[Gmsh] [GMSH] Suggestions for mesh size control requested

[Johannes Neumann]

Dear GMSH-community,
for my research project concerning modelling of asphalt concrete I'd 
like to perform computational homogenisation from periodic 
representative volume elements. Please see the attached picture for an 
example. I have both the problems that I need large geometries, i.e. 
with a high number of grains, and the strong localisation phenomena 
require for fine meshes. The localisation arises from the stiffness 
contrast between grains and matrix. The grains are orders of magnitudes 
stiffer. Therefore I already found that quadratic tets work way better 
than linear ones due to their linear interpolation of stress and strain 
fields.

I currently work with attractors to coarsen the mesh within the grains. 
These are positioned in a periodic manner, so I can achieve a periodic 
and heterogeneously sized mesh. Please find a simple *.geo file that 
realizes this attached.

I absolutely need to further cut down degrees of freedom while 
maintaining a fine mesh in the matrix. The mesh in picture contains ~2.7 
million dof, and mesh convergence has not been achieved yet. I could 
naturally be more aggressive with the attractors. I plan on putting them 
along the medial axis of the polyhedra, but i cannot extend their radius 
of influence further. In the picture, I have marked regions where I 
unvoluntarily coarsened the matrix mesh with red circles.

Any suggestions on how to lose dof within the grains without influencing 
the matrix are welcome.

Just some remarks:
  * The assumption of rigid bodies for the grains does not hold.
  * I have tried to work with background meshes for days, but could not 
make them work for me. Maybe someone can guide me here. I can provide 
seperate input files for matrix and grains.
  * Is it possible to work with linear shape functions within the 
grains. Although there would be hanging nodes at the interface?

Thanks for looking into this lengthy post.

Kind regards,
Johannes Neumann

-- 
Dipl.-Ing. Johannes Neumann
RWTH Aachen University
Institut für Angewandte Mechanik
Mies-van-der-Rohe-Str.1
D-52074 Aachen

Tel.:   +49 (0)241 80 25013
Fax :   +49 (0)241 80 22001
E-Mail: jneumann at ifam.rwth-aachen.de
Web:    www.ifam.rwth-aachen.de
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/*** 13 polyhedra for gmsh ***/
cl = 0.08;
Mesh.Optimize = 0;
Mesh.OptimizeNetgen = 0;
Point(1) = {0.000000, 0.000000, 0.000000, cl};
Point(2) = {0.000000, 0.000000, 0.509147, cl};
Point(3) = {0.000000, 0.000000, 1.068586, cl};
Point(4) = {0.000000, 0.000000, 1.682391, cl};
Point(5) = {0.000000, 0.015368, 0.505141, cl};
Point(6) = {0.000000, 0.111047, 1.297398, cl};
Point(7) = {0.000000, 0.149193, 0.000000, cl};
Point(8) = {0.000000, 0.149193, 1.682391, cl};
Point(9) = {0.000000, 0.183309, 0.344333, cl};
Point(10) = {0.000000, 0.306915, 0.745058, cl};
Point(11) = {0.000000, 0.522540, 0.623490, cl};
Point(12) = {0.000000, 0.522540, 0.863631, cl};
Point(13) = {0.000000, 0.860121, 0.623490, cl};
Point(14) = {0.000000, 0.860121, 0.863631, cl};
Point(15) = {0.000000, 0.974378, 0.514061, cl};
Point(16) = {0.000000, 1.048649, 0.000000, cl};
Point(17) = {0.000000, 1.048649, 1.682391, cl};
Point(18) = {0.000000, 1.096957, 0.745058, cl};
Point(19) = {0.000000, 1.120746, 1.183378, cl};
Point(20) = {0.000000, 1.216482, 0.630584, cl};
Point(21) = {0.000000, 1.361437, 1.069535, cl};
Point(22) = {0.000000, 1.617467, 1.137025, cl};
Point(23) = {0.000000, 1.682391, 0.000000, cl};
Point(24) = {0.000000, 1.682391, 0.509147, cl};
Point(25) = {0.000000, 1.682391, 1.068586, cl};
Point(26) = {0.000000, 1.682391, 1.682391, cl};
Point(27) = {0.089257, 1.337798, 0.124296, cl};
Point(28) = {0.089257, 1.355756, 0.000000, cl};
Point(29) = {0.089257, 1.355756, 1.682391, cl};
Point(30) = {0.089257, 1.374571, 1.552163, cl};
Point(31) = {0.089257, 1.389220, 1.556025, cl};
Point(32) = {0.089257, 1.401741, 0.000000, cl};
Point(33) = {0.089257, 1.401741, 1.682391, cl};
Point(34) = {0.089257, 1.412136, 0.104920, cl};
Point(35) = {0.115767, 0.000000, 1.173431, cl};
Point(36) = {0.115767, 1.682391, 1.173431, cl};
Point(37) = {0.149005, 1.273483, 0.250042, cl};
Point(38) = {0.149005, 1.345457, 1.434271, cl};
Point(39) = {0.149005, 1.410502, 1.451417, cl};
Point(40) = {0.149005, 1.453513, 0.203118, cl};
Point(41) = {0.211338, 0.704112, 0.623490, cl};
Point(42) = {0.211338, 0.704112, 0.863631, cl};
