The name is absent

18

involving the solution of partial differential equations and related problems without de-
veloping their own numerical solvers. PETSc consists a set of libraries containing rou-
tines that enable users creating vectors, matrices and distributed arrays, both sequential
and parallel, as well as libraries of linear and nonlinear numerical solvers. (PETSc han-
dles all parallel message passing communications in using MPI (Message Passing Interfer-
ence [23]) standard.) The more details and all documents about PETSc can be found at
http://www.mcs.anl.gov/petsc/petsc-as/. Since our calculations involve huge computation
of eigenvalues, we take advantage of a novel Shift-and-Invert Parallel Spectral transforma-
tion method (SIPs) [24] built on top of PETSc, which significantly improve the parallel
code performance.

3.2.2 Structure of the code

To provide a straightforward overview of the structure of the code, we put it into a flow
chart as in Fig. 3.1.

As shown in the flow chart, basically we:

1. start with the LDA results or a previously calculated states,

2. then solve the BdG equation for all the states up to the chosen energy cut-off to find
u_nι (z) and ^v∏ι (^r) using SIP module

3. generate the new states using Broyden mixing method [33] if calculation is not
converged

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