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stoch_diffusion_testresults_ex2.txt
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>> stoch_diff_testproblem
Numerical solution of reference stochastic diffusion problem.
Choose specific example:
1. Square domain (-1,1)^2, analytic KL expansion, non-constant source
2. Square domain (0,1)^2, Eigel synthetic random coefficient, constant source
3. Square domain (0,1)^2, Powell synthetic random coefficient, constant source
4. L-shaped domain, synthetic random coefficient, constant source
5. L-shaped domain, Eigel synthetic random coefficient, constant source
6. L-shaped domain, Powell synthetic random coefficient, constant source
7. Crack domain, Eigel synthetic random coefficient, constant source
8. Crack domain, Powell synthetic random coefficient, non-constant source
9. Square domain (0,1)^2, cookie problem, constant source
: 2
P1/P2 approximation 1/2? (default P1) :
Spatial error estimation type:
1. hierarchical estimator (elementwise residual problem)
2. hierarchical estimator (fully assembled sysyem for residual problem)
3. 2-level estimator
(default 1) :
Grid generation for a unit square domain
Grid parameter: 2 for underlying 8x4 grid (default is 3 for 16x8) : 4
Random variables distribution:
Uniform or truncated Gaussian distribution 1/2? (default is 1) :
Using Eigel synthetic random coefficient expansion
Slow/fast coefficient decay 1/2 (default slow) :
Number of active random variables? (default is 5) :
Total polynomial degree? (default is 3) :
Extra active random variables in the detail index set? (default is 1) :
Mesh info:
Number of vertices: 289
Number of elements: 512
Setting up stochastic P1 diffusion matrices...done (0.11567 sec)
MINRES solution of the linear systems:
LU(PQ) factorisation of K_0...done (0.00959 sec)
Call to STOCH_EST_MINRES without error control...
Bingo! Convergence in 17 iterations (0.40000 sec)
Eigenvalue convergence
k lambda Lambda
3 NaN NaN
4 0.6931 1.3069
5 0.6034 1.3966
6 0.5669 1.4331
7 0.5407 1.4593
8 0.5252 1.4748
9 0.5161 1.4839
10 0.5101 1.4899
11 0.5038 1.4962
12 0.4979 1.5021
13 0.4909 1.5091
14 0.4850 1.5150
15 0.4785 1.5215
16 0.4739 1.5261
17 0.4709 1.5291
Linear solver statistics:
Total ndof: 12600
Minimum eigenvalue: 0.470
Stochastic parameters:
Active parameters: 5
Polynomial degree: 3
Computed solution:
Maximum mean value: 7.5750e-02
Maximum variance: 4.9242e-05
Energy norm: 1.8901e-01
A posteriori error estimation
p/M/pM enrichment of the polynomial space 1/2/3? (default 3) :
YP-error estimation
Spatial hierarchical estimator (element residual problems)
yp estimate: intres = 1.7874e-02; edgeres = 2.0158e-02
YP-error estimation took 0.65610 sec
XQ-error estimation
computing new 'Q' indset and GPQ matrices... done
XQ-error estimation took 0.74374 sec
Simplistic YP-estimate of energy error: 1.99654e-02
Simplistic XQ-estimate of energy error: 9.60850e-04
Simplistic estimate of energy error: 1.99885e-02
Plotting expectation, variance and estimated errors...done
To test other detail space options run stoch_diffpost
>> stoch_diffpost
A posteriori error estimation
p/M/pM enrichment of the polynomial space 1/2/3? (default 3) : 2
YP-error estimation
Spatial hierarchical estimator (element residual problems)
yp estimate: intres = 1.7874e-02; edgeres = 2.0158e-02
YP-error estimation took 0.45229 sec
XQ-error estimation
computing new 'Q' indset and GPQ matrices... done
XQ-error estimation took 0.49225 sec
Simplistic YP-estimate of energy error: 1.99654e-02
Simplistic XQ-estimate of energy error: 8.10911e-04
Simplistic estimate of energy error: 1.99818e-02
>> stoch_diffpost
A posteriori error estimation
p/M/pM enrichment of the polynomial space 1/2/3? (default 3) : 1
YP-error estimation
Spatial hierarchical estimator (element residual problems)
yp estimate: intres = 1.7874e-02; edgeres = 2.0158e-02
YP-error estimation took 0.40756 sec
XQ-error estimation
computing new 'Q' indset and GPQ matrices... done
XQ-error estimation took 0.43507 sec
Simplistic YP-estimate of energy error: 1.99654e-02
Simplistic XQ-estimate of energy error: 5.15324e-04
Simplistic estimate of energy error: 1.99720e-02