-
Notifications
You must be signed in to change notification settings - Fork 0
/
SCtest_sl_tp2b.txt
516 lines (407 loc) · 18.8 KB
/
SCtest_sl_tp2b.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
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
: 2
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) : 8
choose type of random variable
1. Uniform
2. Truncated Gaussian
Default is uniform :
SE standard deviation (default is 0.5) :
correlation length in x (default is 1) :
correlation length in y (default is 1) :
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 8x3 grid (default is 3 for 8x12) :
Grid stretch factor (>=1) (default is 1) :
Iteration 0
spatial error estimate is 5.2206e-02 vs 7.9332e-02 (spatial indicator)
parametric error estimate is 3.4948e-02 vs 1.0213e-01 (parametric indicator)
overall estimate from indicators is 1.8146e-01
overall direct error estimate is 8.7154e-02
Iteration 1
spatial error indicator is 7.9332e-02
parametric error indicator is 1.0213e-01
Parametric enrichment step ... new indices added
2 1 1 1 1 1 1 1
spatial error estimate is 5.3537e-02 vs 1.1650e-01 (spatial indicator)
parametric error estimate is 2.2294e-02 vs 6.8535e-02 (parametric indicator)
overall estimate from indicators is 1.8503e-01
overall direct error estimate is 7.5831e-02
Iteration 2
spatial error indicator is 1.1650e-01
parametric error indicator is 6.8535e-02
Spatial refinement step...
original number of elements is 96
new number of elements is 110
spatial error estimate is 5.0089e-02 vs 9.8015e-02 (spatial indicator)
parametric error estimate is 2.2464e-02 vs 6.9201e-02 (parametric indicator)
overall estimate from indicators is 1.6722e-01
overall direct error estimate is 7.2553e-02
Iteration 3
spatial error indicator is 9.8015e-02
parametric error indicator is 6.9201e-02
Spatial refinement step...
original number of elements is 110
new number of elements is 126
spatial error estimate is 4.6269e-02 vs 8.7875e-02 (spatial indicator)
parametric error estimate is 2.2669e-02 vs 6.9987e-02 (parametric indicator)
overall estimate from indicators is 1.5786e-01
overall direct error estimate is 6.8938e-02
Iteration 4
spatial error indicator is 8.7875e-02
parametric error indicator is 6.9987e-02
Spatial refinement step...
original number of elements is 126
new number of elements is 156
spatial error estimate is 3.8997e-02 vs 8.1973e-02 (spatial indicator)
parametric error estimate is 2.2831e-02 vs 7.0546e-02 (parametric indicator)
overall estimate from indicators is 1.5252e-01
overall direct error estimate is 6.1828e-02
Iteration 5
spatial error indicator is 8.1973e-02
parametric error indicator is 7.0546e-02
Spatial refinement step...
original number of elements is 156
new number of elements is 200
spatial error estimate is 3.4265e-02 vs 7.7328e-02 (spatial indicator)
parametric error estimate is 2.3037e-02 vs 7.1257e-02 (parametric indicator)
overall estimate from indicators is 1.4859e-01
overall direct error estimate is 5.7302e-02
Iteration 6
spatial error indicator is 7.7328e-02
parametric error indicator is 7.1257e-02
Spatial refinement step...
original number of elements is 200
new number of elements is 241
spatial error estimate is 3.2154e-02 vs 6.9934e-02 (spatial indicator)
parametric error estimate is 2.3202e-02 vs 7.1891e-02 (parametric indicator)
overall estimate from indicators is 1.4183e-01
overall direct error estimate is 5.5356e-02
Iteration 7
spatial error indicator is 6.9934e-02
parametric error indicator is 7.1891e-02
Parametric enrichment step ... new indices added
1 2 1 1 1 1 1 1
1 1 2 1 1 1 1 1
spatial error estimate is 3.2553e-02 vs 1.2989e-01 (spatial indicator)
parametric error estimate is 1.4218e-02 vs 4.7348e-02 (parametric indicator)
overall estimate from indicators is 1.7723e-01
overall direct error estimate is 4.6772e-02
Iteration 8
spatial error indicator is 1.2989e-01
parametric error indicator is 4.7348e-02
Spatial refinement step...