Point(43) = {0.344258, 0.602685, 0.745058, cl};
Point(44) = {0.344258, 0.842826, 0.745058, cl};
Point(45) = {0.347462, 0.704112, 0.527249, cl};
Point(46) = {0.436612, 1.049774, 0.260959, cl};
Point(47) = {0.480382, 0.602685, 0.648818, cl};
Point(48) = {0.480382, 0.842826, 0.648818, cl};
Point(49) = {0.534409, 1.049774, 1.420556, cl};
Point(50) = {0.543054, 0.704112, 1.164053, cl};
Point(51) = {0.583809, 0.961606, 0.084335, cl};
Point(52) = {0.583809, 0.973790, 0.000000, cl};
Point(53) = {0.583809, 0.973790, 1.682391, cl};
Point(54) = {0.583809, 0.997140, 1.520779, cl};
Point(55) = {0.583809, 1.654349, 1.588154, cl};
Point(56) = {0.583809, 1.663686, 0.000000, cl};
Point(57) = {0.583809, 1.663686, 1.682391, cl};
Point(58) = {0.583809, 1.671093, 0.074759, cl};
Point(59) = {0.607484, 1.049774, 1.432734, cl};
Point(60) = {0.641855, 0.471012, 1.499249, cl};
Point(61) = {0.641855, 0.489158, 0.000000, cl};
Point(62) = {0.641855, 0.489158, 1.682391, cl};
Point(63) = {0.641855, 0.504501, 0.154850, cl};
Point(64) = {0.641855, 0.527775, 0.174002, cl};
Point(65) = {0.641855, 0.552915, 0.000000, cl};
Point(66) = {0.641855, 0.552915, 1.682391, cl};
Point(67) = {0.641855, 0.598844, 1.364499, cl};
Point(68) = {0.648256, 1.049774, 0.226084, cl};
Point(69) = {0.675974, 0.602685, 1.045480, cl};
Point(70) = {0.675974, 0.842826, 1.045480, cl};
Point(71) = {0.774775, 0.369585, 1.380677, cl};
Point(72) = {0.774775, 0.403074, 0.276418, cl};
Point(73) = {0.774775, 0.426348, 0.295571, cl};
Point(74) = {0.774775, 0.497416, 1.245926, cl};
Point(75) = {0.810381, 1.337798, 0.124296, cl};
Point(76) = {0.810381, 1.355756, 0.000000, cl};
Point(77) = {0.810381, 1.355756, 1.682391, cl};
Point(78) = {0.810381, 1.374571, 1.552163, cl};
Point(79) = {0.810381, 1.389220, 1.556025, cl};
Point(80) = {0.810381, 1.401741, 0.000000, cl};
Point(81) = {0.810381, 1.401741, 1.682391, cl};
Point(82) = {0.810381, 1.412136, 0.104920, cl};
Point(83) = {0.822126, 0.602685, 1.069836, cl};
Point(84) = {0.822126, 0.842826, 1.069836, cl};
Point(85) = {0.881996, 0.471012, 1.499249, cl};
Point(86) = {0.881996, 0.489158, 0.000000, cl};
Point(87) = {0.881996, 0.489158, 1.682391, cl};
Point(88) = {0.881996, 0.504501, 0.154850, cl};
Point(89) = {0.881996, 0.527775, 0.174002, cl};
Point(90) = {0.881996, 0.552915, 0.000000, cl};
Point(91) = {0.881996, 0.552915, 1.682391, cl};
Point(92) = {0.881996, 0.598844, 1.364499, cl};
Point(93) = {0.903669, 0.602685, 0.579068, cl};
Point(94) = {0.903669, 0.842826, 0.579068, cl};
Point(95) = {0.929347, 0.704112, 1.188409, cl};
Point(96) = {1.010890, 0.704112, 0.457499, cl};
Point(97) = {1.058273, 0.602685, 0.745058, cl};
Point(98) = {1.058273, 0.842826, 0.745058, cl};
Point(99) = {1.090613, 0.000000, 1.335889, cl};
Point(100) = {1.090613, 1.682391, 1.335889, cl};
Point(101) = {1.127441, 0.000000, 0.323365, cl};
Point(102) = {1.127441, 1.682391, 0.323365, cl};
Point(103) = {1.165495, 0.704112, 0.623490, cl};
Point(104) = {1.165495, 0.704112, 0.863631, cl};
Point(105) = {1.227920, 1.418874, 0.375492, cl};
Point(106) = {1.227920, 1.492421, 1.308695, cl};
Point(107) = {1.227920, 1.521719, 1.316418, cl};
Point(108) = {1.227920, 1.567551, 0.336740, cl};
Point(109) = {1.284512, 0.000000, 1.442170, cl};
Point(110) = {1.284512, 1.682391, 1.442170, cl};
Point(111) = {1.305099, 0.000000, 0.000000, cl};
Point(112) = {1.305099, 0.000000, 1.682391, cl};
Point(113) = {1.305099, 1.682391, 0.000000, cl};
Point(114) = {1.305099, 1.682391, 1.682391, cl};
Point(115) = {1.323406, 0.000000, 0.213609, cl};
Point(116) = {1.323406, 1.682391, 0.213609, cl};
Point(117) = {1.335141, 1.280160, 0.253924, cl};
Point(118) = {1.335141, 1.316847, 0.000000, cl};
Point(119) = {1.335141, 1.316847, 1.682391, cl};
Point(120) = {1.335141, 1.353707, 1.427267, cl};
Point(121) = {1.335141, 1.623146, 1.434990, cl};
Point(122) = {1.335141, 1.647659, 0.000000, cl};
Point(123) = {1.335141, 1.647659, 1.682391, cl};
Point(124) = {1.335141, 1.668978, 0.215172, cl};
Point(125) = {1.347417, 0.000000, 0.559542, cl};
Point(126) = {1.347417, 0.000000, 0.982701, cl};
Point(127) = {1.347417, 0.225439, 0.745058, cl};
Point(128) = {1.347417, 1.166962, 0.745058, cl};
Point(129) = {1.347417, 1.290245, 0.626985, cl};
Point(130) = {1.347417, 1.434193, 1.072910, cl};
Point(131) = {1.347417, 1.564283, 1.107202, cl};
Point(132) = {1.347417, 1.650303, 0.533137, cl};
Point(133) = {1.347417, 1.682391, 0.559542, cl};
