The name is absent

17

3.2.1 Implementation of the code

To implement the strategy above, we need develop an efficient parallelized eigensolver. The
entire numerical scheme we adopted is built on finite element nethod (FEM) (for spatial
discretization) and PETSc (The Portable Extensible Toolkit for Scientific Computation).

The split-step Fourier method we employed in the previous chapter belongs to the cat-
egory of pesudo-spectral method. The FEM, comparing with the spectral methods, is less
accurate but has two advantages. Firstly, the matrix equations generated by FEM are sparse
ones, which cost much less resource in practical computations. Secondly, especially in
multi-dimensional problems, it is well known that FEM can divide the entire region into
sub-domains flexibly, thus almost any degree of nonhomogeneity can be included. There-
fore it is a suitable tool for the current system we are dealing with. Historically, Hartee-
Fock-Bogoliubov (HFB) /BdG calculations have been used extensively in nuclear physics,
in which it is conventionally formulated in the configuration space by expanding the quasi-
particle states in a suitable single-particle space, most popularly, the harmonic oscillator
(HO) basis. The efficiency of this method has been testified by its successful applications
in large-scale HFB calculations, for example, even in the work investigating the polarized
Fermi gas in spherically harmonic trap we just cited [22]. However it is questionable to
use the HO basis when the system is strongly deformed, which may require to use unreal-
istically large configuration space to guarantee convergence. In this situation, we find that
the FEM is the best tool we can use to go beyond those limitation.

PETSc is a set of tools to help users write large-scale code for scientific application

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