---
_id: '60298'
abstract:
- lang: eng
text: In this work, we introduce PHOENIX, a highly optimized explicit open-source
solver for two-dimensional nonlinear Schrödinger equations with extensions. The
nonlinear Schrödinger equation and its extensions (Gross-Pitaevskii equation)
are widely studied to model and analyze complex phenomena in fields such as optics,
condensed matter physics, fluid dynamics, and plasma physics. It serves as a powerful
tool for understanding nonlinear wave dynamics, soliton formation, and the interplay
between nonlinearity, dispersion, and diffraction. By extending the nonlinear
Schrödinger equation, various physical effects such as non-Hermiticity, spin-orbit
interaction, and quantum optical aspects can be incorporated. PHOENIX is designed
to accommodate a wide range of applications by a straightforward extendability
without the need for user knowledge of computing architectures or performance
optimization. The high performance and power efficiency of PHOENIX are demonstrated
on a wide range of entry-class to high-end consumer and high-performance computing
GPUs and CPUs. Compared to a more conventional MATLAB implementation, a speedup
of up to three orders of magnitude and energy savings of up to 99.8% are achieved.
The performance is compared to a performance model showing that PHOENIX performs
close to the relevant performance bounds in many situations. The possibilities
of PHOENIX are demonstrated with a range of practical examples from the realm
of nonlinear (quantum) photonics in planar microresonators with active media including
exciton-polariton condensates. Examples range from solutions on very large grids,
the use of local optimization algorithms, to Monte Carlo ensemble evolutions with
quantum noise enabling the tomography of the system's quantum state.
article_number: '109689'
article_type: original
author:
- first_name: Jan
full_name: Wingenbach, Jan
id: '69187'
last_name: Wingenbach
- first_name: David
full_name: Bauch, David
id: '44172'
last_name: Bauch
- first_name: Xuekai
full_name: Ma, Xuekai
id: '59416'
last_name: Ma
- first_name: Robert
full_name: Schade, Robert
id: '75963'
last_name: Schade
orcid: 0000-0002-6268-5397
- first_name: Christian
full_name: Plessl, Christian
id: '16153'
last_name: Plessl
orcid: 0000-0001-5728-9982
- first_name: Stefan
full_name: Schumacher, Stefan
id: '27271'
last_name: Schumacher
orcid: 0000-0003-4042-4951
citation:
ama: Wingenbach J, Bauch D, Ma X, Schade R, Plessl C, Schumacher S. PHOENIX – Paderborn
highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger
equations with integrated extensions. Computer Physics Communications.
2025;315. doi:10.1016/j.cpc.2025.109689
apa: Wingenbach, J., Bauch, D., Ma, X., Schade, R., Plessl, C., & Schumacher,
S. (2025). PHOENIX – Paderborn highly optimized and energy efficient solver for
two-dimensional nonlinear Schrödinger equations with integrated extensions. Computer
Physics Communications, 315, Article 109689. https://doi.org/10.1016/j.cpc.2025.109689
bibtex: '@article{Wingenbach_Bauch_Ma_Schade_Plessl_Schumacher_2025, title={PHOENIX
– Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear
Schrödinger equations with integrated extensions}, volume={315}, DOI={10.1016/j.cpc.2025.109689},
number={109689}, journal={Computer Physics Communications}, publisher={Elsevier
BV}, author={Wingenbach, Jan and Bauch, David and Ma, Xuekai and Schade, Robert
and Plessl, Christian and Schumacher, Stefan}, year={2025} }'
chicago: Wingenbach, Jan, David Bauch, Xuekai Ma, Robert Schade, Christian Plessl,
and Stefan Schumacher. “PHOENIX – Paderborn Highly Optimized and Energy Efficient
Solver for Two-Dimensional Nonlinear Schrödinger Equations with Integrated Extensions.”
Computer Physics Communications 315 (2025). https://doi.org/10.1016/j.cpc.2025.109689.
ieee: 'J. Wingenbach, D. Bauch, X. Ma, R. Schade, C. Plessl, and S. Schumacher,
“PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional
nonlinear Schrödinger equations with integrated extensions,” Computer Physics
Communications, vol. 315, Art. no. 109689, 2025, doi: 10.1016/j.cpc.2025.109689.'
mla: Wingenbach, Jan, et al. “PHOENIX – Paderborn Highly Optimized and Energy Efficient
Solver for Two-Dimensional Nonlinear Schrödinger Equations with Integrated Extensions.”