Point(134) = {1.347417, 1.682391, 0.982701, cl};
Point(135) = {1.354510, 0.000000, 0.247004, cl};
Point(136) = {1.354510, 1.682391, 0.247004, cl};
Point(137) = {1.400715, 0.000000, 0.000000, cl};
Point(138) = {1.400715, 0.000000, 1.682391, cl};
Point(139) = {1.400715, 1.682391, 0.000000, cl};
Point(140) = {1.400715, 1.682391, 1.682391, cl};
Point(141) = {1.454639, 0.000000, 1.208191, cl};
Point(142) = {1.454639, 0.069340, 0.411568, cl};
Point(143) = {1.454639, 0.326867, 0.623490, cl};
Point(144) = {1.454639, 0.326867, 0.863631, cl};
Point(145) = {1.454639, 1.028248, 0.623490, cl};
Point(146) = {1.454639, 1.028248, 0.863631, cl};
Point(147) = {1.454639, 1.151531, 0.505416, cl};
Point(148) = {1.454639, 1.295479, 1.191483, cl};
Point(149) = {1.454639, 1.665710, 1.225774, cl};
Point(150) = {1.454639, 1.682391, 1.208191, cl};
Point(151) = {1.484382, 0.000000, 1.235128, cl};
Point(152) = {1.484382, 1.682391, 1.235128, cl};
Point(153) = {1.587559, 0.000000, 0.559542, cl};
Point(154) = {1.587559, 0.000000, 0.982701, cl};
Point(155) = {1.587559, 0.225439, 0.745058, cl};
Point(156) = {1.587559, 1.166962, 0.745058, cl};
Point(157) = {1.587559, 1.290245, 0.626985, cl};
Point(158) = {1.587559, 1.434193, 1.072910, cl};
Point(159) = {1.587559, 1.564283, 1.107202, cl};
Point(160) = {1.587559, 1.650303, 0.533137, cl};
Point(161) = {1.587559, 1.682391, 0.559542, cl};
Point(162) = {1.587559, 1.682391, 0.982701, cl};
Point(163) = {1.651681, 0.000000, 0.514207, cl};
Point(164) = {1.651681, 1.682391, 0.514207, cl};
Point(165) = {1.682391, 0.000000, 0.000000, cl};
Point(166) = {1.682391, 0.000000, 0.509147, cl};
Point(167) = {1.682391, 0.000000, 1.068586, cl};
Point(168) = {1.682391, 0.000000, 1.682391, cl};
Point(169) = {1.682391, 0.015368, 0.505141, cl};
Point(170) = {1.682391, 0.111047, 1.297398, cl};
Point(171) = {1.682391, 0.149193, 0.000000, cl};
Point(172) = {1.682391, 0.149193, 1.682391, cl};
Point(173) = {1.682391, 0.183309, 0.344333, cl};
Point(174) = {1.682391, 0.306915, 0.745058, cl};
Point(175) = {1.682391, 0.522540, 0.623490, cl};
Point(176) = {1.682391, 0.522540, 0.863631, cl};
Point(177) = {1.682391, 0.860121, 0.623490, cl};
Point(178) = {1.682391, 0.860121, 0.863631, cl};
Point(179) = {1.682391, 0.974378, 0.514061, cl};
Point(180) = {1.682391, 1.048649, 0.000000, cl};
Point(181) = {1.682391, 1.048649, 1.682391, cl};
Point(182) = {1.682391, 1.096957, 0.745058, cl};
Point(183) = {1.682391, 1.120746, 1.183378, cl};
Point(184) = {1.682391, 1.216482, 0.630584, cl};
Point(185) = {1.682391, 1.361437, 1.069535, cl};
Point(186) = {1.682391, 1.617467, 1.137025, cl};
Point(187) = {1.682391, 1.682391, 0.000000, cl};
Point(188) = {1.682391, 1.682391, 0.509147, cl};
Point(189) = {1.682391, 1.682391, 1.068586, cl};
Point(190) = {1.682391, 1.682391, 1.682391, cl};
//*********************************
//*** periodic attractor points ***
//*********************************
Point(191) = {2.192527, 3.014758, 3.382129};
Point(192) = {0.510136, 3.014758, 3.382129};
Point(193) = {-1.172255, 3.014758, 3.382129};
Point(194) = {2.192527, 1.332367, 3.382129};
Point(195) = {0.510136, 1.332367, 3.382129};
Point(196) = {-1.172255, 1.332367, 3.382129};
Point(197) = {2.192527, -0.350024, 3.382129};
Point(198) = {0.510136, -0.350024, 3.382129};
Point(199) = {-1.172255, -0.350024, 3.382129};
Point(200) = {2.192527, 3.014758, 1.699739};
Point(201) = {0.510136, 3.014758, 1.699739};
Point(202) = {-1.172255, 3.014758, 1.699739};
Point(203) = {2.192527, 1.332367, 1.699739};
Point(204) = {0.510136, 1.332367, 1.699739};
Point(205) = {-1.172255, 1.332367, 1.699739};
Point(206) = {2.192527, -0.350024, 1.699739};
Point(207) = {0.510136, -0.350024, 1.699739};
Point(208) = {-1.172255, -0.350024, 1.699739};
Point(209) = {2.192527, 3.014758, 0.017348};
Point(210) = {0.510136, 3.014758, 0.017348};
Point(211) = {-1.172255, 3.014758, 0.017348};
Point(212) = {2.192527, 1.332367, 0.017348};
Point(213) = {0.510136, 1.332367, 0.017348};
Point(214) = {-1.172255, 1.332367, 0.017348};
Point(215) = {2.192527, -0.350024, 0.017348};
Point(216) = {0.510136, -0.350024, 0.017348};
Point(217) = {-1.172255, -0.350024, 0.017348};
Point(218) = {2.352444, 3.270510, 2.499944};
Point(219) = {3.210001, 2.309766, 3.260817};
Point(220) = {0.670053, 3.270510, 2.499944};
Point(221) = {1.527611, 2.309766, 3.260817};
Point(222) = {-1.012338, 3.270510, 2.499944};
Point(223) = {-0.154780, 2.309766, 3.260817};
Point(224) = {2.352444, 1.588119, 2.499944};
