FEM4EllipticPDE/examples/magnet/sphere.geo

/* This file is part of Lemma, a geophysical modelling and inversion API.
 * More information is available at http://lemmasoftware.org
 */

/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/.
 */

radius = 3.25;     // Radius of the damn thing
lc = radius/5;     //  0.25;   // Target element size

// Total Solution Space
Box = 3*radius; // The down side of potential
X0 = -Box;
X1 =  Box;
Y0 = -Box;
Y1 =  Box;
Z0 = -Box;
Z1 =  Box;

cellSize=radius/10; ///10;
dd = 0 ; //  1e-5; //cellSize; // .01;
pio2=Pi/2;


/////////////////////////////////////
// Large Bounding box
pp = newp;
Point(pp)    = {X0, Y0, Z0, lc};
Point(pp+1)  = {X1, Y0, Z0, lc};
Point(pp+2)  = {X1, Y1, Z0, lc};
Point(pp+3)  = {X0, Y1, Z0, lc};


lv = newl;
Line(lv) = {pp,pp+1};
Line(lv+1) = {pp+1,pp+2};
Line(lv+2) = {pp+2,pp+3};
Line(lv+3) = {pp+3,pp};
Line Loop(lv+4) = {lv, lv+1, lv+2, lv+3};

// Hard coded doom
Plane Surface(125) = {lv+4};

//v = newv;
v[] = Extrude {0, 0, Z1-Z0} { Surface{125}; };

// Calculate offset effect
theta = Asin(dd/radius);
rr = radius * Cos(theta);

///////////////////////////////////
// Positive half sphere
// create inner 1/8 shell
p0 = newp;
Point(p0)   = {      0,   0,       0, cellSize}; // origin
Point(p0+1) = {    -rr,   0,      dd, cellSize};
Point(p0+2) = {      0,  rr,      dd, cellSize};
Point(p0+3) = {      0,   0,  radius, cellSize};
Point(p0+4) = {      0,   0,      dd, cellSize}; // origin

c0 = newc;
Circle(c0  ) = {p0+1, p0+4, p0+2};       // Tricky, This one needs to be offset!
Circle(c0+1) = {p0+3, p0, p0+1};
Circle(c0+2) = {p0+3, p0, p0+2};

Line Loop(10) = {c0, -(c0+2), c0+1} ;
Ruled Surface (60) = {10};

////////////////////////////////////////////////////////////
// Negative half sphere
p = newp;
Point(  p) = {      0,      0,            0, cellSize};
Point(p+1) = {    -rr,      0,          -dd, cellSize};
Point(p+2) = {      0,     rr,          -dd, cellSize};
Point(p+3) = {      0,      0,      -radius, cellSize};
Point(p+4) = {      0,      0,          -dd, cellSize};

cc = newc;
Circle(cc  ) = {p+1, p+4, p+2};
Circle(cc+1) = {p+3, p,   p+1};
Circle(cc+2) = {p+3, p,   p+2};

Circle(cc+3) = {p+3, p, p+2};
Circle(cc+4) = {p+3, p, p+2};
Circle(cc+5) = {p+3, p, p+2};

ccl = newl;
Line(ccl) = { p0+3, p+3 };

Line Loop(11) = {cc, -(cc+2), cc+1} ;
Ruled Surface (61) = {11};

// create remaining 7/8 inner shells
t1[] = Rotate {{0,0,1},{0,0,0},pio2  } {Duplicata{Surface{60};}};
t2[] = Rotate {{0,0,1},{0,0,0},pio2*2} {Duplicata{Surface{60};}};
t3[] = Rotate {{0,0,1},{0,0,0},pio2*3} {Duplicata{Surface{60};}};
//
t4[] = Rotate {{0,0,1},{0,0,0},pio2  } {Duplicata{Surface{61};}};
t5[] = Rotate {{0,0,1},{0,0,0},pio2*2} {Duplicata{Surface{61};}};
t6[] = Rotate {{0,0,1},{0,0,0},pio2*3} {Duplicata{Surface{61};}};

/* This is GOOD */
Surface{60} In Volume{v[1]};
Surface{t1[0]} In Volume{v[1]};
Surface{t2[0]} In Volume{v[1]};
Surface{t3[0]} In Volume{v[1]};

Surface{61} In Volume{v[1]};
Surface{t4[0]} In Volume{v[1]};
Surface{t5[0]} In Volume{v[1]};
Surface{t6[0]} In Volume{v[1]};

///////////////////////////////////////////////
// Attractor Field

// Field[1] = Attractor;
// Field[1].NodesList = {p}; //0, p0+1, p0+2, p0+3, p0+4, p, p+1, p+2, p+3, p+4};
//
// Field[2] = MathEval;
// Field[2].F = Sprintf("(2.25 - F1)^1.01 + %g", radius/10 );  // WORKS
//
// Field[3] = MathEval;
// Field[3].F = Sprintf("(12.25 - F1)^1.01 + %g", radius/5 );  // WORKS
//
// Field[4] = MathEval;
// Field[4].F = Sprintf("(22.25 - F1)^1.01 + %g", radius );  // WORKS
//
// Field[5] = MathEval;
// Field[5].F = Sprintf("(42.25 - F1)^1.01 + %g", radius*5 );  // WORKS
//
// //Field[2].F = Sprintf("(%g - F1)^2 + %g", radius, 2*cellSize );
// //Background Field = 2;
//
// // Finally, let's use the minimum of all the fields as the background mesh field
// Field[7] = Min;
// Field[7].FieldsList = {2, 3, 4, 5};
// Background Field = 7;

// Don't extend the elements sizes from the boundary inside the domain
//Mesh.CharacteristicLengthExtendFromBoundary = 0;

Physical Volume(1) = {v[1]};

// To create the mesh run
// gmsh sphere.gmsh -2 -v 0 -format msh -o sphere.msh
//gmsh -3 -format msh1 -o outfile.msh sphere.geo