[{"citation":{"apa":"Wingenbach, J., Bauch, D., Ma, X., Schade, R., Plessl, C., &#38; Schumacher, S. (2025). PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions. <i>Computer Physics Communications</i>, <i>315</i>, Article 109689. <a href=\"https://doi.org/10.1016/j.cpc.2025.109689\">https://doi.org/10.1016/j.cpc.2025.109689</a>","short":"J. Wingenbach, D. Bauch, X. Ma, R. Schade, C. Plessl, S. Schumacher, Computer Physics Communications 315 (2025).","mla":"Wingenbach, Jan, et al. “PHOENIX – Paderborn Highly Optimized and Energy Efficient Solver for Two-Dimensional Nonlinear Schrödinger Equations with Integrated Extensions.” <i>Computer Physics Communications</i>, vol. 315, 109689, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.cpc.2025.109689\">10.1016/j.cpc.2025.109689</a>.","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={<a href=\"https://doi.org/10.1016/j.cpc.2025.109689\">10.1016/j.cpc.2025.109689</a>}, 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} }","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. <i>Computer Physics Communications</i>. 2025;315. doi:<a href=\"https://doi.org/10.1016/j.cpc.2025.109689\">10.1016/j.cpc.2025.109689</a>","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,” <i>Computer Physics Communications</i>, vol. 315, Art. no. 109689, 2025, doi: <a href=\"https://doi.org/10.1016/j.cpc.2025.109689\">10.1016/j.cpc.2025.109689</a>.","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.” <i>Computer Physics Communications</i> 315 (2025). <a href=\"https://doi.org/10.1016/j.cpc.2025.109689\">https://doi.org/10.1016/j.cpc.2025.109689</a>."},"intvolume":"       315","publication_status":"published","publication_identifier":{"issn":["0010-4655"]},"doi":"10.1016/j.cpc.2025.109689","date_updated":"2025-06-29T12:00:36Z","author":[{"first_name":"Jan","last_name":"Wingenbach","id":"69187","full_name":"Wingenbach, Jan"},{"first_name":"David","id":"44172","full_name":"Bauch, David","last_name":"Bauch"},{"first_name":"Xuekai","id":"59416","full_name":"Ma, Xuekai","last_name":"Ma"},{"id":"75963","full_name":"Schade, Robert","orcid":"0000-0002-6268-5397","last_name":"Schade","first_name":"Robert"},{"id":"16153","full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","first_name":"Christian"},{"last_name":"Schumacher","orcid":"0000-0003-4042-4951","id":"27271","full_name":"Schumacher, Stefan","first_name":"Stefan"}],"volume":315,"status":"public","type":"journal_article","article_type":"original","article_number":"109689","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"_id":"60298","user_id":"75963","department":[{"_id":"27"}],"year":"2025","title":"PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions","publisher":"Elsevier BV","date_created":"2025-06-23T07:38:52Z","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."}],"publication":"Computer Physics Communications","language":[{"iso":"eng"}]},{"doi":"10.1016/j.cpc.2018.09.020","title":"i-PI 2.0: A universal force engine for advanced molecular simulations","date_created":"2021-09-01T09:03:51Z","author":[{"last_name":"Kapil","full_name":"Kapil, Venkat","first_name":"Venkat"},{"last_name":"Rossi","full_name":"Rossi, Mariana","first_name":"Mariana"},{"first_name":"Ondrej","full_name":"Marsalek, Ondrej","last_name":"Marsalek"},{"first_name":"Riccardo","last_name":"Petraglia","full_name":"Petraglia, Riccardo"},{"first_name":"Yair","full_name":"Litman, Yair","last_name":"Litman"},{"first_name":"Thomas","full_name":"Spura, Thomas","last_name":"Spura"},{"last_name":"Cheng","full_name":"Cheng, Bingqing","first_name":"Bingqing"},{"first_name":"Alice","last_name":"Cuzzocrea","full_name":"Cuzzocrea, Alice"},{"full_name":"Meißner, Robert H.","last_name":"Meißner","first_name":"Robert H."