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// catman.fe
// Evolver datafile for catenoid with parameters as in Manual tutorial.
PARAMETER radius = 1 // ring radius; runtime adjustable
PARAMETER height = 0.55 // ring height; runtime adjustable
boundary 1 parameters 1 // upper ring; p1 is ring parameter
x1: radius * cos(p1)
x2: radius * sin(p1)
x3: height
boundary 2 parameters 1 // lower ring
x1: radius * cos(p1)
x2: radius * sin(p1)
x3: -height
vertices /* given by parameter value on a boundary */
1 0*pi/3 boundary 1 fixed
2 1*pi/3 boundary 1 fixed
3 2*pi/3 boundary 1 fixed
4 3*pi/3 boundary 1 fixed
5 4*pi/3 boundary 1 fixed
6 5*pi/3 boundary 1 fixed
7 0*pi/3 boundary 2 fixed
8 1*pi/3 boundary 2 fixed
9 2*pi/3 boundary 2 fixed
10 3*pi/3 boundary 2 fixed
11 4*pi/3 boundary 2 fixed
12 5*pi/3 boundary 2 fixed
edges /* given by endpoint vertices */
1 1 2 boundary 1 fixed
2 2 3 boundary 1 fixed
3 3 4 boundary 1 fixed
4 4 5 boundary 1 fixed
5 5 6 boundary 1 fixed
6 6 1 boundary 1 fixed
7 7 8 boundary 2 fixed
8 8 9 boundary 2 fixed
9 9 10 boundary 2 fixed
10 10 11 boundary 2 fixed
11 11 12 boundary 2 fixed
12 12 7 boundary 2 fixed
13 1 7
14 2 8
15 3 9
16 4 10
17 5 11
18 6 12
faces /* given by oriented edge list */
1 1 14 -7 -13
2 2 15 -8 -14
3 3 16 -9 -15
4 4 17 -10 -16
5 5 18 -11 -17
6 6 13 -12 -18
read
// Demonstrating saddle point due to triangulation arrangement.
// First setting parameters to stable values.
gogo := { g; u; r; g 50; // at this point have nearly a saddle point
g 200; // triangulation twists around to lower energy
}
// Faster version of the above using conjugate gradient
gogo2 := { g; u; r; U; g 25; // at this point have nearly a saddle point
g 35;
}
// High accuracy evolution, using higher-order Lagrange elements.
gogo3 := { u; rmax := cosh(height); recalc;
r; g 5; hessian;
r; g 5; hessian;
lagrange 2; g 5; hessian;
lagrange 4; g 5; hessian;
lagrange 6; g 5; hessian;
lagrange 8; g 5; hessian;
true_area := 2*pi*(height + 0.5*sinh(2*height));
printf"Difference from true area: %g\n",total_area - true_area;
}
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