The folder code/geometry/v6 contains files that create the original geometry. The initial design needs to be input by hand using the NURBS package. It contains functions to create a number of primitive geometric objects; the simplest design flow for 2D geometries starts by describing the outline of the geometry using a number of NURBS curves (e.g. using nrbline or nrbcirc), then divides the relevant part of the geometry into patches bounded by 4 NURBS curves each, and finally creates the necessary NURBS surfaces via nrbcoons or nrbruled. Also 3D geometries may be created using, in particular, nrbextrude, nrbrevolve or nrbruled.
In a last step the geometry needs to be exported to a (text) file format compatible with GeoPDEs. An example for this process is given in write_geometryfile_v6.
The folder code/geometry/optimization contains files to create and handle the deformed geometry during optimization. The function compute_bounds finds the constraints on the control points of the original geometry. The function create_nrb_opt_electrode finds and outputs the NURBS curve that describes the initial shape for the optimization, subject to the least squares fit that is performed in nlopt_fit. The function create_geometry_opt computes and writes the optimized geometry to a file, such that further analyses can be performed (e.g. evaluating the objective functions during the optimization).
We use the GeoPDEs framework to compute the electrostatic field in an axisymmetric setting. The folder code/setup contains files that describe the problem in an abstract sense, e.g. boundary conditions, material parameters, basis function degrees and so on.
The functions that solve the problem are collected in code/iga. Calling the function mp_solve_electrostatics_axi2d allows to solve 2D axisymmetric electrostatic problems as defined using setup_problem from the code/setup folder.
All functions in code/iga are based on the GeoPDEs package and make use of other functionality provided by it. If other problem types (e.g. magnetostatics) are of interest, GeoPDEs also provides a framework for solving them, thus the implementation is not problem dependent in that sense.
Aside from the constraints on the control points, we also consider a volume constraint that is handled by the functions in code/volume-constraint. The decisive function is volume_constraint which returns the value of the constraint in a way compatible with our optimization package of choice NLopt.
A second folder (code/cost-function) contains everything needed to specify and evaluate the objective function, again in a way compatible with NLopt. The key function is cost_function_abs_max as this is the one used for the shape optimization.
The actual optimization is carried out by the script nlopt_main which calls the interface of the package with the previously described constraints and objective function.
To visualize the (optimized) geometry, the boundary conditions and solution of the electric field problem, as well as some quantities related to the particle tracking, a number of plotting functions are collected in code/plot. Examples for some of them are provided in the overview_main script.
In order to save results or prepare them for plotting with pgfplots a number of file writing functions are collected in code/write. The folder also includes the functions necessary to generate the input files for interfacing with the particle tracking software ASTRA. All results are collected in the folder code/results.
The folder code/astra contains the script astra_main, which calls the interface to ASTRA. In order for the script to find all the necessary files, they need to be moved from the respective subfolders of code/results to the main folder code. The program files for ASTRA also need to be placed in the main folder code.
The folder igs contains the geometry files for the different components in IGES format.