},{"last_name":"Wilkins","full_name":"Wilkins, David M.","first_name":"David M."},{"last_name":"Helfrecht","full_name":"Helfrecht, Benjamin A.","first_name":"Benjamin A."},{"full_name":"Juda, Przemysław","last_name":"Juda","first_name":"Przemysław"},{"last_name":"Bienvenue","full_name":"Bienvenue, Sébastien P.","first_name":"Sébastien P."},{"first_name":"Wei","full_name":"Fang, Wei","last_name":"Fang"},{"last_name":"Kessler","full_name":"Kessler, Jan","first_name":"Jan"},{"last_name":"Poltavsky","full_name":"Poltavsky, Igor","first_name":"Igor"},{"first_name":"Steven","last_name":"Vandenbrande","full_name":"Vandenbrande, Steven"},{"last_name":"Wieme","full_name":"Wieme, Jelle","first_name":"Jelle"},{"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.","last_name":"Markland","full_name":"Markland, Thomas E."},{"full_name":"Richardson, Jeremy O.","last_name":"Richardson","first_name":"Jeremy O."},{"last_name":"Tkatchenko","full_name":"Tkatchenko, Alexandre","first_name":"Alexandre"},{"full_name":"Tribello, Gareth A.","last_name":"Tribello","first_name":"Gareth A."},{"full_name":"Van Speybroeck, Veronique","last_name":"Van Speybroeck","first_name":"Veronique"},{"first_name":"Michele","last_name":"Ceriotti","full_name":"Ceriotti, Michele"}],"date_updated":"2022-01-06T06:55:57Z","citation":{"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.” <i>Computer Physics Communications</i>, 2018, 214–23. <a href=\"https://doi.org/10.1016/j.cpc.2018.09.020\">https://doi.org/10.1016/j.cpc.2018.09.020</a>.","ieee":"V. Kapil <i>et al.</i>, “i-PI 2.0: A universal force engine for advanced molecular simulations,” <i>Computer Physics Communications</i>, pp. 214–223, 2018.","ama":"Kapil V, Rossi M, Marsalek O, et al. i-PI 2.0: A universal force engine for advanced molecular simulations. <i>Computer Physics Communications</i>. 2018:214-223. doi:<a href=\"https://doi.org/10.1016/j.cpc.2018.09.020\">10.1016/j.cpc.2018.09.020</a>","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. <i>Computer Physics Communications</i>, 214–223. <a href=\"https://doi.org/10.1016/j.cpc.2018.09.020\">https://doi.org/10.1016/j.cpc.2018.09.020</a>","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={<a href=\"https://doi.org/10.1016/j.cpc.2018.09.020\">10.1016/j.cpc.2018.09.020</a>}, 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} }","mla":"Kapil, Venkat, et al. “I-PI 2.0: A Universal Force Engine for Advanced Molecular Simulations.” <i>Computer Physics Communications</i>, 2018, pp. 214–23, doi:<a href=\"https://doi.org/10.1016/j.cpc.2018.09.020\">10.1016/j.cpc.2018.09.020</a>.","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."