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Nonetheless, even these approaches are eventually hindered by demanding computations due to a sophisticated material response. Here, this issue is addressed for the advanced self\u2010consistent hydrodynamic Drude model (SC\u2010HDM), which captures both nonlocal electron dynamics and electron spill\u2010out, through a volume integral equation (VIE) method. Adopting an IE\u2010based method shifts perspective from the commonly employed differential equation (DE)\u2010based ones, demonstrating significant computational efficiency. The VIE approach is a valuable methodological scaffold: it addresses SC\u2010HDM and simpler models, but can also be adapted to more advanced ones. For spherical nanoparticles (NPs), using the inherent symmetries, similar performance for three increasingly complicated material models is achieved, breaking the taboo that increased sophistication in the material response requires taxing simulations. Mesoscopic material\u2010response functions can be readily extracted from the VIE implementation, thus circumventing the need for lengthy microscopic calculations. This method opens a new way of modeling quantum hydrodynamic NPs and will serve as an essential benchmarking tool for recipes addressing more complicated geometries.<\/jats:p>","DOI":"10.1002\/nap2.70179","type":"journal-article","created":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T13:56:37Z","timestamp":1782827797000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Overcoming Computational Bottlenecks in Quantum Hydrodynamics: A Volume\u2010Based Integral Formalism for Spherical Nanoparticles"],"prefix":"10.1002","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8011-2154","authenticated-orcid":false,"given":"Christos","family":"Mystilidis","sequence":"first","affiliation":[{"name":"POLIMA\u2014Center for Polariton\u2010Driven Light\u2014Matter Interactions University of Southern Denmark  Odense Denmark"},{"name":"School of Electrical and Computer Engineering National Technical University of Athens  Athens Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2075-9036","authenticated-orcid":false,"given":"Christos","family":"Tserkezis","sequence":"additional","affiliation":[{"name":"POLIMA\u2014Center for Polariton\u2010Driven Light\u2014Matter Interactions University of Southern Denmark  Odense Denmark"},{"name":"D\u2010IAS: Danish Institute for Advanced Study University of Southern Denmark  Odense Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guy A. 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