original number of elements is 241
new number of elements is 294
spatial error estimate is 2.9763e-02 vs 1.0699e-01 (spatial indicator)
parametric error estimate is 1.4387e-02 vs 4.7880e-02 (parametric indicator)
overall estimate from indicators is 1.5487e-01
overall direct error estimate is 4.4150e-02
Iteration 9
spatial error indicator is 1.0699e-01
parametric error indicator is 4.7880e-02
Spatial refinement step...
original number of elements is 294
new number of elements is 334
spatial error estimate is 2.7873e-02 vs 9.4482e-02 (spatial indicator)
parametric error estimate is 1.4461e-02 vs 4.8115e-02 (parametric indicator)
overall estimate from indicators is 1.4260e-01
overall direct error estimate is 4.2333e-02
Iteration 10
spatial error indicator is 9.4482e-02
parametric error indicator is 4.8115e-02
Spatial refinement step...
original number of elements is 334
new number of elements is 414
spatial error estimate is 2.4658e-02 vs 8.4327e-02 (spatial indicator)
parametric error estimate is 1.4526e-02 vs 4.8333e-02 (parametric indicator)
overall estimate from indicators is 1.3266e-01
overall direct error estimate is 3.9184e-02
Iteration 11
spatial error indicator is 8.4327e-02
parametric error indicator is 4.8333e-02
Spatial refinement step...
original number of elements is 414
new number of elements is 526
spatial error estimate is 2.2293e-02 vs 7.6988e-02 (spatial indicator)
parametric error estimate is 1.4581e-02 vs 4.8509e-02 (parametric indicator)
overall estimate from indicators is 1.2550e-01
overall direct error estimate is 3.6874e-02
Iteration 12
spatial error indicator is 7.6988e-02
parametric error indicator is 4.8509e-02
Spatial refinement step...
original number of elements is 526
new number of elements is 726
spatial error estimate is 1.9410e-02 vs 7.4513e-02 (spatial indicator)
parametric error estimate is 1.4633e-02 vs 4.8676e-02 (parametric indicator)
overall estimate from indicators is 1.2319e-01
overall direct error estimate is 3.4043e-02
Iteration 13
spatial error indicator is 7.4513e-02
parametric error indicator is 4.8676e-02
Spatial refinement step...
original number of elements is 726
new number of elements is 948
spatial error estimate is 1.7170e-02 vs 6.5014e-02 (spatial indicator)
parametric error estimate is 1.4675e-02 vs 4.8811e-02 (parametric indicator)
overall estimate from indicators is 1.1383e-01
overall direct error estimate is 3.1845e-02
Iteration 14
spatial error indicator is 6.5014e-02
parametric error indicator is 4.8811e-02
Spatial refinement step...
original number of elements is 948
new number of elements is 1132
spatial error estimate is 1.5621e-02 vs 5.6222e-02 (spatial indicator)
parametric error estimate is 1.4707e-02 vs 4.8915e-02 (parametric indicator)
overall estimate from indicators is 1.0514e-01
overall direct error estimate is 3.0328e-02
Iteration 15
spatial error indicator is 5.6222e-02
parametric error indicator is 4.8915e-02
Spatial refinement step...
original number of elements is 1132
new number of elements is 1318
spatial error estimate is 1.4232e-02 vs 4.8094e-02 (spatial indicator)
parametric error estimate is 1.4734e-02 vs 4.9001e-02 (parametric indicator)
overall estimate from indicators is 9.7095e-02
overall direct error estimate is 2.8966e-02
Iteration 16
spatial error indicator is 4.8094e-02
parametric error indicator is 4.9001e-02
Parametric enrichment step ... new indices added
1 1 1 1 2 1 1 1
1 1 1 2 1 1 1 1
spatial error estimate is 1.4299e-02 vs 8.1502e-02 (spatial indicator)
parametric error estimate is 1.0442e-02 vs 3.8802e-02 (parametric indicator)
overall estimate from indicators is 1.2030e-01
overall direct error estimate is 2.4740e-02
Iteration 17
spatial error indicator is 8.1502e-02
parametric error indicator is 3.8802e-02
Spatial refinement step...