},"page":"214-223","year":"2018","publication_status":"published","publication_identifier":{"issn":["0010-4655"]},"language":[{"iso":"eng"}],"user_id":"65425","_id":"23597","status":"public","type":"journal_article","publication":"Computer Physics Communications"},{"user_id":"40778","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"13276","language":[{"iso":"eng"}],"type":"journal_article","publication":"Computer Physics Communications","status":"public","date_created":"2019-09-18T08:50:35Z","author":[{"first_name":"Gábor","last_name":"Rutkai","full_name":"Rutkai, Gábor"},{"first_name":"Andreas","last_name":"Köster","full_name":"Köster, Andreas"},{"last_name":"Guevara-Carrion","full_name":"Guevara-Carrion, Gabriela","first_name":"Gabriela"},{"full_name":"Janzen, Tatjana","last_name":"Janzen","first_name":"Tatjana"},{"full_name":"Schappals, Michael","last_name":"Schappals","first_name":"Michael"},{"first_name":"Colin W.","full_name":"Glass, Colin W.","last_name":"Glass"},{"first_name":"Martin","last_name":"Bernreuther","full_name":"Bernreuther, Martin"},{"first_name":"Amer","last_name":"Wafai","full_name":"Wafai, Amer"},{"full_name":"Stephan, Simon","last_name":"Stephan","first_name":"Simon"},{"first_name":"Maximilian","last_name":"Kohns","full_name":"Kohns, Maximilian"},{"first_name":"Steffen","last_name":"Reiser","full_name":"Reiser, Steffen"},{"first_name":"Stephan","last_name":"Deublein","full_name":"Deublein, Stephan"},{"last_name":"Horsch","full_name":"Horsch, Martin","first_name":"Martin"},{"first_name":"Hans","last_name":"Hasse","full_name":"Hasse, Hans"},{"first_name":"Jadran","last_name":"Vrabec","full_name":"Vrabec, Jadran"}],"volume":221,"date_updated":"2022-01-06T06:51:31Z","doi":"10.1016/j.cpc.2017.07.025","title":"ms2: A Molecular Simulation Tool for Thermodynamic Properties, Release 3.0","publication_status":"published","publication_identifier":{"issn":["0010-4655"]},"citation":{"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={<a href=\"https://doi.org/10.1016/j.cpc.2017.07.025\">10.1016/j.cpc.2017.07.025</a>}, 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} }","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.","mla":"Rutkai, Gábor, et al. “Ms2: A Molecular Simulation Tool for Thermodynamic Properties, Release 3.0.” <i>Computer Physics Communications</i>, vol. 221, 2017, pp. 343–51, doi:<a href=\"https://doi.org/10.1016/j.cpc.2017.07.025\">10.1016/j.cpc.2017.07.025</a>.","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. <i>Computer Physics Communications</i>, <i>221</i>, 343–351. <a href=\"https://doi.org/10.1016/j.cpc.2017.07.025\">https://doi.org/10.1016/j.cpc.2017.07.025</a>","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.” <i>Computer Physics Communications</i> 221 (2017): 343–51. <a href=\"https://doi.org/10.1016/j.cpc.2017.07.025\">https://doi.org/10.1016/j.cpc.2017.07.025</a>.","ieee":"G. Rutkai <i>et al.</i>, “ms2: A Molecular Simulation Tool for Thermodynamic Properties, Release 3.0,” <i>Computer Physics Communications</i>, vol. 221, pp. 343–351, 2017.","ama":"Rutkai G, Köster A, Guevara-Carrion G, et al. ms2: A Molecular Simulation Tool for Thermodynamic Properties, Release 3.0. <i>Computer Physics Communications</i>. 2017;221:343-351. doi:<a href=\"https://doi.org/10.1016/j.cpc.2017.07.025\">10.1016/j.cpc.2017.07.025</a>"},"intvolume":"       221","page":"343-351","year":"2017"},{"language":[{"iso":"eng"}],"ddc":["530"],"external_id":{"arxiv":["0811.2363"],"isi":["000264735800002"]},"file":[{"creator":"schindlm","file_name":"1-s2.0-S0010465508003664-main.pdf","file_size":311274,"content_type":"application/pdf","date_created":"2020-10-05T10:35:14Z","date_updated":"2020-10-05T10:41:07Z","file_id":"19875","access_level":"closed","title":"Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method","description":"© 