Computer Physics Communications, vol. 315, 109689, Elsevier BV, 2025, doi:10.1016/j.cpc.2025.109689.
short: J. Wingenbach, D. Bauch, X. Ma, R. Schade, C. Plessl, S. Schumacher, Computer
Physics Communications 315 (2025).
date_created: 2025-06-23T07:38:52Z
date_updated: 2025-06-29T12:00:36Z
department:
- _id: '27'
doi: 10.1016/j.cpc.2025.109689
intvolume: ' 315'
language:
- iso: eng
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Computer Physics Communications
publication_identifier:
issn:
- 0010-4655
publication_status: published
publisher: Elsevier BV
status: public
title: PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional
nonlinear Schrödinger equations with integrated extensions
type: journal_article
user_id: '75963'
volume: 315
year: '2025'
...
---
_id: '23597'
author:
- first_name: Venkat
full_name: Kapil, Venkat
last_name: Kapil
- first_name: Mariana
full_name: Rossi, Mariana
last_name: Rossi
- first_name: Ondrej
full_name: Marsalek, Ondrej
last_name: Marsalek
- first_name: Riccardo
full_name: Petraglia, Riccardo
last_name: Petraglia
- first_name: Yair
full_name: Litman, Yair
last_name: Litman
- first_name: Thomas
full_name: Spura, Thomas
last_name: Spura
- first_name: Bingqing
full_name: Cheng, Bingqing
last_name: Cheng
- first_name: Alice
full_name: Cuzzocrea, Alice
last_name: Cuzzocrea
- first_name: Robert H.
full_name: Meißner, Robert H.
last_name: Meißner
- first_name: David M.
full_name: Wilkins, David M.
last_name: Wilkins
- first_name: Benjamin A.
full_name: Helfrecht, Benjamin A.
last_name: Helfrecht
- first_name: Przemysław
full_name: Juda, Przemysław
last_name: Juda
- first_name: Sébastien P.
full_name: Bienvenue, Sébastien P.
last_name: Bienvenue
- first_name: Wei
full_name: Fang, Wei
last_name: Fang
- first_name: Jan
full_name: Kessler, Jan
last_name: Kessler
- first_name: Igor
full_name: Poltavsky, Igor
last_name: Poltavsky
- first_name: Steven
full_name: Vandenbrande, Steven
last_name: Vandenbrande
- first_name: Jelle
full_name: Wieme, Jelle
last_name: Wieme
- first_name: Clemence
full_name: Corminboeuf, Clemence
last_name: Corminboeuf
- first_name: Thomas D.
full_name: Kühne, Thomas D.
last_name: Kühne
- first_name: David E.
full_name: Manolopoulos, David E.
last_name: Manolopoulos
- first_name: Thomas E.
full_name: Markland, Thomas E.
last_name: Markland
- first_name: Jeremy O.
full_name: Richardson, Jeremy O.
last_name: Richardson
- first_name: Alexandre
full_name: Tkatchenko, Alexandre
last_name: Tkatchenko
- first_name: Gareth A.
full_name: Tribello, Gareth A.
last_name: Tribello
- first_name: Veronique
full_name: Van Speybroeck, Veronique
last_name: Van Speybroeck
- first_name: Michele
full_name: Ceriotti, Michele
last_name: Ceriotti
citation:
ama: 'Kapil V, Rossi M, Marsalek O, et al. i-PI 2.0: A universal force engine for
advanced molecular simulations. Computer Physics Communications. 2018:214-223.
