Two level MLMC

[jbrezmorf]

• [x] process.py can sample fracture network, create 2d mesh, run Flow, extract effective tensor
• [x] add sampling of correlated random field
• [x] coarse mesh + fine fracture network, discontinuous mesh for every element, effective conductivity for every element
• [x] determine properties of resulting conductivity field
• [ ] connect into Two level MLMC, compute second level variance

[jbrezmorf]

Issues:

• wire wanrings during GMSH run: probable point of error: GEdgeLoop::nextOne They treat the wire as unsorted set, looking for edges that can prolongate from the last vertex. Unfortunately it seems that the code can not work for dendrites as any doubled edge in the wire is removed and reinserted only once.

• slight misfit in effective conductivity tensor

• physically relevant aperture to fracture size ratio

• flow123d reporting all fracture boundary points as lonely boundary, however these are real boundary points, connected to the fractures hitting the boundary

[jbrezmorf]

We observe assembly 1ms per element. Possible reasons:

• inefficient elementwise evaluation
• inefficient application of anisotropic conductivity tensor

[jbrezmorf]

MLMC issues: Many issues force me to implement all necessary my self (as long as I just want only two level MLMC).

• [x] Need a way how to pass some internal data with the samples (serialization, deserialization) YAML should be fine as long as we can pass also numpy arrays (seems to not work out of the box, but doable)
• [x] pass seeds used for samples, support repeatable calculations

[jbrezmorf]

Principal problems:

• seems that coarse conductivity array is not the lognormal
• not sure about no correlation for the angle, two fuzzy variogram?

[jbrezmorf]

TODO:

try to estimate E[P_f - P_c] = 0 estimate variance