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Xavier Andrade edited Introduction.tex
over 9 years ago
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Discretizing in a real-space grids does not benefit from a direct physical connection to the system being simulated. However, the method has another advantages. In first place, a real-space discretization is, in most cases, straight-forward to perform starting from the continuum description of the electronic problem. Operations like integration are directly translated into sums overs the grid and differential operators can be discretized using finite-differences. In fact, most electronic structure codes must rely on an auxiliary real-space discretization used, for example, for the calculation of the exchange and correlation term of DFT.
Grids are flexible enough to directly simulate different kinds of systems, finite systems and fully or partially periodic. It is also
practical possible to perform simulations with reduced (or increased) dimensionality. Additionally the discretization error can be systematically and continuously controlled by adjusting the spacing between mesh points, and the
pjysical physical extension of the grid.
The simple discretization and flexibility of the real space grids makes them an ideal framework to
implement, develop and test new ideas. Of course, an additional ingredient is required. As electronic structure codes are quite complex,
developers researchers usually need to
work over an resort to existing
framework. codes to implement their developments.
We have found that the Octopus code~\cite{Marques_2003,Castro_2006} provides an ideal framework for people.