2008 Elsevier B.V.","relation":"main_file"}],"abstract":[{"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.","lang":"eng"}],"publication":"Computer Physics Communications","title":"Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method","date_created":"2020-08-28T22:50:49Z","publisher":"Elsevier","year":"2009","issue":"3","quality_controlled":"1","file_date_updated":"2020-10-05T10:41:07Z","isi":"1","article_type":"original","user_id":"16199","department":[{"_id":"296"},{"_id":"35"},{"_id":"15"},{"_id":"170"},{"_id":"230"}],"_id":"18636","status":"public","type":"journal_article","doi":"10.1016/j.cpc.2008.10.009","author":[{"first_name":"Christoph","full_name":"Friedrich, Christoph","last_name":"Friedrich"},{"first_name":"Arno","last_name":"Schindlmayr","orcid":"0000-0002-4855-071X","full_name":"Schindlmayr, Arno","id":"458"},{"first_name":"Stefan","last_name":"Blügel","full_name":"Blügel, Stefan"}],"volume":180,"date_updated":"2025-12-16T11:10:22Z","citation":{"mla":"Friedrich, Christoph, et al. “Efficient Calculation of the Coulomb Matrix and Its Expansion around K=0 within the FLAPW Method.” <i>Computer Physics Communications</i>, vol. 180, no. 3, Elsevier, 2009, pp. 347–59, doi:<a href=\"https://doi.org/10.1016/j.cpc.2008.10.009\">10.1016/j.cpc.2008.10.009</a>.","short":"C. Friedrich, A. Schindlmayr, S. Blügel, Computer Physics Communications 180 (2009) 347–359.","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={<a href=\"https://doi.org/10.1016/j.cpc.2008.10.009\">10.1016/j.cpc.2008.10.009</a>}, number={3}, journal={Computer Physics Communications}, publisher={Elsevier}, author={Friedrich, Christoph and Schindlmayr, Arno and Blügel, Stefan}, year={2009}, pages={347–359} }","apa":"Friedrich, C., Schindlmayr, A., &#38; Blügel, S. (2009). Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method. <i>Computer Physics Communications</i>, <i>180</i>(3), 347–359. <a href=\"https://doi.org/10.1016/j.cpc.2008.10.009\">https://doi.org/10.1016/j.cpc.2008.10.009</a>","chicago":"Friedrich, Christoph, Arno Schindlmayr, and Stefan Blügel. “Efficient Calculation of the Coulomb Matrix and Its Expansion around K=0 within the FLAPW Method.” <i>Computer Physics Communications</i> 180, no. 3 (2009): 347–59. <a href=\"https://doi.org/10.1016/j.cpc.2008.10.009\">https://doi.org/10.1016/j.cpc.2008.10.009</a>.","ieee":"C. Friedrich, A. Schindlmayr, and S. Blügel, “Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method,” <i>Computer Physics Communications</i>, vol. 180, no. 3, pp. 347–359, 2009, doi: <a href=\"https://doi.org/10.1016/j.cpc.2008.10.009\">10.1016/j.cpc.2008.10.009</a>.","ama":"Friedrich C, Schindlmayr A, Blügel S. Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method. <i>Computer Physics Communications</i>. 2009;180(3):347-359. doi:<a href=\"https://doi.org/10.1016/j.cpc.2008.10.009\">10.1016/j.cpc.2008.10.009</a>"},"page":"347-359","intvolume":"       180","publication_status":"published","has_accepted_license":"1","publication_identifier":{"issn":["0010-4655"]}},{"status":"public","type":"journal_article","article_type":"original","isi":"1","file_date_updated":"2020-08-30T15:35:32Z","extern":"1","_id":"18595","user_id":"458","page":"1-13","intvolume":"       