doi:10.1016/j.cpc.2018.09.020'
apa: 'Kapil, V., Rossi, M., Marsalek, O., Petraglia, R., Litman, Y., Spura, T.,
… Ceriotti, M. (2018). i-PI 2.0: A universal force engine for advanced molecular
simulations. Computer Physics Communications, 214–223. https://doi.org/10.1016/j.cpc.2018.09.020'
bibtex: '@article{Kapil_Rossi_Marsalek_Petraglia_Litman_Spura_Cheng_Cuzzocrea_Meißner_Wilkins_et
al._2018, title={i-PI 2.0: A universal force engine for advanced molecular simulations},
DOI={10.1016/j.cpc.2018.09.020},
journal={Computer Physics Communications}, author={Kapil, Venkat and Rossi, Mariana
and Marsalek, Ondrej and Petraglia, Riccardo and Litman, Yair and Spura, Thomas
and Cheng, Bingqing and Cuzzocrea, Alice and Meißner, Robert H. and Wilkins, David
M. and et al.}, year={2018}, pages={214–223} }'
chicago: 'Kapil, Venkat, Mariana Rossi, Ondrej Marsalek, Riccardo Petraglia, Yair
Litman, Thomas Spura, Bingqing Cheng, et al. “I-PI 2.0: A Universal Force Engine
for Advanced Molecular Simulations.” Computer Physics Communications, 2018,
214–23. https://doi.org/10.1016/j.cpc.2018.09.020.'
ieee: 'V. Kapil et al., “i-PI 2.0: A universal force engine for advanced
molecular simulations,” Computer Physics Communications, pp. 214–223, 2018.'
mla: 'Kapil, Venkat, et al. “I-PI 2.0: A Universal Force Engine for Advanced Molecular
Simulations.” Computer Physics Communications, 2018, pp. 214–23, doi:10.1016/j.cpc.2018.09.020.'
short: V. Kapil, M. Rossi, O. Marsalek, R. Petraglia, Y. Litman, T. Spura, B. Cheng,
A. Cuzzocrea, R.H. Meißner, D.M. Wilkins, B.A. Helfrecht, P. Juda, S.P. Bienvenue,
W. Fang, J. Kessler, I. Poltavsky, S. Vandenbrande, J. Wieme, C. Corminboeuf,
T.D. Kühne, D.E. Manolopoulos, T.E. Markland, J.O. Richardson, A. Tkatchenko,
G.A. Tribello, V. Van Speybroeck, M. Ceriotti, Computer Physics Communications
(2018) 214–223.
date_created: 2021-09-01T09:03:51Z
date_updated: 2022-01-06T06:55:57Z
doi: 10.1016/j.cpc.2018.09.020
language:
- iso: eng
page: 214-223
publication: Computer Physics Communications
publication_identifier:
issn:
- 0010-4655
publication_status: published
status: public
title: 'i-PI 2.0: A universal force engine for advanced molecular simulations'
type: journal_article
user_id: '65425'
year: '2018'
...
---
_id: '13276'
author:
- first_name: Gábor
full_name: Rutkai, Gábor
last_name: Rutkai
- first_name: Andreas
full_name: Köster, Andreas
last_name: Köster
- first_name: Gabriela
full_name: Guevara-Carrion, Gabriela
last_name: Guevara-Carrion
- first_name: Tatjana
full_name: Janzen, Tatjana
last_name: Janzen
- first_name: Michael
full_name: Schappals, Michael
last_name: Schappals
- first_name: Colin W.
full_name: Glass, Colin W.
last_name: Glass
- first_name: Martin
full_name: Bernreuther, Martin
last_name: Bernreuther
- first_name: Amer
full_name: Wafai, Amer
last_name: Wafai
- first_name: Simon
full_name: Stephan, Simon
last_name: Stephan
- first_name: Maximilian
full_name: Kohns, Maximilian
last_name: Kohns
- first_name: Steffen
full_name: Reiser, Steffen
last_name: Reiser
- first_name: Stephan
full_name: Deublein, Stephan
last_name: Deublein
- first_name: Martin
full_name: Horsch, Martin
last_name: Horsch
- first_name: Hans
full_name: Hasse, Hans
last_name: Hasse
- first_name: Jadran
full_name: Vrabec, Jadran
last_name: Vrabec
citation:
ama: 'Rutkai G, Köster A, Guevara-Carrion G, et al. ms2: A Molecular Simulation
Tool for Thermodynamic Properties, Release 3.0. Computer Physics Communications.