original number of elements is 1318
new number of elements is 1648
spatial error estimate is 1.3001e-02 vs 7.2400e-02 (spatial indicator)
parametric error estimate is 1.0457e-02 vs 3.8858e-02 (parametric indicator)
overall estimate from indicators is 1.1126e-01
overall direct error estimate is 2.3458e-02
Iteration 18
spatial error indicator is 7.2400e-02
parametric error indicator is 3.8858e-02
Spatial refinement step...
original number of elements is 1648
new number of elements is 2222
spatial error estimate is 1.1438e-02 vs 6.6092e-02 (spatial indicator)
parametric error estimate is 1.0467e-02 vs 3.8893e-02 (parametric indicator)
overall estimate from indicators is 1.0499e-01
overall direct error estimate is 2.1904e-02
Iteration 19
spatial error indicator is 6.6092e-02
parametric error indicator is 3.8893e-02
Spatial refinement step...
original number of elements is 2222
new number of elements is 3044
spatial error estimate is 9.5621e-03 vs 6.0720e-02 (spatial indicator)
parametric error estimate is 1.0478e-02 vs 3.8933e-02 (parametric indicator)
overall estimate from indicators is 9.9653e-02
overall direct error estimate is 2.0040e-02
Iteration 20
spatial error indicator is 6.0720e-02
parametric error indicator is 3.8933e-02
Spatial refinement step...
original number of elements is 3044
new number of elements is 4050
spatial error estimate is 8.4605e-03 vs 5.2402e-02 (spatial indicator)
parametric error estimate is 1.0488e-02 vs 3.8967e-02 (parametric indicator)
overall estimate from indicators is 9.1369e-02
overall direct error estimate is 1.8949e-02
Iteration 21
spatial error indicator is 5.2402e-02
parametric error indicator is 3.8967e-02
Spatial refinement step...
original number of elements is 4050
new number of elements is 4766
spatial error estimate is 7.6383e-03 vs 4.4217e-02 (spatial indicator)
parametric error estimate is 1.0494e-02 vs 3.8986e-02 (parametric indicator)
overall estimate from indicators is 8.3203e-02
overall direct error estimate is 1.8132e-02
Iteration 22
spatial error indicator is 4.4217e-02
parametric error indicator is 3.8986e-02
Spatial refinement step...
original number of elements is 4766
new number of elements is 5796
spatial error estimate is 7.0007e-03 vs 3.8290e-02 (spatial indicator)
parametric error estimate is 1.0498e-02 vs 3.9000e-02 (parametric indicator)
overall estimate from indicators is 7.7290e-02
overall direct error estimate is 1.7499e-02
Iteration 23
spatial error indicator is 3.8290e-02
parametric error indicator is 3.9000e-02
Parametric enrichment step ... new indices added
1 1 1 1 1 2 1 1
1 1 1 1 1 1 2 1
spatial error estimate is 7.0190e-03 vs 5.5470e-02 (spatial indicator)
parametric error estimate is 6.5863e-03 vs 3.2827e-02 (parametric indicator)
overall estimate from indicators is 8.8297e-02
overall direct error estimate is 1.3605e-02
Iteration 24
spatial error indicator is 5.5470e-02
parametric error indicator is 3.2827e-02
Spatial refinement step...
original number of elements is 5796
new number of elements is 7480
spatial error estimate is 6.2596e-03 vs 5.0086e-02 (spatial indicator)
parametric error estimate is 6.5884e-03 vs 3.2836e-02 (parametric indicator)
overall estimate from indicators is 8.2923e-02
overall direct error estimate is 1.2848e-02
Iteration 25
spatial error indicator is 5.0086e-02
parametric error indicator is 3.2836e-02
Spatial refinement step...
original number of elements is 7480
new number of elements is 10564
spatial error estimate is 5.2265e-03 vs 4.5865e-02 (spatial indicator)
parametric error estimate is 6.5904e-03 vs 3.2846e-02 (parametric indicator)
overall estimate from indicators is 7.8711e-02
overall direct error estimate is 1.1817e-02
Iteration 26
spatial error indicator is 4.5865e-02
parametric error indicator is 3.2846e-02
Spatial refinement step...
original number of elements is 10564
new number of elements is 14604
spatial error estimate is 4.4980e-03 vs 4.0909e-02 (spatial indicator)
parametric error estimate is 6.5922e-03 vs 3.2854e-02 (parametric indicator)
overall estimate from indicators is 7.3762e-02
overall direct error estimate is 1.1090e-02
Iteration 27
spatial error indicator is 4.0909e-02
parametric error indicator is 3.2854e-02
Spatial refinement step...
