ¶

Stiffness Matrix ¶

Elastic Stiffness Matrix ¶