Point(225) = {3.210001, 0.627375, 3.260817};
Point(226) = {0.670053, 1.588119, 2.499944};
Point(227) = {1.527611, 0.627375, 3.260817};
Point(228) = {-1.012338, 1.588119, 2.499944};
Point(229) = {-0.154780, 0.627375, 3.260817};
Point(230) = {2.352444, -0.094272, 2.499944};
Point(231) = {3.210001, -1.055016, 3.260817};
Point(232) = {0.670053, -0.094272, 2.499944};
Point(233) = {1.527611, -1.055016, 3.260817};
Point(234) = {-1.012338, -0.094272, 2.499944};
Point(235) = {-0.154780, -1.055016, 3.260817};
Point(236) = {2.352444, 3.270510, 0.817553};
Point(237) = {3.210001, 2.309766, 1.578426};
Point(238) = {0.670053, 3.270510, 0.817553};
Point(239) = {1.527611, 2.309766, 1.578426};
Point(240) = {-1.012338, 3.270510, 0.817553};
Point(241) = {-0.154780, 2.309766, 1.578426};
Point(242) = {2.352444, 1.588119, 0.817553};
Point(243) = {3.210001, 0.627375, 1.578426};
Point(244) = {0.670053, 1.588119, 0.817553};
Point(245) = {1.527611, 0.627375, 1.578426};
Point(246) = {-1.012338, 1.588119, 0.817553};
Point(247) = {-0.154780, 0.627375, 1.578426};
Point(248) = {2.352444, -0.094272, 0.817553};
Point(249) = {3.210001, -1.055016, 1.578426};
Point(250) = {0.670053, -0.094272, 0.817553};
Point(251) = {1.527611, -1.055016, 1.578426};
Point(252) = {-1.012338, -0.094272, 0.817553};
Point(253) = {-0.154780, -1.055016, 1.578426};
Point(254) = {2.352444, 3.270510, -0.864838};
Point(255) = {3.210001, 2.309766, -0.103965};
Point(256) = {0.670053, 3.270510, -0.864838};
Point(257) = {1.527611, 2.309766, -0.103965};
Point(258) = {-1.012338, 3.270510, -0.864838};
Point(259) = {-0.154780, 2.309766, -0.103965};
Point(260) = {2.352444, 1.588119, -0.864838};
Point(261) = {3.210001, 0.627375, -0.103965};
Point(262) = {0.670053, 1.588119, -0.864838};
Point(263) = {1.527611, 0.627375, -0.103965};
Point(264) = {-1.012338, 1.588119, -0.864838};
Point(265) = {-0.154780, 0.627375, -0.103965};
Point(266) = {2.352444, -0.094272, -0.864838};
Point(267) = {3.210001, -1.055016, -0.103965};
Point(268) = {0.670053, -0.094272, -0.864838};
Point(269) = {1.527611, -1.055016, -0.103965};
Point(270) = {-1.012338, -0.094272, -0.864838};
Point(271) = {-0.154780, -1.055016, -0.103965};
//*********************************
Line(1) = {113, 122};
Line(2) = {122, 139};
Line(3) = {139, 187};
Line(4) = {187, 180};
Line(5) = {180, 118};
Line(6) = {118, 90};
Line(7) = {90, 86};
Line(8) = {86, 111};
Line(9) = {111, 1};
Line(10) = {1, 7};
Line(11) = {7, 61};
Line(12) = {61, 65};
Line(13) = {65, 16};
Line(14) = {16, 23};
Line(15) = {23, 113};
Line(16) = {28, 52};
Line(17) = {52, 76};
Line(18) = {76, 80};
Line(19) = {80, 56};
Line(20) = {56, 32};
Line(21) = {32, 28};
Line(22) = {171, 165};
Line(23) = {165, 137};
Line(24) = {137, 171};
Line(25) = {167, 154};
Line(26) = {154, 153};
Line(27) = {153, 163};
Line(28) = {163, 166};
Line(29) = {166, 165};
Line(30) = {137, 135};
Line(31) = {135, 115};
Line(32) = {115, 111};
Line(33) = {1, 2};
Line(34) = {2, 101};
Line(35) = {101, 125};
Line(36) = {125, 126};
Line(37) = {126, 99};
Line(38) = {99, 35};
Line(39) = {35, 3};
Line(40) = {3, 4};
Line(41) = {4, 112};
Line(42) = {112, 109};
Line(43) = {109, 141};
Line(44) = {141, 151};
Line(45) = {151, 138};
Line(46) = {138, 168};
Line(47) = {168, 167};
Line(48) = {189, 186};
Line(49) = {186, 185};
Line(50) = {185, 182};
Line(51) = {182, 184};
Line(52) = {184, 188};
Line(53) = {188, 187};
Line(54) = {180, 179};
Line(55) = {179, 177};
Line(56) = {177, 175};
Line(57) = {175, 173};
Line(58) = {173, 171};
Line(59) = {166, 169};
Line(60) = {169, 174};
Line(61) = {174, 167};
Line(62) = {168, 172};
Line(63) = {172, 170};
Line(64) = {170, 176};
Line(65) = {176, 178};
Line(66) = {178, 183};
Line(67) = {183, 181};
Line(68) = {181, 190};
Line(69) = {190, 189};
Line(70) = {25, 22};
Line(71) = {22, 21};
Line(72) = {21, 18};
Line(73) = {18, 20};
Line(74) = {20, 24};
Line(75) = {24, 23};
Line(76) = {16, 15};
Line(77) = {15, 13};
Line(78) = {13, 11};
Line(79) = {11, 9};
Line(80) = {9, 7};
Line(81) = {2, 5};
Line(82) = {5, 10};
Line(83) = {10, 3};
Line(84) = {4, 8};
Line(85) = {8, 6};
Line(86) = {6, 12};
Line(87) = {12, 14};
Line(88) = {14, 19};
Line(89) = {19, 17};
Line(90) = {17, 26};
Line(91) = {26, 25};
Line(92) = {189, 162};
Line(93) = {162, 161};
Line(94) = {161, 164};
Line(95) = {164, 188};
Line(96) = {139, 136};
Line(97) = {136, 116};
Line(98) = {116, 113};
Line(99) = {24, 102};
Line(100) = {102, 133};
Line(101) = {133, 134};
Line(102) = {134, 100};
