1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Efficient and accurate solver of the three-dimensional screened and unscreened Poisson's equation with generic boundary conditions
Rent:
Rent this article for
USD
10.1063/1.4755349
/content/aip/journal/jcp/137/13/10.1063/1.4755349
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/13/10.1063/1.4755349
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Accuracy of the approximation of the function e x /x with 136 Gaussians used in the solution of the screened Poisson's equation for the case of free BC. The range of the independent variable x is [10−9, 33]. We plot both the absolute and the relative error because the latter is a better indicator close to the origin (where the fitted function takes on very large values), while the former is a reliable signature of the goodness of the fit towards the opposite end. Note that at x = 33, the function e x /x is already smaller than the machine precision.

Image of FIG. 2.
FIG. 2.

Accuracy of the approximation of the Green's function with 144 Gaussians as used in the solution of the screened Poisson's equation for the case of wire-like BC. The range of the independent variable x is [10−9, 30] for the function and [10−9, 1] for log (x).

Image of FIG. 3.
FIG. 3.

Accuracy test for the case of free/isolated boundary conditions in the absence of screening (m is the order of the ISF, h the grid spacing).

Image of FIG. 4.
FIG. 4.

Accuracy test for the case of free/isolated boundary conditions in the presence of screening (m = 16 is the order of the ISF, h the grid spacing).

Image of FIG. 5.
FIG. 5.

Influence of the (cubic) simulation box size on the accuracy of the Hartree energy. L stands for the box size, whereas L ref. stands for the box size for which ρ(r = L) = 2.21 × 10−12 bohr−3.

Image of FIG. 6.
FIG. 6.

Accuracy test for the case of surface-like boundary conditions in the absence of screening (m is the order of the ISF, h the grid spacing).

Image of FIG. 7.
FIG. 7.

Accuracy test for the case of surface-like boundary conditions in the presence of screening (m = 16 is the order of the ISF, h the grid spacing).

Image of FIG. 8.
FIG. 8.

Accuracy test for the case of wire-like boundary conditions in the absence of screening (m is the order of the ISF, h the grid spacing).

Image of FIG. 9.
FIG. 9.

Accuracy test for the case of wire-like boundary conditions in the presence of screening (m = 16 is the order of the ISF, h the grid spacing).

Image of FIG. 10.
FIG. 10.

Accuracy test for the case of wire-like boundary conditions (WBC) with monopolar charge density distribution (m is the order of the ISF, h the grid spacing).

Image of FIG. 11.
FIG. 11.

Accuracy in the computation of the Hartree linear energy density—see Eq. (37)—in the case of wire-like boundary conditions (WBC) with monopolar charge density distribution (m is the order of the ISF, h the grid spacing). In our setup, .

Image of FIG. 12.
FIG. 12.

Gaussian density charge distribution (red, dashed mesh) as a function of the isolated directions (x, y in our notation) and the corresponding electrostatic potential (black, solid mesh) evaluated for different values of the screening, namely upon increasing boundary thickness. The charge density is implicitly periodic along z (wire-like BC). The amplitude of the plotted density charge distribution is multiplied by a factor 10 with respect to the actual value in order to improve the readability of the picture. Only half of the solution is drawn to highlight its profile.

Image of FIG. 13.
FIG. 13.

Electrostatic potential generated by a pair of planar charge distributions of opposite sign (positive in red/solid; negative in black/dashed) modelling a planar capacitor unlimited in the periodic directions. The piecewise planar behavior corresponds to the case with no screening (μ0 = 0), whereas the other solutions are obtained with upon increasing the boundary thickness. The potential is more and more localized around the capacitor's plates and falls rapidly to zero as μ0 is increased. Each curve is normalised to one to improve readability.

Image of FIG. 14.
FIG. 14.

Electrostatic potential generated by a cylindrical capacitor, periodic in the vertical direction. The different solutions correspond to upon increasing the boundary thickness. Each curve is normalised to one for sake of readability. Only half of the solution is drawn so as to highlight the potential profile.

Loading

Article metrics loading...

/content/aip/journal/jcp/137/13/10.1063/1.4755349
2012-10-04
2014-04-18
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Efficient and accurate solver of the three-dimensional screened and unscreened Poisson's equation with generic boundary conditions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/13/10.1063/1.4755349
10.1063/1.4755349
SEARCH_EXPAND_ITEM