Surface Evolver Documentation

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This is a collection helpful hints gained from my own experience with Evolver and from helping others.

Checking your datafile

You should always check your initial datafile to be sure it is doing exactly what you want. It is easy to get signs on integrands wrong, or apply quantities to the wrong elements. When you load the initial datafile, the initial energy, body volumes, and quantities values should be exactly what you expect, either from hand calculation or from another datafile you trust. In particular, when using constraint integrals to replace omitted facets, I suggest you make a separate datafile with facets instead of integrals just for checking the agreement between the two.

With the named methods and quantities feature, it is possible to get very detailed information on where numbers are coming from. If you give the "convert_to_quantities" command, every energy, volume, and constraint integrand will be internally converted to named methods and quantities (although the user interface for all remains the same). These internal quantities are ordinarily not displayed by the 'v' or 'Q' commands, but if you do "show_all_quantities" then they will be displayed. Further, 'Q' will show all the component method instances also. For an example, consider the following output:

 Enter command: convert_to_quantities
 Enter command: show_all_quantities
 Enter command: Q
Quantities and instances:
(showing internal quantities also; to suppress, do "show_all_quantities off")
 1. default_length                        64.2842712474619  info_only quantity
                            modulus       1.00000000000000
 2. default_area                          4.00000000000000  energy quantity
                            modulus       1.00000000000000
 3. constraint_1_energy                 -0.342020143325669  energy quantity
                            modulus       1.00000000000000
 4. constraint_2_energy                 -0.342020143325669  energy quantity
                            modulus       1.00000000000000
 5. body_1_vol                            1.00000000000000  fixed quantity
                             target       1.00000000000000
                            modulus       1.00000000000000
    body_1_vol_meth                      0.000000000000000  method instance
                            modulus       1.00000000000000
    body_1_con_2_meth                     1.00000000000000  method instance
                            modulus       1.00000000000000
 6. gravity_quant                        0.000000000000000  energy quantity
                            modulus      0.000000000000000
Here's a detailed explanation of the output of the Q command above:

default_length - total edge length, using the edge_length method. This would be the default energy in the string model, and I guess it really doesn't need to exist here. But it's an info_only quantity, which means it is only evaluated when somebody asks to know its value.

default_area - the default energy in the soapfilm model, and included in the energy here, as indicated by "energy quantity" at the right.

constraint_1_energy - the energy integral of constraint 1, using the edge_vector_integral method applied to all edges on constraint 1.

constraint_2_energy - the energy integral of constraint 2, using the edge_vector_integral method applied to all edges on constraint 2.

body_1_vol - the volume of body 1, as a sum of several method instances. body_1_vol_meth is the facet_vector_integral of (0,0,z) over all the facets on the body. body_con_2_meth is the integral of the constraint 2 content integrand over all edges on facets of body 1 which are edges on constraint 2.

gravity_quant - the total gravitational energy of all bodies with assigned densities. This quantity is always present even if you don't have any bodies, or don't have any body densities. But you'll notice the modulus is 0, which means its evaluation is skipped, so the presence of this quantity doesn't harm anything.

You can find the quantity or method contribution of single elements by using the quantity or method name as an attribute of elements. Using a quantity name really means summing over all its constituent methods that apply to the element. For example, in plates_column,

 Enter command: foreach edge ee where on_constraint 2 do printf "%d  %f\n",id, ee.body_1_con_2_meth
5  0.000000
6  0.000000
7  1.000000
8  0.000000
Enter command: foreach edge where constraint_1_energy != 0 do print constraint_1_energy

Reasonable scale factors.

Trouble in evolving is usually signaled by a small scale, which means there is some obstacle to evolution. Of course, that means you have to know what a reasonable scale is, and that depends on the type of energy you are using and how refined your surface si. In normal evolution, the size of the scale is set by the development of small-scale roughness in the surface. Combined with a little dimensional analysis, that leads to the conclusion that the scale should vary as L2-q, where L is the typical edge length and the units of energy are lengthq. The dimensional analysis goes like this: Let D be the perturbation of one vertex away from an equilibrium surface. In general, energy is quadratic around an equibrium, so
   E = D2Lq-2
So the gradient of energy at the vertex is
    grad E = 2D Lq-2
The motion is the scale times the gradient, which we want proportional to D, so
    scale * grad E = scale * 2 D Lq-2 = D  
So scale is on the order of L 2-q. Some examples:
Dimensional Dependence of Scale
EnergyEnergy dimension Scale Example file
Area of soapfilm L2 L0 quad.fe
Length of string L1 L1 flower.fe
Squared curvature of string L-1 L3 elastic8.fe
Squared mean curvature of soapfilm L0 L2 sqcube.fe
In particular, the scale for area evolution is independent of refinement, but for most other energies the scale decreases with refinement.

Another common influence on the scale for area evolution is the surface tension. Doing a liquid solder simulation in a system of units where the surface tension of facets is assigned a value 470, say, means that all calculated gradients are multiplied by 470, so the scale decreases by a factor of 470 to get the same geometric motion. Thus you should set scale_limit to be the inverse of the surface tension.

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