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SCtest_sl_tp1.txt
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SCtest_sl_tp1.txt
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singlelevelSC
Numerical solution of reference stochastic diffusion problem.
Choose specific example:
1. Square domain (0,1)^2, affine random coefficient (Eigel expansion), constant source
2. L-shaped domain, exponential random coefficient (with analytic KL-expansion), constant source
3. Square domain (-4,4)^2, constant coefficient, random one-peak source
4. Square domain (0,1)^2, quadratic random coefficient (with Eigel expansion), constant source
5. Square domain (0,1)^2, exponential random coefficient (with Eigel expansion), constant source
6. L-shaped domain, quadratic random coefficient (with analytic KL-expansion), constant source
7. L-shaped domain, affine random coefficient (Eigel expansion), constant source
8. Square domain (0,1)^2, cookie problem (9 round inclusions), constant source
9. Square domain (0,1)^2, cookie problem (4 square inclusions), discontinuous source
10. Square domain (0,1)^2, affine random coefficient (Bachmayr expansion), constant source
: 1
1 file(s) copied.
1 file(s) copied.
1 file(s) copied.
1 file(s) copied.
1 file(s) copied.
Dimension of parametric space (default is 4) :
choose type of random variable
1. Uniform
2. Truncated Gaussian
Default is uniform :
Eigel standard deviation (default is 0.547) :
Piecewise linear (P1) finite element approximation
Error estimation: linear/quadratic bubble functions 1/2? (default 1) :
Estimator type:
1. hierarchical estimator (elementwise residual problems)
2. hierarchical estimator (fully assembled system for residual problem)
3. 2-level estimator
(default 1) :
Marking strategy: maximum or equilibration 1/2? (default 2) :
Threshold parameter (default 0.3) :
choose type of collocation nodes
1. Leja
2. CC
default is CC nodes :
Threshold parameter for marking indices (default 0.3) :
set the error tolerance (default is 6e-3) :
set the number of adaptive steps (default is 40) :
Grid parameter: 2 for underlying 8x4 grid (default is 3 for 16x8) :
Iteration 0
spatial error estimate is 3.8939e-02 vs 3.6465e-02 (spatial indicator)
parametric error estimate is 3.3651e-02 vs 5.5985e-02 (parametric indicator)
overall estimate from indicators is 9.2451e-02
overall direct error estimate is 7.2590e-02
Iteration 1
spatial error indicator is 3.6465e-02
parametric error indicator is 5.5985e-02
Parametric enrichment step ... new indices added
2 1 1 1
spatial error estimate is 4.3447e-02 vs 5.6326e-02 (spatial indicator)
parametric error estimate is 7.9253e-03 vs 1.7231e-02 (parametric indicator)
overall estimate from indicators is 7.3557e-02
overall direct error estimate is 5.1372e-02
Iteration 2
spatial error indicator is 5.6326e-02
parametric error indicator is 1.7231e-02
Spatial refinement step...
original number of elements is 128
new number of elements is 144
spatial error estimate is 3.9991e-02 vs 4.3453e-02 (spatial indicator)
parametric error estimate is 8.0181e-03 vs 1.7529e-02 (parametric indicator)
overall estimate from indicators is 6.0981e-02
overall direct error estimate is 4.8009e-02
Iteration 3
spatial error indicator is 4.3453e-02
parametric error indicator is 1.7529e-02
Spatial refinement step...
original number of elements is 144
new number of elements is 182
spatial error estimate is 3.3849e-02 vs 4.0016e-02 (spatial indicator)
parametric error estimate is 8.1786e-03 vs 1.8030e-02 (parametric indicator)
overall estimate from indicators is 5.8046e-02
overall direct error estimate is 4.2028e-02
Iteration 4
spatial error indicator is 4.0016e-02
parametric error indicator is 1.8030e-02
Spatial refinement step...
original number of elements is 182
new number of elements is 243
spatial error estimate is 2.8954e-02 vs 3.4251e-02 (spatial indicator)
parametric error estimate is 8.3901e-03 vs 1.8641e-02 (parametric indicator)
overall estimate from indicators is 5.2891e-02
overall direct error estimate is 3.7345e-02
Iteration 5
spatial error indicator is 3.4251e-02
parametric error indicator is 1.8641e-02
Spatial refinement step...
original number of elements is 243
new number of elements is 288
spatial error estimate is 2.6315e-02 vs 2.8463e-02 (spatial indicator)
parametric error estimate is 8.5191e-03 vs 1.9009e-02 (parametric indicator)
overall estimate from indicators is 4.7472e-02
overall direct error estimate is 3.4834e-02
Iteration 6
spatial error indicator is 2.8463e-02
parametric error indicator is 1.9009e-02
Spatial refinement step...
