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However, the RBF-based boundary problem necessitates solving a large dense linear system with cubic arithmetic complexity that is computationally expensive and prohibitive in terms of memory footprint. In this article, we accelerate the computations of 3D unstructured mesh deformation based on RBF interpolations by exploiting the rank structured property of the matrix operator. The main idea consists in approximating the matrix off-diagonal tiles up to an application-dependent accuracy threshold. We highlight the robustness of our multiscale solver by assessing its numerical accuracy using realistic 3D geometries. In particular, we model the 3D mesh deformation on a population of the novel coronaviruses. We report and compare performance results on various parallel systems against existing state-of-the-art matrix solvers.<\/jats:p>","DOI":"10.1145\/3512756","type":"journal-article","created":{"date-parts":[[2022,3,24]],"date-time":"2022-03-24T22:38:03Z","timestamp":1648161483000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["High-performance 3D Unstructured Mesh Deformation Using Rank Structured Matrix Computations"],"prefix":"10.1145","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9911-6094","authenticated-orcid":false,"given":"Rabab","family":"Alomairy","sequence":"first","affiliation":[{"name":"Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal, Jeddah, KSA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7627-4655","authenticated-orcid":false,"given":"Wael","family":"Bader","sequence":"additional","affiliation":[{"name":"Centre for Material Forming, MINES ParisTech, PSL University, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6897-1095","authenticated-orcid":false,"given":"Hatem","family":"Ltaief","sequence":"additional","affiliation":[{"name":"Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal, Jeddah, KSA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5136-5435","authenticated-orcid":false,"given":"Youssef","family":"Mesri","sequence":"additional","affiliation":[{"name":"Centre for Material Forming, MINES ParisTech, PSL University, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4052-7224","authenticated-orcid":false,"given":"David","family":"Keyes","sequence":"additional","affiliation":[{"name":"Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal, Jeddah, KSA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2022,3,23]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"42nd AIAA Aerospace Sciences Meeting and Exhibit","author":"Aftosmis Michael","year":"2004","unstructured":"Michael Aftosmis, Marsha Berger, and Scott Murman. 2004. 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