RAtom Files

RAtom
Author: Zbigniew Romanowski
e-mail: romz@wp.pl
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RAtom solves nonlinear Kohn-Sham equation for an neutral atom.
The adaptive algorithm based on finite element method (FEM) is implemented.

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The implemented algorithm is described in the following papers:

1. Z. Romanowski, Adaptive solver of a Kohn-Sham equation for an atom
   Modelling Simul. Mater. Sci. Eng. vol. 17, 045001 (2009)
   
2. Z. Romanowski: Application of h-adaptive, high order finite 
   element method to solve radial Schrödinger equation,
   Molecular Physics, vol. 107, pp. 1339-1348  (2009).

3. Z. Romanowski, A B-spline finite element solution of Kohn Sham equation for an atom
   Modelling and Simulation in Materials Science and Engineering, vol. 16, p. 015003 (2008)
   http://iopscience.iop.org/article/10.1088/0965-0393/16/1/015003/meta (abstract)

4. Z. Romanowski, Numerical Solution of Kohn–Sham Equation for Atom,
   Acta Physica Polonica B, vol. 38, p. 3263 (2007)
   http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=38&page=3263 (full paper)
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1. RAtom is the solver for non-linear Kohn-Sham equation, which is
   non-linear differential, second order, eigenvalue problem.

2. This class is the wrapper for all required resources.

3. RAtom solves linear Kohn-Sham equation by Finite Element Method (FEM)
   with Lobatto polynomials as basis functions.

4. RAtom solves the non-linear Kohn-Sham equation iteratively
   by so called Self Consistent Field (SCF) procedure.

5. In order to calculate interaction potential in linear Kohn-Sham equation,
   Poisson equation is solved.

6. The Poisson equation is the differential, second order, equation.
   RAtom solves Poisson equation by Finite Element Method (FEM) with
   Lobatto polynomials as the basis functions.

7. For Poisson equation and Kohn-Sham equation, the electron density is needed.
   The electron density is represented (approximated), as the linear
   combination of Lobatto polynomials.

8. The distinguished feature of RAtom is the implemented h-adaptive procedure.
   The following problems are solved adaptively:
      a) Linear Kohn-Sham equation
      b) Poisson equation
      c) Approximation of electron density

9. The disctretization of linear Kohn-Sham equation leads to the generalized eigenvalue problem,
   which is solved by procedures from LAPACK libraries.


10. High order Gauss quadratures are applied in order to obtain 
    the total energy of atom with absolute accuracy of 1E-6 hartree.

11. The program RAtom is implemented in C++, it runs as a single thread. 


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In order to compile RAtom, type 'make' in the main directory.
First, the LAPACK library is compiled. It requires gfortran compiler.
Second, RAtom is compiled and it is compiled with g++ compiler.

After compilation the binary file ratom.x is stored in ./bin directory.
Program ratom.x requires one input parameter, which is a path to file
with keywords. The format of input file for ratom.x is very simple, and can be
figure out by checking the examples located in exm directory.

In order to check the functionality of RAtom program go to ./exm directory.
There are 92 sub-directories. Each of the sub-directory
contains an input file named "atom.inp" for the atoms from Hydrogen to Uranium.
Additionally, each atom-specific directory contains referential solution stored in
"solution.dat.ref". 
In order to run all prepared examples (tests), go to ./exm directory and type ./run.
Obtained solutions (i.e. total energies and eigenvalues) are listed
in the file solution.dat in each sub-directory and compared to the referential data.


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Directory ./src contains the source code of RAtom plus Makefile. 
It is recommended to start reading the program RAtom
from "src/main.cpp" file.


Kind regards,
Zbigniew Romanowski
romz@wp.pl

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