The Amandus subproject of Explicit is used for working with minimal surfaces defined via the Weierstrass representation formula (another project dealing with (approximations of discrete) minimal surfaces is the Dual project, see section 8.2.7). The corresponding class Amandus adds instances variables for the Weierstrass data and an additional geometry (which is needed for the analytic continuation of functions) to its superclass Explicit, see section 7.4.6.1.
There is a large number of Amandus surfaces build into GRAPE, the corresponding description files should be located in the geometry/amandus subdirectory of the demo directory. You should also take a look at our GRAPE Minimal Surface Library at http://numod.ins.uni-bonn.de/grape/EXAMPLES/AMANDUS/amandus.html.
Implementing a new Amandus surface always requires programming, the Weierstrass functions and a function for computing the domain of the surface have to be linked to the GRAPE executable, see section 8.2.6.1.
Two different versions of the Weierstrass representation formula are available, the local version
where only the two complex functions g(z) and f(z) have to specified and the global version
where the differential dh is implicitly given by the function poly(g, dh). The derivative of this function with respect to g has to be supplied in dzpoly, supplying the derivative dwpoly of poly with respect to dh is optional but greatly speeds up the Newton method.
For a description of the construction of minimal surfaces via the Weierstrass representation formula refer to [Kar1] or [Kar2] where you can also find the Weierstrass data for most of the examples of the GRAPE Minimal Surface Library.
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