Line(103) = {100, 36};
Line(104) = {36, 25};
Line(105) = {26, 114};
Line(106) = {114, 110};
Line(107) = {110, 150};
Line(108) = {150, 152};
Line(109) = {152, 140};
Line(110) = {140, 190};
Line(111) = {114, 123};
Line(112) = {123, 140};
Line(113) = {181, 119};
Line(114) = {119, 91};
Line(115) = {91, 87};
Line(116) = {87, 112};
Line(117) = {8, 62};
Line(118) = {62, 66};
Line(119) = {66, 17};
Line(120) = {29, 53};
Line(121) = {53, 77};
Line(122) = {77, 81};
Line(123) = {81, 57};
Line(124) = {57, 33};
Line(125) = {33, 29};
Line(126) = {138, 172};
Line(127) = {160, 164};
Line(128) = {161, 160};
Line(129) = {156, 157};
Line(130) = {157, 184};
Line(131) = {182, 156};
Line(132) = {157, 160};
Line(133) = {156, 158};
Line(134) = {158, 185};
Line(135) = {158, 159};
Line(136) = {159, 186};
Line(137) = {162, 159};
Line(138) = {155, 153};
Line(139) = {154, 155};
Line(140) = {169, 163};
Line(141) = {174, 155};
Line(142) = {149, 150};
Line(143) = {152, 149};
Line(144) = {121, 110};
Line(145) = {123, 121};
Line(146) = {149, 121};
Line(147) = {59, 54};
Line(148) = {54, 49};
Line(149) = {49, 59};
Line(150) = {38, 39};
Line(151) = {39, 31};
Line(152) = {31, 30};
Line(153) = {30, 38};
Line(154) = {49, 38};
Line(155) = {30, 29};
Line(156) = {53, 54};
Line(157) = {77, 78};
Line(158) = {78, 59};
Line(159) = {55, 39};
Line(160) = {31, 33};
Line(161) = {57, 55};
Line(162) = {55, 79};
Line(163) = {79, 78};
Line(164) = {79, 81};
Line(165) = {36, 22};
Line(166) = {44, 48};
Line(167) = {48, 20};
Line(168) = {18, 44};
Line(169) = {107, 131};
Line(170) = {131, 134};
Line(171) = {100, 107};
Line(172) = {130, 106};
Line(173) = {106, 84};
Line(174) = {84, 98};
Line(175) = {98, 128};
Line(176) = {128, 130};
Line(177) = {106, 107};
Line(178) = {131, 130};
Line(179) = {84, 70};
Line(180) = {70, 21};
Line(181) = {44, 70};
Line(182) = {128, 129};
Line(183) = {129, 132};
Line(184) = {132, 133};
Line(185) = {132, 108};
Line(186) = {108, 102};
Line(187) = {129, 105};
Line(188) = {105, 108};
Line(189) = {48, 94};
Line(190) = {94, 98};
Line(191) = {94, 105};
Line(192) = {148, 146};
Line(193) = {146, 178};
Line(194) = {183, 148};
Line(195) = {104, 146};
Line(196) = {176, 144};
Line(197) = {144, 104};
Line(198) = {144, 141};
Line(199) = {151, 170};
Line(200) = {148, 120};
Line(201) = {120, 95};
Line(202) = {95, 104};
Line(203) = {120, 119};
Line(204) = {95, 92};
Line(205) = {92, 91};
Line(206) = {109, 85};
Line(207) = {85, 92};
Line(208) = {87, 85};
Line(209) = {71, 99};
Line(210) = {35, 71};
Line(211) = {69, 83};
Line(212) = {83, 74};
Line(213) = {74, 69};
Line(214) = {127, 126};
Line(215) = {125, 127};
Line(216) = {93, 73};
Line(217) = {73, 47};
Line(218) = {47, 93};
Line(219) = {72, 101};
Line(220) = {5, 72};
Line(221) = {43, 10};
Line(222) = {71, 74};
Line(223) = {69, 43};
Line(224) = {127, 97};
Line(225) = {97, 83};
Line(226) = {97, 93};
Line(227) = {47, 43};
Line(228) = {73, 72};
Line(229) = {42, 14};
Line(230) = {12, 42};
Line(231) = {50, 42};
Line(232) = {19, 50};
Line(233) = {67, 50};
Line(234) = {66, 67};
Line(235) = {6, 60};
Line(236) = {60, 67};
Line(237) = {62, 60};
Line(238) = {124, 136};
Line(239) = {116, 124};
Line(240) = {124, 122};
Line(241) = {51, 68};
Line(242) = {68, 46};
Line(243) = {46, 51};
Line(244) = {75, 76};
Line(245) = {52, 51};
Line(246) = {68, 75};
Line(247) = {46, 37};
Line(248) = {37, 40};
Line(249) = {40, 58};
Line(250) = {58, 82};
Line(251) = {82, 75};
Line(252) = {82, 80};
Line(253) = {40, 34};
Line(254) = {34, 32};
Line(255) = {56, 58};
Line(256) = {37, 27};
Line(257) = {27, 28};
Line(258) = {27, 34};
Line(259) = {145, 147};
Line(260) = {147, 117};
Line(261) = {117, 96};
Line(262) = {96, 103};
Line(263) = {103, 145};
Line(264) = {88, 86};
Line(265) = {115, 88};
Line(266) = {117, 118};
Line(267) = {90, 89};
Line(268) = {89, 96};
Line(269) = {89, 88};
Line(270) = {179, 147};
Line(271) = {177, 145};
Line(272) = {103, 143};
Line(273) = {143, 175};
Line(274) = {143, 142};
Line(275) = {142, 173};
Line(276) = {142, 135};
Line(277) = {41, 13};
Line(278) = {11, 41};
Line(279) = {64, 45};
Line(280) = {45, 15};
Line(281) = {65, 64};
Line(282) = {9, 63};
Line(283) = {63, 64};
Line(284) = {45, 41};
Line(285) = {63, 61};
Line(286) = {189, 188};
Line(287) = {167, 166};
Line(288) = {140, 114};
Line(289) = {25, 24};
Line(290) = {172, 181};
Line(291) = {138, 112};
Line(292) = {3, 2};
Line(293) = {8, 17};
Line(294) = {139, 113};
Line(295) = {180, 171};
Line(296) = {137, 111};
