Feature/mixed mimetic discretization

[OmarDuran]

This PR introduce the building blocks for assembling and solving mimetic operators for flow as a saddle point problem. The solution of this saddle point system consist on a adaptive mimetic discretization where TPFA inner product is combined with a consistent one on regions TPFA can be consistent.

The associated theory can be found in the link
https://arxiv.org/abs/2607.23568

The following is an toy example of consistency adaptation on the full SPE10, where the green regions (MFD subregion) represent a simplex region connected with a large portion of hexahedral cells (TPFA subregion).

The following figure shows the MFD sub-region automatically identified employing a consistencyTolerance="0.01"

The following figures show the pressure colormaps for adaptive-MFD (left panel), TPFA on a hexahedral mesh (middle panel), and TPFA on the hybrid mesh (right panel). The TPFA approximation on the hybrid mesh exhibits a visible effect due to the consistency error localized in the simplex cells. The adaptive-MFD approximation is quite similar to the TPFA approximation on the hexahedral mesh, where it is exact. The small differences are due to the different types of meshes.

The following table was constructed using 8 ranks to show the following features:

1. Optimal convergence of the pressure in l2-norm on smooth solutions;
2. Robustness of the MGR solution strategy w.r.t refinement and material constrast;
3. Reduction in the number of iterations with an increasing share of TPFA cells.

relative $L^2$ pressure error / GMRES iterations / linear solve time [s] (setup excluded); $\text{krylovTol} = 1.0\times 10^{-6}$
isotropic permeability in series along the flow ($x$): $k = 10^{-14}\text{ m}^2$ on $x < 0.5$, $k = 10^{-14} / \text{contrast}$ on $x > 0.5$; smooth exact pressure solution
$\text{unknowns} = \text{cells} + \text{faces}$ of the assembled matrix; $\text{reduced} = \text{cells} + \text{non-condensed flux dofs}$, the coupled system after the condensation (a condensed flux is a one-way closure row)

