Galerkin FEM for elliptic PDEs
Vous ne pouvez pas sélectionner plus de 25 sujets Les noms de sujets doivent commencer par une lettre ou un nombre, peuvent contenir des tirets ('-') et peuvent comporter jusqu'à 35 caractères.

sphere.geo 4.2KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148
  1. /* This file is part of Lemma, a geophysical modelling and inversion API.
  2. * More information is available at http://lemmasoftware.org
  3. */
  4. /* This Source Code Form is subject to the terms of the Mozilla Public
  5. * License, v. 2.0. If a copy of the MPL was not distributed with this
  6. * file, You can obtain one at http://mozilla.org/MPL/2.0/.
  7. */
  8. radius = 4.25; // Radius of the damn thing
  9. lc = radius/5; // 0.25; // Target element size
  10. // Total Solution Space
  11. Box = 5*radius; // The down side of potential
  12. X0 = -Box;
  13. X1 = Box;
  14. Y0 = -Box;
  15. Y1 = Box;
  16. Z0 = -Box;
  17. Z1 = Box;
  18. cellSize=radius/10; ///10;
  19. dd = 0 ; // 1e-5; //cellSize; // .01;
  20. pio2=Pi/2;
  21. /////////////////////////////////////
  22. // Large Bounding box
  23. pp = newp;
  24. Point(pp) = {X0, Y0, Z0, lc};
  25. Point(pp+1) = {X1, Y0, Z0, lc};
  26. Point(pp+2) = {X1, Y1, Z0, lc};
  27. Point(pp+3) = {X0, Y1, Z0, lc};
  28. lv = newl;
  29. Line(lv) = {pp,pp+1};
  30. Line(lv+1) = {pp+1,pp+2};
  31. Line(lv+2) = {pp+2,pp+3};
  32. Line(lv+3) = {pp+3,pp};
  33. Line Loop(lv+4) = {lv, lv+1, lv+2, lv+3};
  34. // Hard coded doom
  35. Plane Surface(125) = {lv+4};
  36. //v = newv;
  37. v[] = Extrude {0, 0, Z1-Z0} { Surface{125}; };
  38. // Calculate offset effect
  39. theta = Asin(dd/radius);
  40. rr = radius * Cos(theta);
  41. ///////////////////////////////////
  42. // Positive half sphere
  43. // create inner 1/8 shell
  44. p0 = newp;
  45. Point(p0) = { 0, 0, 0, cellSize}; // origin
  46. Point(p0+1) = { -rr, 0, dd, cellSize};
  47. Point(p0+2) = { 0, rr, dd, cellSize};
  48. Point(p0+3) = { 0, 0, radius, cellSize};
  49. Point(p0+4) = { 0, 0, dd, cellSize}; // origin
  50. c0 = newc;
  51. Circle(c0 ) = {p0+1, p0+4, p0+2}; // Tricky, This one needs to be offset!
  52. Circle(c0+1) = {p0+3, p0, p0+1};
  53. Circle(c0+2) = {p0+3, p0, p0+2};
  54. Line Loop(10) = {c0, -(c0+2), c0+1} ;
  55. Ruled Surface (60) = {10};
  56. ////////////////////////////////////////////////////////////
  57. // Negative half sphere
  58. p = newp;
  59. Point( p) = { 0, 0, 0, cellSize};
  60. Point(p+1) = { -rr, 0, -dd, cellSize};
  61. Point(p+2) = { 0, rr, -dd, cellSize};
  62. Point(p+3) = { 0, 0, -radius, cellSize};
  63. Point(p+4) = { 0, 0, -dd, cellSize};
  64. cc = newc;
  65. Circle(cc ) = {p+1, p+4, p+2};
  66. Circle(cc+1) = {p+3, p, p+1};
  67. Circle(cc+2) = {p+3, p, p+2};
  68. Circle(cc+3) = {p+3, p, p+2};
  69. Circle(cc+4) = {p+3, p, p+2};
  70. Circle(cc+5) = {p+3, p, p+2};
  71. ccl = newl;
  72. Line(ccl) = { p0+3, p+3 };
  73. Line Loop(11) = {cc, -(cc+2), cc+1} ;
  74. Ruled Surface (61) = {11};
  75. // create remaining 7/8 inner shells
  76. t1[] = Rotate {{0,0,1},{0,0,0},pio2 } {Duplicata{Surface{60};}};
  77. t2[] = Rotate {{0,0,1},{0,0,0},pio2*2} {Duplicata{Surface{60};}};
  78. t3[] = Rotate {{0,0,1},{0,0,0},pio2*3} {Duplicata{Surface{60};}};
  79. //
  80. t4[] = Rotate {{0,0,1},{0,0,0},pio2 } {Duplicata{Surface{61};}};
  81. t5[] = Rotate {{0,0,1},{0,0,0},pio2*2} {Duplicata{Surface{61};}};
  82. t6[] = Rotate {{0,0,1},{0,0,0},pio2*3} {Duplicata{Surface{61};}};
  83. /* This is GOOD */
  84. Surface{60} In Volume{v[1]};
  85. Surface{t1[0]} In Volume{v[1]};
  86. Surface{t2[0]} In Volume{v[1]};
  87. Surface{t3[0]} In Volume{v[1]};
  88. Surface{61} In Volume{v[1]};
  89. Surface{t4[0]} In Volume{v[1]};
  90. Surface{t5[0]} In Volume{v[1]};
  91. Surface{t6[0]} In Volume{v[1]};
  92. ///////////////////////////////////////////////
  93. // Attractor Field
  94. // Field[1] = Attractor;
  95. // Field[1].NodesList = {p}; //0, p0+1, p0+2, p0+3, p0+4, p, p+1, p+2, p+3, p+4};
  96. //
  97. // Field[2] = MathEval;
  98. // Field[2].F = Sprintf("(2.25 - F1)^1.01 + %g", radius/10 ); // WORKS
  99. //
  100. // Field[3] = MathEval;
  101. // Field[3].F = Sprintf("(12.25 - F1)^1.01 + %g", radius/5 ); // WORKS
  102. //
  103. // Field[4] = MathEval;
  104. // Field[4].F = Sprintf("(22.25 - F1)^1.01 + %g", radius ); // WORKS
  105. //
  106. // Field[5] = MathEval;
  107. // Field[5].F = Sprintf("(42.25 - F1)^1.01 + %g", radius*5 ); // WORKS
  108. //
  109. // //Field[2].F = Sprintf("(%g - F1)^2 + %g", radius, 2*cellSize );
  110. // //Background Field = 2;
  111. //
  112. // // Finally, let's use the minimum of all the fields as the background mesh field
  113. // Field[7] = Min;
  114. // Field[7].FieldsList = {2, 3, 4, 5};
  115. // Background Field = 7;
  116. // Don't extend the elements sizes from the boundary inside the domain
  117. //Mesh.CharacteristicLengthExtendFromBoundary = 0;
  118. Physical Volume(1) = {v[1]};
  119. // To create the mesh run
  120. // gmsh sphere.gmsh -2 -v 0 -format msh -o sphere.msh
  121. //gmsh -3 -format msh1 -o outfile.msh sphere.geo