Line(297) = {7, 16};
Line Loop(1) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
Line Loop(2) = {16, 17, 18, 19, 20, 21};
Line Loop(3) = {22, 23, 24};
Line Loop(4) = {25, 26, 27, 28, 29, 23, 30, 31, 32, 9, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47};
Line Loop(5) = {48, 49, 50, 51, 52, 53, 4, 54, 55, 56, 57, 58, 22, -29, 59, 60, 61, -47, 62, 63, 64, 65, 66, 67, 68, 69};
Line Loop(6) = {70, 71, 72, 73, 74, 75, -14, 76, 77, 78, 79, 80, -10, 33, 81, 82, 83, 40, 84, 85, 86, 87, 88, 89, 90, 91};
Line Loop(7) = {92, 93, 94, 95, 53, -3, 96, 97, 98, -15, -75, 99, 100, 101, 102, 103, 104, -91, 105, 106, 107, 108, 109, 110, 69};
Line Loop(8) = {111, 112, 110, -68, 113, 114, 115, 116, -41, 84, 117, 118, 119, 90, 105};
Line Loop(9) = {120, 121, 122, 123, 124, 125};
Line Loop(10) = {-62, -46, 126};
Line Loop(11) = {127, -94, 128};
Line Loop(12) = {129, 130, -51, 131};
Line Loop(13) = {132, 127, 95, -52, -130};
Line Loop(14) = {133, 134, 50, 131};
Line Loop(15) = {135, 136, 49, -134};
Line Loop(16) = {129, 132, -128, -93, 137, -135, -133};
Line Loop(17) = {136, -48, 92, 137};
Line Loop(18) = {138, -26, 139};
Line Loop(19) = {59, 140, 28};
Line Loop(20) = {-139, -25, -61, 141};
Line Loop(21) = {138, 27, -140, 60, 141};
Line Loop(22) = {142, 108, 143};
Line Loop(23) = {144, -106, 111, 145};
Line Loop(24) = {146, -145, 112, -109, 143};
Line Loop(25) = {146, 144, 107, -142};
Line Loop(26) = {147, 148, 149};
Line Loop(27) = {150, 151, 152, 153};
Line Loop(28) = {148, 154, -153, 155, 120, 156};
Line Loop(29) = {147, -156, 121, 157, 158};
Line Loop(30) = {159, 151, 160, -124, 161};
Line Loop(31) = {-152, 160, 125, -155};
Line Loop(32) = {-149, 154, 150, -159, 162, 163, 158};
Line Loop(33) = {-163, 164, -122, 157};
Line Loop(34) = {-162, -161, -123, -164};
Line Loop(35) = {-70, -104, 165};
Line Loop(36) = {166, 167, -73, 168};
Line Loop(37) = {169, 170, 102, 171};
Line Loop(38) = {172, 173, 174, 175, 176};
Line Loop(39) = {172, 177, 169, 178};
Line Loop(40) = {179, 180, -71, -165, -103, 171, -177, 173};
Line Loop(41) = {181, 180, 72, 168};
Line Loop(42) = {-176, 182, 183, 184, 101, -170, 178};
Line Loop(43) = {185, 186, 100, -184};
Line Loop(44) = {-183, 187, 188, -185};
Line Loop(45) = {166, 189, 190, -174, 179, -181};
Line Loop(46) = {189, 191, 188, 186, -99, -74, -167};
Line Loop(47) = {175, 182, 187, -191, 190};
Line Loop(48) = {192, 193, 66, 194};
Line Loop(49) = {195, 193, -65, 196, 197};
Line Loop(50) = {198, 44, 199, 64, 196};
Line Loop(51) = {199, -63, -126, -45};
Line Loop(52) = {200, 201, 202, 195, -192};
Line Loop(53) = {200, 203, -113, -67, 194};
Line Loop(54) = {204, 205, -114, -203, 201};
Line Loop(55) = {-197, 198, -43, 206, 207, -204, 202};
Line Loop(56) = {-206, -42, -116, 208};
Line Loop(57) = {-207, -208, -115, -205};
Line Loop(58) = {209, 38, 210};
Line Loop(59) = {211, 212, 213};
Line Loop(60) = {214, -36, 215};
Line Loop(61) = {216, 217, 218};
Line Loop(62) = {219, -34, 81, 220};
Line Loop(63) = {221, 83, -39, 210, 222, 213, 223};
Line Loop(64) = {209, -37, -214, 224, 225, 212, -222};
Line Loop(65) = {-223, 211, -225, 226, -218, 227};
Line Loop(66) = {224, 226, 216, 228, 219, 35, 215};
Line Loop(67) = {221, -82, 220, -228, 217, 227};
Line Loop(68) = {229, -87, 230};
Line Loop(69) = {231, 229, 88, 232};
Line Loop(70) = {233, -232, 89, -119, 234};
Line Loop(71) = {233, 231, -230, -86, 235, 236};
Line Loop(72) = {-235, -85, 117, 237};
Line Loop(73) = {-236, -237, 118, 234};
Line Loop(74) = {238, 97, 239};
Line Loop(75) = {240, 2, 96, -238};
Line Loop(76) = {240, -1, -98, 239};
Line Loop(77) = {241, 242, 243};
Line Loop(78) = {244, -17, 245, 241, 246};
Line Loop(79) = {-246, 242, 247, 248, 249, 250, 251};
Line Loop(80) = {-251, 252, -18, -244};
Line Loop(81) = {253, 254, -20, 255, -249};
Line Loop(82) = {-250, -255, -19, -252};
Line Loop(83) = {256, 257, 16, 245, -243, 247};
Line Loop(84) = {254, 21, -257, 258};
Line Loop(85) = {248, 253, -258, -256};
Line Loop(86) = {259, 260, 261, 262, 263};
Line Loop(87) = {264, 8, -32, 265};
Line Loop(88) = {266, 6, 267, 268, -261};
Line Loop(89) = {269, 264, -7, 267};
Line Loop(90) = {260, 266, -5, 54, 270};
Line Loop(91) = {259, -270, 55, 271};
Line Loop(92) = {-263, 272, 273, -56, 271};
Line Loop(93) = {274, 275, -57, -273};
Line Loop(94) = {272, 274, 276, 31, 265, -269, 268, 262};
Line Loop(95) = {275, 58, -24, 30, -276};
Line Loop(96) = {277, 78, 278};
Line Loop(97) = {279, 280, -76, -13, 281};
