/********************************************************************* * * Gmsh tutorial 5 * * Characteristic lengths, arrays of variables, functions, loops * *********************************************************************/ // Again, we start be defining some characteristic lengths: lcar1 = .1; lcar2 = .0005; lcar3 = .055; // If we wanted to change these lengths globally (without changing the // above definitions), we could give a global scaling factor for all // characteristic lengths on the command line with the `-clscale' // option (or with `Mesh.CharacteristicLengthFactor' in an option // file). For example, with: // // > gmsh t5.geo -clscale 1 // // this input file produces a mesh of approximately 3,000 nodes and // 15,000 tetrahedra. With // // > gmsh t5.geo -clscale 0.2 // // the mesh counts approximately 600,000 nodes and 3.6 million // tetrahedra. // We proceed by defining some elementary entities describing a // truncated cube: Point(1) = {0.5,0.5,0.5,lcar2}; Point(2) = {0.5,0.5,0,lcar1}; Point(3) = {0,0.5,0.5,lcar1}; Point(4) = {0,0,0.5,lcar1}; Point(5) = {0.5,0,0.5,lcar1}; Point(6) = {0.5,0,0,lcar1}; Point(7) = {0,0.5,0,lcar1}; Point(8) = {0,1,0,lcar1}; Point(9) = {1,1,0,lcar1}; Point(10) = {0,0,1,lcar1}; Point(11) = {0,1,1,lcar1}; Point(12) = {1,1,1,lcar1}; Point(13) = {1,0,1,lcar1}; Point(14) = {1,0,0,lcar1}; Line(1) = {8,9}; Line(2) = {9,12}; Line(3) = {12,11}; Line(4) = {11,8}; Line(5) = {9,14}; Line(6) = {14,13}; Line(7) = {13,12}; Line(8) = {11,10}; Line(9) = {10,13}; Line(10) = {10,4}; Line(11) = {4,5}; Line(12) = {5,6}; Line(13) = {6,2}; Line(14) = {2,1}; Line(15) = {1,3}; Line(16) = {3,7}; Line(17) = {7,2}; Line(18) = {3,4}; Line(19) = {5,1}; Line(20) = {7,8}; Line(21) = {6,14}; Line Loop(22) = {-11,-19,-15,-18}; Plane Surface(23) = {22}; Line Loop(24) = {16,17,14,15}; Plane Surface(25) = {24}; Line Loop(26) = {-17,20,1,5,-21,13}; Plane Surface(27) = {26}; Line Loop(28) = {-4,-1,-2,-3}; Plane Surface(29) = {28}; Line Loop(30) = {-7,2,-5,-6}; Plane Surface(31) = {30}; Line Loop(32) = {6,-9,10,11,12,21}; Plane Surface(33) = {32}; Line Loop(34) = {7,3,8,9}; Plane Surface(35) = {34}; Line Loop(36) = {-10,18,-16,-20,4,-8}; Plane Surface(37) = {36}; Line Loop(38) = {-14,-13,-12,19}; Plane Surface(39) = {38}; // Instead of using included files, we now use a user-defined function // in order to carve some holes in the cube: Function CheeseHole // In the following commands we use the reserved variable name // `newp', which automatically selects a new point number. This // number is chosen as the highest current point number, plus // one. (Note that, analogously to `newp', the variables `newc', // `news', `newv' and `newreg' select the highest number amongst // currently defined curves, surfaces, volumes and `any entities // other than points', respectively.) p1 = newp; Point(p1) = {x, y, z, lcar3} ; p2 = newp; Point(p2) = {x+r,y, z, lcar3} ; p3 = newp; Point(p3) = {x, y+r,z, lcar3} ; p4 = newp; Point(p4) = {x, y, z+r,lcar3} ; p5 = newp; Point(p5) = {x-r,y, z, lcar3} ; p6 = newp; Point(p6) = {x, y-r,z, lcar3} ; p7 = newp; Point(p7) = {x, y, z-r,lcar3} ; c1 = newreg; Circle(c1) = {p2,p1,p7}; c2 = newreg; Circle(c2) = {p7,p1,p5}; c3 = newreg; Circle(c3) = {p5,p1,p4}; c4 = newreg; Circle(c4) = {p4,p1,p2}; c5 = newreg; Circle(c5) = {p2,p1,p3}; c6 = newreg; Circle(c6) = {p3,p1,p5}; c7 = newreg; Circle(c7) = {p5,p1,p6}; c8 = newreg; Circle(c8) = {p6,p1,p2}; c9 = newreg; Circle(c9) = {p7,p1,p3}; c10 = newreg; Circle(c10) = {p3,p1,p4}; c11 = newreg; Circle(c11) = {p4,p1,p6}; c12 = newreg; Circle(c12) = {p6,p1,p7}; // We need non-plane surfaces to define the spherical holes. Here we // use ruled surfaces, which can have 3 or 4 sides: l1 = newreg; Line Loop(l1) = {c5,c10,c4}; Ruled Surface(newreg) = {l1}; l2 = newreg; Line Loop(l2) = {c9,-c5,c1}; Ruled Surface(newreg) = {l2}; l3 = newreg; Line Loop(l3) = {c12,-c8,-c1}; Ruled Surface(newreg) = {l3}; l4 = newreg; Line Loop(l4) = {c8,-c4,c11}; Ruled Surface(newreg) = {l4}; l5 = newreg; Line Loop(l5) = {-c10,c6,c3}; Ruled Surface(newreg) = {l5}; l6 = newreg; Line Loop(l6) = {-c11,-c3,c7}; Ruled Surface(newreg) = {l6}; l7 = newreg; Line Loop(l7) = {-c2,-c7,-c12};Ruled Surface(newreg) = {l7}; l8 = newreg; Line Loop(l8) = {-c6,-c9,c2}; Ruled Surface(newreg) = {l8}; // We then store the surface loops identification numbers in list // for later reference (we will need these to define the final // volume): theloops[t] = newreg ; Surface Loop(theloops[t]) = {l8+1,l5+1,l1+1,l2+1,l3+1,l7+1,l6+1,l4+1}; thehole = newreg ; Volume(thehole) = theloops[t] ; Return // We can use a `For' loop to generate five holes in the cube: x = 0 ; y = 0.75 ; z = 0 ; r = 0.09 ; For t In {1:5} x += 0.166 ; z += 0.166 ; Call CheeseHole ; // We define a physical volume for each hole: Physical Volume (t) = thehole ; // We also print some variables on the terminal (note that, since // all variables are treated internally as floating point numbers, // the format string should only contain valid floating point format // specifiers): Printf("Hole %g (center = {%g,%g,%g}, radius = %g) has number %g!", t, x, y, z, r, thehole) ; EndFor // We can then define the surface loop for the exterior surface of the // cube: theloops[0] = newreg ; Surface Loop(theloops[0]) = {35,31,29,37,33,23,39,25,27} ; // The volume of the cube, without the 5 holes, is now defined by 6 // surface loops (the exterior surface and the five interior loops). // To reference an array of variables, its identifier is followed by // '[]': Volume(186) = {theloops[]} ; // We finally define a physical volume for the elements discretizing // the cube, without the holes (whose elements were already tagged // with numbers 1 to 5 in the `For' loop): Physical Volume (10) = 186 ;