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The fast multipole method (FMM) known from the literature was included into modified PIES. To consider complex curvilinear shapes of a boundary, the modification of a binary tree used by the FMM is proposed. The FMM combined with the PIES, called the fast PIES, also allows a significant reduction of random access memory (RAM) utilization. Therefore, it is possible to solve complex engineering problems on a standard personal computer (PC). The proposed algorithm is based on the modified PIES and allows for obtaining accurate solutions of complex BVPs described by the curvilinear boundary at a reasonable time on the PC.<\/jats:p>","DOI":"10.1007\/s11075-020-01066-6","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T11:02:51Z","timestamp":1617188571000},"page":"1025-1050","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2247-2714","authenticated-orcid":false,"given":"Andrzej","family":"Ku\u017celewski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eugeniusz","family":"Zieniuk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"key":"1066_CR1","volume-title":"The Finite Element Method","author":"OC Zienkiewicz","year":"1977","unstructured":"Zienkiewicz, O.C.: The Finite Element Method. 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