Hi!

I am using MMG with its KratosMultiphysics interface for 2D meshes and I’m interested in achieving very small element sizes.

If I keep decrease the element size prescribed (1e-4 or lower), at a certain point MMG returns the error:

## Error: MMG5_interpmet22: null metric det : 0.000000E+00

## Error: MMG2D_intmet_ani: at least 1 naive interpolation.

Im not sure if it is a problem on my side, in the way we are prescribing the metrics, or if it is something on MMG side.

I attach the .sol and .mesh files for this case. The full terminal output is the following:

MAXIMUM MEMORY AUTHORIZED (MB) 12027

%% out_step=0.mesh OPENED

NUMBER OF VERTICES 40275 CORNERS 0

NUMBER OF TRIANGLES 80489

NUMBER OF EDGES 2691

%% out_step=0.sol OPENED

MmgProcess: Step data size: 12 Buffer size: 1

MmgProcess: ////////* MMG LIBRARY CALL *////////&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

MODULE MMG2D: 5.4.3 (Feb. 26, 2020)

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&– MMG2DLIB: INPUT DATA

– INPUT DATA COMPLETED. 0.000s– PHASE 1 : DATA ANALYSIS

– MESH QUALITY 80489

BEST 1.000000 AVRG. 0.953957 WRST. 0.538874 (18404)

HISTOGRAMM: 100.00 % > 0.12

100.00 % > 0.5

0.8 < Q < 1.0 79908 99.28 %

0.6 < Q < 0.8 578 0.72 %

0.4 < Q < 0.6 3 0.00 %

Connected component or subdomains: 45

Tagged edges: 4122, ridges: 59, refs: 4063

1840 corners, 0 singular points and 65 non manifold points detected

2910 calculated normal vectors– RESULTING EDGE LENGTHS 120704

AVERAGE LENGTH 1.7347

SMALLEST EDGE LENGTH 0.1027 32868 40140

LARGEST EDGE LENGTH 35.8375 20330 8508

0.60 < L < 1.30 58853 48.76 %`HISTOGRAMM: 0.00 < L < 0.30 3224 2.67 % 0.30 < L < 0.60 5667 4.69 % 0.60 < L < 0.71 3187 2.64 % 0.71 < L < 0.90 10527 8.72 % 0.90 < L < 1.30 45139 37.40 % 1.30 < L < 1.41 8763 7.26 % 1.41 < L < 2.00 19028 15.76 % 2.00 < L < 5.00 19486 16.14 % 5. < L 5683 4.71 %`

– PHASE 1 COMPLETED. 0.033s

– PHASE 2 : ANISOTROPIC MESHING

** GEOMETRIC MESH

4171 splitted, 0 collapsed, 8396 swapped

830 splitted, 63 collapsed, 886 swapped

520 splitted, 81 collapsed, 319 swapped

362 splitted, 55 collapsed, 201 swapped

356 splitted, 30 collapsed, 176 swapped

** COMPUTATIONAL MESH– GRADATION : 1.300000 (2.300000)

gradation: 4051 updated, 5 iter.

31573 splitted, 1651 collapsed, 26154 swapped## Error: MMG5_interpmet22: null metric det : 0.000000E+00

## Error: MMG2D_intmet_ani: at least 1 naive interpolation.

`34548 splitted, 1174 collapsed, 11465 swapped 13075 splitted, 736 collapsed, 4630 swapped 1845 splitted, 539 collapsed, 880 swapped 141 splitted, 306 collapsed, 181 swapped 100525 splitted, 47633 collapsed, 34525 swapped, 175215 moved 11774 splitted, 13277 collapsed, 7142 swapped, 173669 moved 4932 splitted, 6042 collapsed, 3783 swapped, 172577 moved 3164 splitted, 4116 collapsed, 3021 swapped, 171651 moved 2407 splitted, 3463 collapsed, 2757 swapped, 170584 moved`

– PHASE 2 COMPLETED. 10.827s

– MESH QUALITY 346241

BEST 1.000000 AVRG. 0.945662 WRST. 0.000000 (82729)

HISTOGRAMM: 100.00 % > 0.12

99.96 % > 0.5

0.8 < Q < 1.0 340138 98.24 %

0.6 < Q < 0.8 5769 1.67 %

0.4 < Q < 0.6 259 0.07 %

0.2 < Q < 0.4 50 0.01 %

0.0 < Q < 0.2 25 0.01 %## Error: MMG5_minQualCheck: too bad quality for the worst element: (elt 82729 -> 0.000000e+00)

`NUMBER OF VERTICES 173155 CORNERS 1840 NUMBER OF TRIANGLES 346241 NUMBER OF EDGES 20554`

These are the min size and max/min norms of the metrics for this problem that I computed before calling MMG:

min_elemental_size : 0.000100024

min_metric_norm : 0.0230676

max_metric_norm : 1.28358e+08

Are these too low or too high?

out_step=0.mesh (2.5 MB) out_step=0.sol (1.4 MB)