Added magnet example

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

examples/magnet/sphere.sh

+#!/usr/bin/env bash
+gmsh  -3 -format vtk -o sphere.vtk  sphere.geo 
+gmsh  -2 -format stl -o sphereBox.stl  sphereBox.geo 
+../ResampleWithDataset  sphere.vtk  sphereBox.stl  MergedSphere.vtu 
+../VTKEdgeGsphere MergedSphere.vtu   3.25  magnet  sphereMag.vtu
+../FEM4EllipticPDE_bhmag  sphereMag.vtu  sphereMag.vtu   sphereOutMag.vtu 
+
+#paraview --data=sphereOutGrav.vtu 

examples/magnet/sphereBox.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/.
+ */
+
+D0 = 10;          // Top of magnet
+D1 = 11;          // Bottom of magnet
+radius = 3.25;     // Radius of the damn thing
+
+lc = radius;   //  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=lc; //300;
+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)^2 + %g", cellSize*10 );  // WORKS
+// //Field[2].F = Sprintf("(%g - F1)^2 + %g", radius, 2*cellSize );
+// //Background Field = 2;
+//
+// // 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