Line Loop(98) = {-278, 79, 282, 283, 279, 284};
Line Loop(99) = {-284, 280, 77, -277};
Line Loop(100) = {285, -11, -80, 282};
Line Loop(101) = {-283, 285, 12, 281};
Line Loop(102) = {-51, -50, -49, -48, 286, -52};
Line Loop(103) = {-93, -92, 286, -95, -94};
Line Loop(104) = {59, 60, 61, 287};
Line Loop(105) = {-26, -25, 287, -28, -27};
Line Loop(106) = {112, 288, 111};
Line Loop(107) = {108, 109, 288, 106, 107};
Line Loop(108) = {102, 103, 104, 289, 99, 100, 101};
Line Loop(109) = {-73, -72, -71, -70, 289, -74};
Line Loop(110) = {-66, -65, -64, -63, 290, -67};
Line Loop(111) = {44, 45, 291, 42, 43};
Line Loop(112) = {-114, -113, -290, -126, 291, -116, -115};
Line Loop(113) = {81, 82, 83, 292};
Line Loop(114) = {37, 38, 39, 292, 34, 35, 36};
Line Loop(115) = {-88, -87, -86, -85, 293, -89};
Line Loop(116) = {-118, -117, 293, -119};
Line Loop(117) = {2, 294, 1};
Line Loop(118) = {98, -294, 96, 97};
Line Loop(119) = {-6, -5, 295, -24, 296, -8, -7};
Line Loop(120) = {56, 57, 58, -295, 54, 55};
Line Loop(121) = {32, -296, 30, 31};
Line Loop(122) = {78, 79, 80, 297, 76, 77};
Line Loop(123) = {-12, -11, 297, -13};
Plane Surface(1) = {1, 2};
Plane Surface(2) = {3};
Plane Surface(3) = {4};
Plane Surface(4) = {5};
Plane Surface(5) = {6};
Plane Surface(6) = {7};
Plane Surface(7) = {8, 9};
Plane Surface(8) = {10};
Plane Surface(9) = {11};
Plane Surface(10) = {12};
Plane Surface(11) = {13};
Plane Surface(12) = {14};
Plane Surface(13) = {15};
Plane Surface(14) = {16};
Plane Surface(15) = {17};
Plane Surface(16) = {18};
Plane Surface(17) = {19};
Plane Surface(18) = {20};
Plane Surface(19) = {21};
Plane Surface(20) = {22};
Plane Surface(21) = {23};
Plane Surface(22) = {24};
Plane Surface(23) = {25};
Plane Surface(24) = {26};
Plane Surface(25) = {27};
Plane Surface(26) = {28};
Plane Surface(27) = {29};
Plane Surface(28) = {30};
Plane Surface(29) = {31};
Plane Surface(30) = {32};
Plane Surface(31) = {33};
Plane Surface(32) = {34};
Plane Surface(33) = {35};
Plane Surface(34) = {36};
Plane Surface(35) = {37};
Plane Surface(36) = {38};
Plane Surface(37) = {39};
Plane Surface(38) = {40};
Plane Surface(39) = {41};
Plane Surface(40) = {42};
Plane Surface(41) = {43};
Plane Surface(42) = {44};
Plane Surface(43) = {45};
Plane Surface(44) = {46};
Plane Surface(45) = {47};
Plane Surface(46) = {48};
Plane Surface(47) = {49};
Plane Surface(48) = {50};
Plane Surface(49) = {51};
Plane Surface(50) = {52};
Plane Surface(51) = {53};
Plane Surface(52) = {54};
Plane Surface(53) = {55};
Plane Surface(54) = {56};
Plane Surface(55) = {57};
Plane Surface(56) = {58};
Plane Surface(57) = {59};
Plane Surface(58) = {60};
Plane Surface(59) = {61};
Plane Surface(60) = {62};
Plane Surface(61) = {63};
Plane Surface(62) = {64};
Plane Surface(63) = {65};
Plane Surface(64) = {66};
Plane Surface(65) = {67};
Plane Surface(66) = {68};
Plane Surface(67) = {69};
Plane Surface(68) = {70};
Plane Surface(69) = {71};
Plane Surface(70) = {72};
Plane Surface(71) = {73};
Plane Surface(72) = {74};
Plane Surface(73) = {75};
Plane Surface(74) = {76};
Plane Surface(75) = {77};
Plane Surface(76) = {78};
Plane Surface(77) = {79};
Plane Surface(78) = {80};
Plane Surface(79) = {81};
Plane Surface(80) = {82};
Plane Surface(81) = {83};
Plane Surface(82) = {84};
Plane Surface(83) = {85};
Plane Surface(84) = {86};
Plane Surface(85) = {87};
Plane Surface(86) = {88};
Plane Surface(87) = {89};
Plane Surface(88) = {90};
Plane Surface(89) = {91};
Plane Surface(90) = {92};
Plane Surface(91) = {93};
Plane Surface(92) = {94};
Plane Surface(93) = {95};
Plane Surface(94) = {96};
Plane Surface(95) = {97};
Plane Surface(96) = {98};
Plane Surface(97) = {99};
Plane Surface(98) = {100};
Plane Surface(99) = {101};
Plane Surface(100) = {102};
Plane Surface(101) = {103};
Plane Surface(102) = {104};
Plane Surface(103) = {105};
Plane Surface(104) = {106};
Plane Surface(105) = {107};
Plane Surface(106) = {9};
Plane Surface(107) = {108};
Plane Surface(108) = {109};
Plane Surface(109) = {110};
Plane Surface(110) = {111};
Plane Surface(111) = {112};
Plane Surface(112) = {113};
Plane Surface(113) = {114};
Plane Surface(114) = {115};
Plane Surface(115) = {116};
Plane Surface(116) = {117};
Plane Surface(117) = {118};
Plane Surface(118) = {2};
Plane Surface(119) = {119};
Plane Surface(120) = {120};
Plane Surface(121) = {121};
Plane Surface(122) = {122};
Plane Surface(123) = {123};
// Periodicity:
//The master surface is on the right of the equal sign.
