{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:10Z","timestamp":1760145070611,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T00:00:00Z","timestamp":1718668800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101625","2023YFB3001704","2022A1515010831","61976104"],"award-info":[{"award-number":["12101625","2023YFB3001704","2022A1515010831","61976104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Research and Development Program of China","award":["12101625","2023YFB3001704","2022A1515010831","61976104"],"award-info":[{"award-number":["12101625","2023YFB3001704","2022A1515010831","61976104"]}]},{"name":"Natural Science Foundation of Guangdong Province, China","award":["12101625","2023YFB3001704","2022A1515010831","61976104"],"award-info":[{"award-number":["12101625","2023YFB3001704","2022A1515010831","61976104"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101625","2023YFB3001704","2022A1515010831","61976104"],"award-info":[{"award-number":["12101625","2023YFB3001704","2022A1515010831","61976104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In off-boundary computations of layer potentials, the near-singularities in integrals near the boundary presents challenges for conventional quadrature methods in achieving high precision. Additionally, the significant complexity of O(n2) interactions between n targets and n sources reduces the efficiency of these methods. A fast and accurate numerical algorithm is presented for computing the Laplace layer potentials on a circle with a boundary described by a polar curve. This method can maintain high precision even when evaluating targets located at a close distance from the boundary. The radial symmetry of the integral kernels simplifies their description. By exploiting the polar form of the boundary and applying a one-dimensional exponential sum approximation along the radial direction, an approximation of layer potentials by the convolution sum is obtained. The algorithm uses FFT convolution to accelerate computation and employs a local quadrature to maintain accuracy for nearly singular terms. Consequently, it achieves spectral accuracy in regions outside of a sufficiently small neighborhood of the boundary and requires O(nlogn) arithmetic operations. With the help of this algorithm, layer potentials can be efficiently evaluated on a computational domain.<\/jats:p>","DOI":"10.3390\/sym16060764","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T05:27:19Z","timestamp":1718861239000},"page":"764","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Fast Method for the Off-Boundary Evaluation of Laplace Layer Potentials by Convolution Sums"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7586-1947","authenticated-orcid":false,"given":"Wenchao","family":"Guan","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Guangdong Province Key Lab of Computational Science, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhicheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Computer School, Jiaying University, Meizhou 514015, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leqi","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Guangdong Province Key Lab of Computational Science, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yueen","family":"Hou","sequence":"additional","affiliation":[{"name":"Computer School, Jiaying University, Meizhou 514015, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kress, R. 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