2017;221:343-351. doi:10.1016/j.cpc.2017.07.025'
apa: 'Rutkai, G., Köster, A., Guevara-Carrion, G., Janzen, T., Schappals, M., Glass,
C. W., … Vrabec, J. (2017). ms2: A Molecular Simulation Tool for Thermodynamic
Properties, Release 3.0. Computer Physics Communications, 221, 343–351.
https://doi.org/10.1016/j.cpc.2017.07.025'
bibtex: '@article{Rutkai_Köster_Guevara-Carrion_Janzen_Schappals_Glass_Bernreuther_Wafai_Stephan_Kohns_et
al._2017, title={ms2: A Molecular Simulation Tool for Thermodynamic Properties,
Release 3.0}, volume={221}, DOI={10.1016/j.cpc.2017.07.025},
journal={Computer Physics Communications}, author={Rutkai, Gábor and Köster, Andreas
and Guevara-Carrion, Gabriela and Janzen, Tatjana and Schappals, Michael and Glass,
Colin W. and Bernreuther, Martin and Wafai, Amer and Stephan, Simon and Kohns,
Maximilian and et al.}, year={2017}, pages={343–351} }'
chicago: 'Rutkai, Gábor, Andreas Köster, Gabriela Guevara-Carrion, Tatjana Janzen,
Michael Schappals, Colin W. Glass, Martin Bernreuther, et al. “Ms2: A Molecular
Simulation Tool for Thermodynamic Properties, Release 3.0.” Computer Physics
Communications 221 (2017): 343–51. https://doi.org/10.1016/j.cpc.2017.07.025.'
ieee: 'G. Rutkai et al., “ms2: A Molecular Simulation Tool for Thermodynamic
Properties, Release 3.0,” Computer Physics Communications, vol. 221, pp.
343–351, 2017.'
mla: 'Rutkai, Gábor, et al. “Ms2: A Molecular Simulation Tool for Thermodynamic
Properties, Release 3.0.” Computer Physics Communications, vol. 221, 2017,
pp. 343–51, doi:10.1016/j.cpc.2017.07.025.'
short: G. Rutkai, A. Köster, G. Guevara-Carrion, T. Janzen, M. Schappals, C.W. Glass,
M. Bernreuther, A. Wafai, S. Stephan, M. Kohns, S. Reiser, S. Deublein, M. Horsch,
H. Hasse, J. Vrabec, Computer Physics Communications 221 (2017) 343–351.
date_created: 2019-09-18T08:50:35Z
date_updated: 2022-01-06T06:51:31Z
doi: 10.1016/j.cpc.2017.07.025
intvolume: ' 221'
language:
- iso: eng
page: 343-351
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Computer Physics Communications
publication_identifier:
issn:
- 0010-4655
publication_status: published
status: public
title: 'ms2: A Molecular Simulation Tool for Thermodynamic Properties, Release 3.0'
type: journal_article
user_id: '40778'
volume: 221
year: '2017'
...
---
_id: '18636'
abstract:
- lang: eng
text: We derive formulas for the Coulomb matrix within the full-potential linearized
augmented-plane-wave (FLAPW) method. The Coulomb matrix is a central ingredient
in implementations of many-body perturbation theory, such as the Hartree–Fock
and GW approximations for the electronic self-energy or the random-phase approximation
for the dielectric function. It is represented in the mixed product basis, which
combines numerical muffin-tin functions and interstitial plane waves constructed
from products of FLAPW basis functions. The interstitial plane waves are here
expanded with the Rayleigh formula. The resulting algorithm is very efficient
in terms of both computational cost and accuracy and is superior to an implementation
with the Fourier transform of the step function. In order to allow an analytic
treatment of the divergence at k=0 in reciprocal space, we expand the Coulomb
matrix analytically around this point without resorting to a projection onto plane
waves. Without additional approximations, we then apply a basis transformation
that diagonalizes the Coulomb matrix and confines the divergence to a single eigenvalue.
At the same time, response matrices like the dielectric function separate into
head, wings, and body with the same mathematical properties as in a plane-wave
basis. As an illustration we apply the formulas to electron-energy-loss spectra
(EELS) for nickel at different k vectors including k=0. The convergence of the
spectra towards the result at k=0 is clearly seen. Our all-electron treatment
also allows to include transitions from 3s and 3p core states in the EELS spectrum
that give rise to a shallow peak at high energies and lead to good agreement with
experiment.