original number of elements is 14604
new number of elements is 17770
spatial error estimate is 4.0193e-03 vs 3.4120e-02 (spatial indicator)
parametric error estimate is 6.5936e-03 vs 3.2859e-02 (parametric indicator)
overall estimate from indicators is 6.6979e-02
overall direct error estimate is 1.0613e-02
Iteration 28
spatial error indicator is 3.4120e-02
parametric error indicator is 3.2859e-02
Spatial refinement step...
original number of elements is 17770
new number of elements is 21421
spatial error estimate is 3.6477e-03 vs 2.9211e-02 (spatial indicator)
parametric error estimate is 6.5944e-03 vs 3.2862e-02 (parametric indicator)
overall estimate from indicators is 6.2074e-02
overall direct error estimate is 1.0242e-02
Iteration 29
spatial error indicator is 2.9211e-02
parametric error indicator is 3.2862e-02
Parametric enrichment step ... new indices added
1 1 1 1 1 1 1 2
2 1 2 1 1 1 1 1
2 2 1 1 1 1 1 1
redundant sparse grid solutions ..
spatial error estimate is 3.6577e-03 vs 3.4253e-02 (spatial indicator)
parametric error estimate is 3.3365e-03 vs 2.3605e-02 (parametric indicator)
overall estimate from indicators is 5.7858e-02
overall direct error estimate is 6.9942e-03
Iteration 30
spatial error indicator is 3.4253e-02
parametric error indicator is 2.3605e-02
Spatial refinement step...
original number of elements is 21421
new number of elements is 27206
redundant sparse grid solutions ..
spatial error estimate is 3.2765e-03 vs 3.0132e-02 (spatial indicator)
parametric error estimate is 3.3368e-03 vs 2.3607e-02 (parametric indicator)
overall estimate from indicators is 5.3739e-02
overall direct error estimate is 6.6133e-03
Iteration 31
spatial error indicator is 3.0132e-02
parametric error indicator is 2.3607e-02
Spatial refinement step...
original number of elements is 27206
new number of elements is 38599
redundant sparse grid solutions ..
spatial error estimate is 2.7778e-03 vs 2.7637e-02 (spatial indicator)
parametric error estimate is 3.3370e-03 vs 2.3609e-02 (parametric indicator)
overall estimate from indicators is 5.1245e-02
overall direct error estimate is 6.1148e-03
Iteration 32
spatial error indicator is 2.7637e-02
parametric error indicator is 2.3609e-02
Spatial refinement step...
original number of elements is 38599
new number of elements is 54636
redundant sparse grid solutions ..
spatial error estimate is 2.3114e-03 vs 2.4746e-02 (spatial indicator)
parametric error estimate is 3.3372e-03 vs 2.3611e-02 (parametric indicator)
overall estimate from indicators is 4.8356e-02
overall direct error estimate is 5.6486e-03
Final sparse grid
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 2
1 1 1 1 1 1 1 3
1 1 1 1 1 1 2 1
1 1 1 1 1 1 3 1
1 1 1 1 1 2 1 1
1 1 1 1 1 3 1 1
1 1 1 1 2 1 1 1
1 1 1 1 3 1 1 1
1 1 1 2 1 1 1 1
1 1 1 3 1 1 1 1
1 1 2 1 1 1 1 1
1 1 3 1 1 1 1 1
1 2 1 1 1 1 1 1
1 3 1 1 1 1 1 1
2 1 1 1 1 1 1 1
2 1 2 1 1 1 1 1
2 1 3 1 1 1 1 1
2 2 1 1 1 1 1 1
2 3 1 1 1 1 1 1
3 1 1 1 1 1 1 1
3 1 2 1 1 1 1 1
3 1 3 1 1 1 1 1
3 2 1 1 1 1 1 1
3 3 1 1 1 1 1 1
Tolerance was reached in 32 iterations
after 5 parametric refinements
Mean maximum 0.055757
Variance maximum 0.000115
Standard Deviation maximum 0.010728
Total elapsed time: 911.73 sec
To compute a reference solution run the script referenceSC