DOI: 10.1063/1.524800. Solution of Poisson’s equation: Beyond Ewald-type methods

Solution of Poisson’s equation: Beyond Ewald-type methods

10.1063/1.524800

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

A general method for solving Poisson’s equation without shape approximation for an arbitrary periodic charge distribution is presented. The method is based on the concept of multipole potentials and the boundary value problem for a sphere. In contrast to the usual Ewald-type methods, this method has only absolutely and uniformly convergent reciprocal space sums, and treats all components of the charge density equivalently. Applications to band structure calculations and lattice summations are also discussed.

Bibliography

Weinert, M. (1981). Solution of Poissonâs equation: Beyond Ewald-type methods. Journal of Mathematical Physics, 22(11), 2433â2439.

Authors 1

M. Weinert (first)

References 23 Referenced 280

10.1103/PhysRev.153.931 / Phys. Rev. (1967)
10.1103/PhysRevB.7.3520 / Phys. Rev. B (1973)
10.1103/PhysRevB.13.5362 / Phys. Rev. B (1976)
10.1103/PhysRevB.15.4716 / Phys. Rev. B (1977)
{'key': '2024021022244480400_r2', 'first-page': '524', 'volume': '19', 'year': '1918', 'journal-title': 'Z. Phys.'} / Z. Phys. (1918)
{'key': '2024021022244480400_r3', 'first-page': '253', 'volume': '64', 'year': '1921', 'journal-title': 'Ann. Phys.'} / Ann. Phys. (1921)
10.1016/S0081-1947(08)60515-9 / Solid State Phys. (1964)
10.1016/S0031-8914(57)92124-9 / Physica (1957)
10.1016/S0031-8914(58)95803-8 / Physica (1958)
10.1016/S0031-8914(58)80132-9 / Physica (1958)
10.1103/PhysRev.117.1466 / Phys. Rev. (1960)
10.1103/PhysRev.181.1020 / Phys. Rev. (1969)
10.1016/0022-3697(58)90219-1 / J. Phys. Chem. Solids (1958)
{'key': '2024021022244480400_r9'}
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{'key': '2024021022244480400_r12'}
{'key': '2024021022244480400_r13'}
10.1103/PhysRevB.21.5601 / Phys. Rev. B (1980)
{'key': '2024021022244480400_r15', 'first-page': '1280', 'volume': '23a', 'year': '1968', 'journal-title': 'Z. Naturforsch'} / Z. Naturforsch (1968)
{'key': '2024021022244480400_r16'}
{'key': '2024021022244480400_r17'}
{'key': '2024021022244480400_r18'}

Dates

Type	When
Created	22 years, 5 months ago (March 7, 2003, 12:40 p.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 5:24 p.m.)
Indexed	1 week, 2 days ago (Aug. 19, 2025, 6:51 a.m.)
Issued	43 years, 9 months ago (Nov. 1, 1981)
Published	43 years, 9 months ago (Nov. 1, 1981)
Published Print	43 years, 9 months ago (Nov. 1, 1981)

Funders 0

None

BibTeX

@article{Weinert_1981, title={Solution of Poisson’s equation: Beyond Ewald-type methods}, volume={22}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.524800}, DOI={10.1063/1.524800}, number={11}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Weinert, M.}, year={1981}, month=nov, pages={2433–2439} }

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