article_type: original
author:
- first_name: Christoph
full_name: Friedrich, Christoph
last_name: Friedrich
- first_name: Arno
full_name: Schindlmayr, Arno
id: '458'
last_name: Schindlmayr
orcid: 0000-0002-4855-071X
- first_name: Stefan
full_name: Blügel, Stefan
last_name: Blügel
citation:
ama: Friedrich C, Schindlmayr A, Blügel S. Efficient calculation of the Coulomb
matrix and its expansion around k=0 within the FLAPW method. Computer Physics
Communications. 2009;180(3):347-359. doi:10.1016/j.cpc.2008.10.009
apa: Friedrich, C., Schindlmayr, A., & Blügel, S. (2009). Efficient calculation
of the Coulomb matrix and its expansion around k=0 within the FLAPW method. Computer
Physics Communications, 180(3), 347–359. https://doi.org/10.1016/j.cpc.2008.10.009
bibtex: '@article{Friedrich_Schindlmayr_Blügel_2009, title={Efficient calculation
of the Coulomb matrix and its expansion around k=0 within the FLAPW method}, volume={180},
DOI={10.1016/j.cpc.2008.10.009},
number={3}, journal={Computer Physics Communications}, publisher={Elsevier}, author={Friedrich,
Christoph and Schindlmayr, Arno and Blügel, Stefan}, year={2009}, pages={347–359}
}'
chicago: 'Friedrich, Christoph, Arno Schindlmayr, and Stefan Blügel. “Efficient
Calculation of the Coulomb Matrix and Its Expansion around K=0 within the FLAPW
Method.” Computer Physics Communications 180, no. 3 (2009): 347–59. https://doi.org/10.1016/j.cpc.2008.10.009.'
ieee: 'C. Friedrich, A. Schindlmayr, and S. Blügel, “Efficient calculation of the
Coulomb matrix and its expansion around k=0 within the FLAPW method,” Computer
Physics Communications, vol. 180, no. 3, pp. 347–359, 2009, doi: 10.1016/j.cpc.2008.10.009.'
mla: Friedrich, Christoph, et al. “Efficient Calculation of the Coulomb Matrix and
Its Expansion around K=0 within the FLAPW Method.” Computer Physics Communications,
vol. 180, no. 3, Elsevier, 2009, pp. 347–59, doi:10.1016/j.cpc.2008.10.009.
short: C. Friedrich, A. Schindlmayr, S. Blügel, Computer Physics Communications
180 (2009) 347–359.
date_created: 2020-08-28T22:50:49Z
date_updated: 2025-12-16T11:10:22Z
ddc:
- '530'
department:
- _id: '296'
- _id: '35'
- _id: '15'
- _id: '170'
- _id: '230'
doi: 10.1016/j.cpc.2008.10.009
external_id:
arxiv:
- '0811.2363'
isi:
- '000264735800002'
file:
- access_level: closed
content_type: application/pdf
creator: schindlm
date_created: 2020-10-05T10:35:14Z
date_updated: 2020-10-05T10:41:07Z
description: © 2008 Elsevier B.V.
file_id: '19875'
file_name: 1-s2.0-S0010465508003664-main.pdf
file_size: 311274
relation: main_file
title: Efficient calculation of the Coulomb matrix and its expansion around k=0
within the FLAPW method
file_date_updated: 2020-10-05T10:41:07Z
has_accepted_license: '1'
intvolume: ' 180'
isi: '1'
issue: '3'
language:
- iso: eng
page: 347-359
publication: Computer Physics Communications
publication_identifier:
issn:
- 0010-4655
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Efficient calculation of the Coulomb matrix and its expansion around k=0 within
the FLAPW method
type: journal_article
user_id: '16199'
volume: 180
year: '2009'
...
---
_id: '18595'
abstract:
- lang: eng
text: Excited-state calculations, notably for quasiparticle band structures, are
nowadays routinely performed within the GW approximation for the electronic self-energy.