//All master surfaces and all slave surfaces must lie on the same side of the volume, respectively.
Periodic Surface 7{111, 112, 110, -68, 113, 114, 115, 116, -41, 84, 117, 118, 119, 90, 105, 120, 121, 122, 123, 124, 125} = 1{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21};
Periodic Surface 8{-62, -46, 126} = 2{22, 23, 24};
Periodic Surface 6{92, 93, 94, 95, 53, -3, 96, 97, 98, -15, -75, 99, 100, 101, 102, 103, 104, -91, 105, 106, 107, 108, 109, 110, 69} = 3{25, 26, 27, 28, 29, 23, 30, 31, 32, 9, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47};
Periodic Surface 4{48, 49, 50, 51, 52, 53, 4, 54, 55, 56, 57, 58, 22, -29, 59, 60, 61, -47, 62, 63, 64, 65, 66, 67, 68, 69} = 5{70, 71, 72, 73, 74, 75, -14, 76, 77, 78, 79, 80, -10, 33, 81, 82, 83, 40, 84, 85, 86, 87, 88, 89, 90, 91};
Periodic Surface 101{-93, -92, 286, -95, -94} = 103{-26, -25, 287, -28, -27};
Periodic Surface 100{-51, -50, -49, -48, 286, -52} = 108{-73, -72, -71, -70, 289, -74};
Periodic Surface 105{108, 109, 288, 106, 107} = 110{44, 45, 291, 42, 43};
Periodic Surface 102{59, 60, 61, 287} = 112{81, 82, 83, 292};
Periodic Surface 107{102, 103, 104, 289, 99, 100, 101} = 113{37, 38, 39, 292, 34, 35, 36};
Periodic Surface 109{-66, -65, -64, -63, 290, -67} = 114{-88, -87, -86, -85, 293, -89};
Periodic Surface 104{112, 288, 111} = 116{2, 294, 1};
Periodic Surface 106{120, 121, 122, 123, 124, 125} = 118{16, 17, 18, 19, 20, 21};
Periodic Surface 111{-114, -113, -290, -126, 291, -116, -115} = 119{-6, -5, 295, -24, 296, -8, -7};
Periodic Surface 117{98, -294, 96, 97} = 121{32, -296, 30, 31};
Periodic Surface 120{56, 57, 58, -295, 54, 55} = 122{78, 79, 80, 297, 76, 77};
Periodic Surface 115{-118, -117, 293, -119} = 123{-12, -11, 297, -13};
//********************************
Surface Loop(1) = {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};
Surface Loop(2) = {9, 10, 11, 100, 12, 13, 14, 101, 15};
Surface Loop(3) = {16, 17, 18, 102, 19, 103};
Surface Loop(4) = {104, 20, 105, 21, 22, 23};
Surface Loop(5) = {24, 25, 26, 27, 106, 28, 29, 30, 31, 32};
Surface Loop(6) = {33, 34, 35, 36, 37, 107, 38, 108, 39, 40, 41, 42, 43, 44, 45};
Surface Loop(7) = {46, 109, 47, 110, 48, 49, 50, 51, 52, 53, 111, 54, 55};
Surface Loop(8) = {56, 57, 58, 59, 60, 112, 61, 62, 63, 113, 64, 65};
Surface Loop(9) = {66, 114, 67, 68, 69, 115, 70, 71};
Surface Loop(10) = {116, 72, 73, 117, 74};
Surface Loop(11) = {75, 76, 77, 78, 118, 79, 80, 81, 82, 83};
Surface Loop(12) = {84, 85, 86, 87, 119, 88, 89, 90, 120, 91, 92, 93, 121};
Surface Loop(13) = {94, 122, 95, 96, 97, 123, 98, 99};
Volume(1) = {1};
Volume(2) = {2};
Volume(3) = {3};
Volume(4) = {4};
Volume(5) = {5};
Volume(6) = {6};
Volume(7) = {7};
Volume(8) = {8};
Volume(9) = {9};
Volume(10) = {10};
Volume(11) = {11};
Volume(12) = {12};
Volume(13) = {13};
Physical Volume(0) = {1};
Physical Volume(1) = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13};
//*********************************
Field[1] = Attractor;
Field[1].NodesList = {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};
Field[2] = Threshold;
Field[2].IField = 1;
Field[2].LcMin = cl;
Field[2].LcMax = 5*cl;
Field[2].DistMin = 0.222793;
Field[2].DistMax = 0.111396;
Field[3] = Attractor;
Field[3].NodesList = {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};
Field[4] = Threshold;
Field[4].IField = 3;
Field[4].LcMin = cl;
Field[4].LcMax = 5*cl;
Field[4].DistMin = 0.455055;
Field[4].DistMax = 0.227528;
Field[5] = Max;
Field[5].FieldsList = {2, 4};
Background Field = 5;
Mesh.CharacteristicLengthExtendFromBoundary = 0;
Mesh.CharacteristicLengthFromPoints = 0;