original number of elements is 288
new number of elements is 386
spatial error estimate is 2.3610e-02 vs 2.6915e-02 (spatial indicator)
parametric error estimate is 8.5687e-03 vs 1.9106e-02 (parametric indicator)
overall estimate from indicators is 4.6020e-02
overall direct error estimate is 3.2178e-02
Iteration 7
spatial error indicator is 2.6915e-02
parametric error indicator is 1.9106e-02
Spatial refinement step...
original number of elements is 386
new number of elements is 480
spatial error estimate is 2.0960e-02 vs 2.1823e-02 (spatial indicator)
parametric error estimate is 8.6020e-03 vs 1.9169e-02 (parametric indicator)
overall estimate from indicators is 4.0993e-02
overall direct error estimate is 2.9562e-02
Iteration 8
spatial error indicator is 2.1823e-02
parametric error indicator is 1.9169e-02
Spatial refinement step...
original number of elements is 480
new number of elements is 656
spatial error estimate is 1.7900e-02 vs 1.9759e-02 (spatial indicator)
parametric error estimate is 8.6295e-03 vs 1.9262e-02 (parametric indicator)
overall estimate from indicators is 3.9022e-02
overall direct error estimate is 2.6530e-02
Iteration 9
spatial error indicator is 1.9759e-02
parametric error indicator is 1.9262e-02
Spatial refinement step...
original number of elements is 656
new number of elements is 904
spatial error estimate is 1.6006e-02 vs 1.8108e-02 (spatial indicator)
parametric error estimate is 8.6941e-03 vs 1.9426e-02 (parametric indicator)
overall estimate from indicators is 3.7534e-02
overall direct error estimate is 2.4700e-02
Iteration 10
spatial error indicator is 1.8108e-02
parametric error indicator is 1.9426e-02
Parametric enrichment step ... new indices added
1 2 1 1
spatial error estimate is 1.6060e-02 vs 2.4203e-02 (spatial indicator)
parametric error estimate is 6.1654e-03 vs 1.7248e-02 (parametric indicator)
overall estimate from indicators is 4.1451e-02
overall direct error estimate is 2.2226e-02
Iteration 11
spatial error indicator is 2.4203e-02
parametric error indicator is 1.7248e-02
Spatial refinement step...
original number of elements is 904
new number of elements is 1160
spatial error estimate is 1.3580e-02 vs 1.9965e-02 (spatial indicator)
parametric error estimate is 6.2219e-03 vs 1.7399e-02 (parametric indicator)
overall estimate from indicators is 3.7364e-02
overall direct error estimate is 1.9802e-02
Iteration 12
spatial error indicator is 1.9965e-02
parametric error indicator is 1.7399e-02
Spatial refinement step...
original number of elements is 1160
new number of elements is 1520
spatial error estimate is 1.2192e-02 vs 1.7318e-02 (spatial indicator)
parametric error estimate is 6.2397e-03 vs 1.7451e-02 (parametric indicator)
overall estimate from indicators is 3.4769e-02
overall direct error estimate is 1.8432e-02
Iteration 13
spatial error indicator is 1.7318e-02
parametric error indicator is 1.7451e-02
Parametric enrichment step ... new indices added
2 2 1 1
redundant sparse grid solutions ..
spatial error estimate is 1.2253e-02 vs 1.9011e-02 (spatial indicator)
parametric error estimate is 4.9119e-03 vs 1.0437e-02 (parametric indicator)
overall estimate from indicators is 2.9448e-02
overall direct error estimate is 1.7165e-02
Iteration 14
spatial error indicator is 1.9011e-02
parametric error indicator is 1.0437e-02
Spatial refinement step...
original number of elements is 1520
new number of elements is 1940
redundant sparse grid solutions ..
spatial error estimate is 1.1073e-02 vs 1.6362e-02 (spatial indicator)
parametric error estimate is 4.9194e-03 vs 1.0456e-02 (parametric indicator)
overall estimate from indicators is 2.6818e-02
overall direct error estimate is 1.5993e-02
Iteration 15
spatial error indicator is 1.6362e-02
parametric error indicator is 1.0456e-02
Spatial refinement step...
original number of elements is 1940
new number of elements is 2690
redundant sparse grid solutions ..
spatial error estimate is 9.1872e-03 vs 1.4283e-02 (spatial indicator)
parametric error estimate is 4.9288e-03 vs 1.0475e-02 (parametric indicator)
overall estimate from indicators is 2.4758e-02
overall direct error estimate is 1.4116e-02
Iteration 16
spatial error indicator is 1.4283e-02
parametric error indicator is 1.0475e-02
Spatial refinement step...
original number of elements is 2690
new number of elements is 3942
redundant sparse grid solutions ..
