This title appears in the Scientific Report :
2021
Please use the identifier:
http://hdl.handle.net/2128/27390 in citations.
Please use the identifier: http://dx.doi.org/10.3389/fphy.2020.618142 in citations.
Solution to the modified Helmholtz equation for arbitrary periodic charge densities
Solution to the modified Helmholtz equation for arbitrary periodic charge densities
We present a general method for solving the modified Helmholtz equation without shape approximation for an arbitrary periodic charge distribution, whose solution is known as the Yukawa potential or the screened Coulomb potential. The method is an extension of Weinert's pseudo-charge method [M....
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Personal Name(s): | Winkelmann, Miriam (Corresponding author) |
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Di Napoli, Edoardo / Wortmann, Daniel / Blügel, Stefan | |
Contributing Institute: |
Jülich Supercomputing Center; JSC Quanten-Theorie der Materialien; PGI-1 Quanten-Theorie der Materialien; IAS-1 |
Published in: | Frontiers in physics, 8 (2021) S. 618142 |
Imprint: |
Lausanne
Frontiers Media
2021
|
DOI: |
10.3389/fphy.2020.618142 |
Document Type: |
Journal Article |
Research Program: |
Simulation and Data Laboratory Quantum Materials (SDLQM) MAterials design at the eXascale. European Centre of Excellence in materials modelling, simulations, and design Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups Quantum Materials |
Link: |
OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://dx.doi.org/10.3389/fphy.2020.618142 in citations.
We present a general method for solving the modified Helmholtz equation without shape approximation for an arbitrary periodic charge distribution, whose solution is known as the Yukawa potential or the screened Coulomb potential. The method is an extension of Weinert's pseudo-charge method [M. Weinert, J. Math. Phys. 22, 2433 (1981)] for solving the Poisson equation for the same class of charge density distributions. The inherent differences between the Poisson and the modified Helmholtz equation are in their respective radial solutions. These are polynomial functions, for the Poisson equation, and modified spherical Bessel functions, for the modified Helmholtz equation. This leads to a definition of a modified pseudo-charge density and modified multipole moments. We have shown that Weinert's convergence analysis of an absolutely and uniformly convergent Fourier series of the pseudo-charge density is transferred to the modified pseudo-charge density. We conclude by illustrating the algorithmic changes necessary to turn an available implementation of the Poisson solver into a solver for the modified Helmholtz equation. |