Nevertheless, certain numerical approximations and simplifications are still employed
in practice to make the computations feasible. An important aspect for periodic
systems is the proper treatment of the singularity of the screened Coulomb interaction
in reciprocal space, which results from the slow 1/r decay in real space. This
must be done without introducing artificial interactions between the quasiparticles
and their periodic images in repeated cells, which occur when integrals of the
screened Coulomb interaction are discretised in reciprocal space. An adequate
treatment of both aspects is crucial for a numerically stable computation of the
self-energy. In this article we build on existing schemes for isotropic screening
and present an extension for anisotropic systems. We also show how the contributions
to the dielectric function arising from the non-local part of the pseudopotentials
can be computed efficiently. These improvements are crucial for obtaining a fast
convergence with respect to the number of points used for the Brillouin zone integration
and prove to be essential to make GW calculations for strongly anisotropic systems,
such as slabs or multilayers, efficient.
article_type: original
author:
- first_name: Christoph
full_name: Freysoldt, Christoph
last_name: Freysoldt
- first_name: Philipp
full_name: Eggert, Philipp
last_name: Eggert
- first_name: Patrick
full_name: Rinke, Patrick
last_name: Rinke
- first_name: Arno
full_name: Schindlmayr, Arno
id: '458'
last_name: Schindlmayr
orcid: 0000-0002-4855-071X
- first_name: Rex W.
full_name: Godby, Rex W.
last_name: Godby
- first_name: Matthias
full_name: Scheffler, Matthias
last_name: Scheffler
citation:
ama: Freysoldt C, Eggert P, Rinke P, Schindlmayr A, Godby RW, Scheffler M. Dielectric
anisotropy in the GW space–time method. Computer Physics Communications.
2007;176(1):1-13. doi:10.1016/j.cpc.2006.07.018
apa: Freysoldt, C., Eggert, P., Rinke, P., Schindlmayr, A., Godby, R. W., &
Scheffler, M. (2007). Dielectric anisotropy in the GW space–time method. Computer
Physics Communications, 176(1), 1–13. https://doi.org/10.1016/j.cpc.2006.07.018
bibtex: '@article{Freysoldt_Eggert_Rinke_Schindlmayr_Godby_Scheffler_2007, title={Dielectric
anisotropy in the GW space–time method}, volume={176}, DOI={10.1016/j.cpc.2006.07.018},
number={1}, journal={Computer Physics Communications}, publisher={Elsevier}, author={Freysoldt,
Christoph and Eggert, Philipp and Rinke, Patrick and Schindlmayr, Arno and Godby,
Rex W. and Scheffler, Matthias}, year={2007}, pages={1–13} }'
chicago: 'Freysoldt, Christoph, Philipp Eggert, Patrick Rinke, Arno Schindlmayr,
Rex W. Godby, and Matthias Scheffler. “Dielectric Anisotropy in the GW Space–Time
Method.” Computer Physics Communications 176, no. 1 (2007): 1–13. https://doi.org/10.1016/j.cpc.2006.07.018.'
ieee: 'C. Freysoldt, P. Eggert, P. Rinke, A. Schindlmayr, R. W. Godby, and M. Scheffler,
“Dielectric anisotropy in the GW space–time method,” Computer Physics Communications,
vol. 176, no. 1, pp. 1–13, 2007, doi: 10.1016/j.cpc.2006.07.018.'
mla: Freysoldt, Christoph, et al. “Dielectric Anisotropy in the GW Space–Time Method.”
Computer Physics Communications, vol. 176, no. 1, Elsevier, 2007, pp. 1–13,
doi:10.1016/j.cpc.2006.07.018.
short: C. Freysoldt, P. Eggert, P. Rinke, A. Schindlmayr, R.W. Godby, M. Scheffler,
Computer Physics Communications 176 (2007) 1–13.
date_created: 2020-08-28T16:52:21Z
date_updated: 2022-11-11T06:50:39Z
ddc:
- '530'
doi: 10.1016/j.cpc.2006.07.018
extern: '1'
external_id:
arxiv:
- cond-mat/0608215
isi:
- '000243680100001'
file:
- access_level: closed
content_type: application/pdf
creator: schindlm
date_created: 2020-08-28T17:56:51Z
date_updated: 2020-08-30T15:35:32Z
description: © 2006 Elsevier B.V.
file_id: '18596'
file_name: CPC-176-1-2007.pdf
file_size: 267788
relation: main_file
title: Dielectric anisotropy in the GW space-time method
file_date_updated: 2020-08-30T15:35:32Z
has_accepted_license: '1'
intvolume: ' 176'
isi: '1'
issue: '1'
language:
- iso: eng
page: 1-13
publication: Computer Physics Communications
publication_identifier:
issn:
- 0010-4655
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Dielectric anisotropy in the GW space–time method
type: journal_article
user_id: '458'
volume: 176
year: '2007'
...