spatial error estimate is 7.7729e-03 vs 1.2239e-02 (spatial indicator)
parametric error estimate is 4.9481e-03 vs 1.0513e-02 (parametric indicator)
overall estimate from indicators is 2.2752e-02
overall direct error estimate is 1.2721e-02
Iteration 17
spatial error indicator is 1.2239e-02
parametric error indicator is 1.0513e-02
Spatial refinement step...
original number of elements is 3942
new number of elements is 5302
redundant sparse grid solutions ..
spatial error estimate is 6.6520e-03 vs 1.0216e-02 (spatial indicator)
parametric error estimate is 4.9544e-03 vs 1.0526e-02 (parametric indicator)
overall estimate from indicators is 2.0742e-02
overall direct error estimate is 1.1606e-02
Iteration 18
spatial error indicator is 1.0216e-02
parametric error indicator is 1.0526e-02
Parametric enrichment step ... new indices added
3 1 1 1
spatial error estimate is 6.5207e-03 vs 1.3966e-02 (spatial indicator)
parametric error estimate is 3.6784e-03 vs 7.9393e-03 (parametric indicator)
overall estimate from indicators is 2.1905e-02
overall direct error estimate is 1.0199e-02
Iteration 19
spatial error indicator is 1.3966e-02
parametric error indicator is 7.9393e-03
Spatial refinement step...
original number of elements is 5302
new number of elements is 7030
spatial error estimate is 5.6669e-03 vs 1.1912e-02 (spatial indicator)
parametric error estimate is 3.6806e-03 vs 7.9452e-03 (parametric indicator)
overall estimate from indicators is 1.9857e-02
overall direct error estimate is 9.3475e-03
Iteration 20
spatial error indicator is 1.1912e-02
parametric error indicator is 7.9452e-03
Spatial refinement step...
original number of elements is 7030
new number of elements is 9306
spatial error estimate is 4.8759e-03 vs 1.0137e-02 (spatial indicator)
parametric error estimate is 3.6819e-03 vs 7.9492e-03 (parametric indicator)
overall estimate from indicators is 1.8087e-02
overall direct error estimate is 8.5578e-03
Iteration 21
spatial error indicator is 1.0137e-02
parametric error indicator is 7.9492e-03
Spatial refinement step...
original number of elements is 9306
new number of elements is 14013
spatial error estimate is 4.0868e-03 vs 8.8229e-03 (spatial indicator)
parametric error estimate is 3.6852e-03 vs 7.9574e-03 (parametric indicator)
overall estimate from indicators is 1.6780e-02
overall direct error estimate is 7.7719e-03
Iteration 22
spatial error indicator is 8.8229e-03
parametric error indicator is 7.9574e-03
Spatial refinement step...
original number of elements is 14013
new number of elements is 18934
spatial error estimate is 3.4765e-03 vs 7.5949e-03 (spatial indicator)
parametric error estimate is 3.6866e-03 vs 7.9609e-03 (parametric indicator)
overall estimate from indicators is 1.5556e-02
overall direct error estimate is 7.1631e-03
Iteration 23
spatial error indicator is 7.5949e-03
parametric error indicator is 7.9609e-03
Parametric enrichment step ... new indices added
1 1 2 1
spatial error estimate is 3.4827e-03 vs 9.5339e-03 (spatial indicator)
parametric error estimate is 2.9250e-03 vs 7.9216e-03 (parametric indicator)
overall estimate from indicators is 1.7456e-02
overall direct error estimate is 6.4077e-03
Iteration 24
spatial error indicator is 9.5339e-03
parametric error indicator is 7.9216e-03
Spatial refinement step...
original number of elements is 18934
new number of elements is 24148
spatial error estimate is 3.0836e-03 vs 8.0244e-03 (spatial indicator)
parametric error estimate is 2.9251e-03 vs 7.9223e-03 (parametric indicator)
overall estimate from indicators is 1.5947e-02
overall direct error estimate is 6.0086e-03
Iteration 25
spatial error indicator is 8.0244e-03
parametric error indicator is 7.9223e-03
Spatial refinement step...
original number of elements is 24148
new number of elements is 32456
spatial error estimate is 2.6280e-03 vs 6.8245e-03 (spatial indicator)
parametric error estimate is 2.9256e-03 vs 7.9240e-03 (parametric indicator)
overall estimate from indicators is 1.4748e-02
overall direct error estimate is 5.5536e-03
Final sparse grid
1 1 1 1
1 1 2 1
1 1 3 1
1 2 1 1
1 3 1 1
2 1 1 1
2 2 1 1
2 3 1 1
3 1 1 1
3 2 1 1
3 3 1 1
4 1 1 1
5 1 1 1
Tolerance was reached in 25 iterations
after 5 parametric refinements
Mean maximum 0.075810
Variance maximum 0.000050
Standard Deviation maximum 0.007078
Total elapsed time: 139.44 sec
To compute a reference solution run the script referenceSC