176","citation":{"apa":"Freysoldt, C., Eggert, P., Rinke, P., Schindlmayr, A., Godby, R. W., &#38; Scheffler, M. (2007). Dielectric anisotropy in the GW space–time method. <i>Computer Physics Communications</i>, <i>176</i>(1), 1–13. <a href=\"https://doi.org/10.1016/j.cpc.2006.07.018\">https://doi.org/10.1016/j.cpc.2006.07.018</a>","bibtex":"@article{Freysoldt_Eggert_Rinke_Schindlmayr_Godby_Scheffler_2007, title={Dielectric anisotropy in the GW space–time method}, volume={176}, DOI={<a href=\"https://doi.org/10.1016/j.cpc.2006.07.018\">10.1016/j.cpc.2006.07.018</a>}, 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} }","short":"C. Freysoldt, P. Eggert, P. Rinke, A. Schindlmayr, R.W. Godby, M. Scheffler, Computer Physics Communications 176 (2007) 1–13.","mla":"Freysoldt, Christoph, et al. “Dielectric Anisotropy in the GW Space–Time Method.” <i>Computer Physics Communications</i>, vol. 176, no. 1, Elsevier, 2007, pp. 1–13, doi:<a href=\"https://doi.org/10.1016/j.cpc.2006.07.018\">10.1016/j.cpc.2006.07.018</a>.","ama":"Freysoldt C, Eggert P, Rinke P, Schindlmayr A, Godby RW, Scheffler M. Dielectric anisotropy in the GW space–time method. <i>Computer Physics Communications</i>. 2007;176(1):1-13. doi:<a href=\"https://doi.org/10.1016/j.cpc.2006.07.018\">10.1016/j.cpc.2006.07.018</a>","ieee":"C. Freysoldt, P. Eggert, P. Rinke, A. Schindlmayr, R. W. Godby, and M. Scheffler, “Dielectric anisotropy in the GW space–time method,” <i>Computer Physics Communications</i>, vol. 176, no. 1, pp. 1–13, 2007, doi: <a href=\"https://doi.org/10.1016/j.cpc.2006.07.018\">10.1016/j.cpc.2006.07.018</a>.","chicago":"Freysoldt, Christoph, Philipp Eggert, Patrick Rinke, Arno Schindlmayr, Rex W. Godby, and Matthias Scheffler. “Dielectric Anisotropy in the GW Space–Time Method.” <i>Computer Physics Communications</i> 176, no. 1 (2007): 1–13. <a href=\"https://doi.org/10.1016/j.cpc.2006.07.018\">https://doi.org/10.1016/j.cpc.2006.07.018</a>."},"has_accepted_license":"1","publication_identifier":{"issn":["0010-4655"]},"publication_status":"published","doi":"10.1016/j.cpc.2006.07.018","date_updated":"2022-11-11T06:50:39Z","volume":176,"author":[{"first_name":"Christoph","last_name":"Freysoldt","full_name":"Freysoldt, Christoph"},{"first_name":"Philipp","full_name":"Eggert, Philipp","last_name":"Eggert"},{"last_name":"Rinke","full_name":"Rinke, Patrick","first_name":"Patrick"},{"first_name":"Arno","orcid":"0000-0002-4855-071X","last_name":"Schindlmayr","full_name":"Schindlmayr, Arno","id":"458"},{"first_name":"Rex W.","full_name":"Godby, Rex W.","last_name":"Godby"},{"first_name":"Matthias","full_name":"Scheffler, Matthias","last_name":"Scheffler"}],"abstract":[{"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.","lang":"eng"}],"file":[{"relation":"main_file","date_updated":"2020-08-30T15:35:32Z","date_created":"2020-08-28T17:56:51Z","title":"Dielectric anisotropy in the GW space-time method","description":"© 2006 Elsevier B.V.","file_id":"18596","access_level":"closed","content_type":"application/pdf","creator":"schindlm","file_size":267788,"file_name":"CPC-176-1-2007.pdf"}],"publication":"Computer Physics Communications","ddc":["530"],"language":[{"iso":"eng"}],"external_id":{"isi":["000243680100001"],"arxiv":["cond-mat/0608215"]},"year":"2007","quality_controlled":"1","issue":"1","title":"Dielectric anisotropy in the GW space–time method","publisher":"Elsevier","date_created":"2020-08-28T16:52:21Z"}]