mesh	mfd%	n	cells	unknowns	reduced	contrast 1	contrast 10000	contrast 1e+07
hex	0	2	16	84	16	3.33e-01 / 4 / 0.000	1.00e+00 / 5 / 0.000	1.00e+00 / 5 / 0.000
hex	0	4	128	592	128	8.54e-02 / 7 / 0.001	3.33e-01 / 7 / 0.001	3.33e-01 / 7 / 0.001
hex	0	8	1024	4416	1024	2.14e-02 / 8 / 0.003	8.54e-02 / 9 / 0.003	8.54e-02 / 9 / 0.003
hex	0	16	8192	34048	8192	5.35e-03 / 10 / 0.027	2.14e-02 / 10 / 0.028	2.14e-02 / 10 / 0.027
hex	0	32	65536	267264	65536	1.34e-03 / 11 / 0.278	5.35e-03 / 11 / 0.277	5.35e-03 / 11 / 0.279
hex	0	64	524288	2117632	524288	3.34e-04 / 12 / 2.649	1.34e-03 / 12 / 2.677	1.34e-03 / 12 / 2.683
hex	25	2	16	84	36	2.74e-01 / 6 / 0.000	8.34e-01 / 6 / 0.000	8.35e-01 / 6 / 0.000
hex	25	4	128	592	256	7.11e-02 / 9 / 0.001	2.82e-01 / 9 / 0.001	2.82e-01 / 11 / 0.001
hex	25	8	1024	4416	1920	1.79e-02 / 11 / 0.004	7.26e-02 / 13 / 0.005	7.27e-02 / 15 / 0.006
hex	25	16	8192	34048	14848	4.47e-03 / 13 / 0.037	1.82e-02 / 14 / 0.041	1.82e-02 / 18 / 0.056
hex	25	32	65536	267264	116736	1.12e-03 / 14 / 0.365	4.56e-03 / 16 / 0.433	4.56e-03 / 20 / 0.581
hex	25	64	524288	2117632	925696	2.80e-04 / 16 / 3.759	1.14e-03 / 19 / 4.689	1.14e-03 / 21 / 5.343
hex	75	2	16	84	68	1.50e-01 / 6 / 0.000	4.69e-01 / 8 / 0.000	4.69e-01 / 8 / 0.000
hex	75	4	128	592	480	3.95e-02 / 9 / 0.001	1.62e-01 / 9 / 0.001	1.62e-01 / 11 / 0.001
hex	75	8	1024	4416	3584	9.99e-03 / 12 / 0.005	4.21e-02 / 13 / 0.005	4.22e-02 / 14 / 0.006
hex	75	16	8192	34048	27648	2.51e-03 / 13 / 0.037	1.06e-02 / 15 / 0.045	1.06e-02 / 18 / 0.058
hex	75	32	65536	267264	217088	6.27e-04 / 15 / 0.392	2.66e-03 / 17 / 0.465	2.66e-03 / 21 / 0.614
hex	75	64	524288	2117632	1720320	1.57e-04 / 16 / 3.710	6.65e-04 / 19 / 4.668	6.65e-04 / 21 / 5.295
hex	100	2	16	84	84	6.67e-02 / 10 / 0.000	2.00e-01 / 11 / 0.000	2.00e-01 / 11 / 0.000
hex	100	4	128	592	592	1.71e-02 / 13 / 0.001	6.66e-02 / 13 / 0.001	6.67e-02 / 14 / 0.001
hex	100	8	1024	4416	4416	4.28e-03 / 17 / 0.007	1.71e-02 / 18 / 0.007	1.71e-02 / 19 / 0.008
hex	100	16	8192	34048	34048	1.07e-03 / 18 / 0.057	4.28e-03 / 20 / 0.065	4.28e-03 / 24 / 0.084
hex	100	32	65536	267264	267264	2.67e-04 / 20 / 0.568	1.07e-03 / 23 / 0.685	1.07e-03 / 27 / 0.851
hex	100	64	524288	2117632	2117632	6.69e-05 / 23 / 5.944	2.67e-04 / 26 / 7.096	2.67e-04 / 28 / 7.840
tet	0	2	96	328	96	6.04e-01 / 9 / 0.000	1.04e+00 / 9 / 0.001	1.04e+00 / 9 / 0.000
tet	0	4	768	2464	768	4.82e-01 / 11 / 0.002	6.04e-01 / 11 / 0.002	6.04e-01 / 11 / 0.002
tet	0	8	6144	19072	6144	4.54e-01 / 13 / 0.020	4.82e-01 / 13 / 0.020	4.82e-01 / 13 / 0.020
tet	0	16	49152	150016	49152	4.47e-01 / 13 / 0.171	4.54e-01 / 14 / 0.189	4.54e-01 / 14 / 0.188
tet	0	32	393216	1189888	393216	4.45e-01 / 14 / 1.704	4.47e-01 / 14 / 1.699	4.47e-01 / 14 / 1.701
tet	0	64	3145728	9478144	3145728	4.45e-01 / 15 / 14.798	4.45e-01 / 15 / 15.138	4.45e-01 / 15 / 15.088
tet	25	2	96	328	160	5.16e-01 / 11 / 0.001	9.23e-01 / 13 / 0.001	9.23e-01 / 15 / 0.001
tet	25	4	768	2464	1216	3.83e-01 / 15 / 0.003	5.07e-01 / 17 / 0.004	5.07e-01 / 18 / 0.004
tet	25	8	6144	19072	9472	3.56e-01 / 16 / 0.027	4.00e-01 / 19 / 0.034	4.00e-01 / 21 / 0.038
tet	25	16	49152	150016	74752	3.50e-01 / 17 / 0.243	3.74e-01 / 19 / 0.279	3.74e-01 / 23 / 0.369
tet	25	32	393216	1189888	593920	3.48e-01 / 18 / 2.365	3.68e-01 / 21 / 2.880	3.68e-01 / 22 / 3.076
tet	25	64	3145728	9478144	4734976	3.48e-01 / 20 / 21.675	3.66e-01 / 21 / 23.160	3.66e-01 / 25 / 29.386
tet	75	2	96	328	272	3.08e-01 / 11 / 0.001	6.65e-01 / 13 / 0.001	6.65e-01 / 16 / 0.001
tet	75	4	768	2464	2048	1.79e-01 / 15 / 0.003	2.93e-01 / 17 / 0.004	2.93e-01 / 19 / 0.005
tet	75	8	6144	19072	15872	1.59e-01 / 17 / 0.029	2.10e-01 / 20 / 0.035	2.10e-01 / 22 / 0.041
tet	75	16	49152	150016	124928	1.54e-01 / 17 / 0.246	1.92e-01 / 19 / 0.290	1.92e-01 / 23 / 0.370
tet	75	32	393216	1189888	991232	1.53e-01 / 18 / 2.347	1.88e-01 / 21 / 2.873	1.88e-01 / 23 / 3.235
tet	75	64	3145728	9478144	7897088	1.53e-01 / 19 / 20.239	1.87e-01 / 21 / 23.089	1.87e-01 / 25 / 29.282
tet	100	2	96	328	328	1.46e-01 / 15 / 0.001	5.12e-01 / 17 / 0.001	5.12e-01 / 20 / 0.001
tet	100	4	768	2464	2464	3.69e-02 / 19 / 0.004	1.46e-01 / 20 / 0.005	1.46e-01 / 22 / 0.005
tet	100	8	6144	19072	19072	9.22e-03 / 21 / 0.038	3.68e-02 / 23 / 0.043	3.69e-02 / 25 / 0.049
tet	100	16	49152	150016	150016	2.30e-03 / 20 / 0.309	9.21e-03 / 23 / 0.368	9.22e-03 / 27 / 0.460
tet	100	32	393216	1189888	1189888	5.76e-04 / 22 / 3.052	2.30e-03 / 24 / 3.435	2.30e-03 / 26 / 3.841
tet	100	64	3145728	9478144	9478144	1.44e-04 / 22 / 24.415	5.76e-04 / 25 / 29.192	5.76e-04 / 52 / 87.726