{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T08:06:24Z","timestamp":1789718784420,"version":"4.0.1"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/501100004063","name":"Knut och Alice Wallenbergs Stiftelse","doi-asserted-by":"publisher","award":["2020.0258"],"award-info":[{"award-number":["2020.0258"]}],"id":[{"id":"10.13039\/501100004063","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than evaluating the volume potential over the given domain, we first extend the source data to a geometrically simpler region with high order accuracy. This allows us to accelerate the evaluation of the volume potential using an efficient, geometry-unaware fast multipole-based algorithm. To impose the desired boundary condition, it remains only to solve the Laplace equation with suitably modified boundary data. This is accomplished with existing fast and accurate boundary integral methods. The novelty of our solver is the scheme used for creating the source extension, assuming it is provided on an adaptive quad-tree. For leaf boxes intersected by the boundary, we construct a universal \u201cstencil\u201d and require that the data be provided at the subset of those points that lie within the domain interior. This universality permits us to precompute and store an interpolation matrix which is used to extrapolate the source data to an extended set of leaf nodes with full tensor-product grids on each. We demonstrate the method\u2019s speed, robustness, and high order convergence with several examples, including domains with piecewise smooth boundaries.<\/jats:p>\n                  <jats:p>Reproducibility of computational results. This paper has been awarded the \u201cSIAM Reproducibility Badge: code and data available\u201d, as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https:\/\/github.com\/fryklund\/p2d . [Formula: see text]<\/jats:p>","DOI":"10.1137\/22m153495x","type":"journal-article","created":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T04:00:34Z","timestamp":1701662434000},"page":"A3001-A3019","source":"Crossref","is-referenced-by-count":6,"title":["An FMM Accelerated Poisson Solver for Complicated Geometries in the Plane Using Function Extension"],"prefix":"10.1137","volume":"45","author":[{"given":"Fredrik","family":"Fryklund","sequence":"first","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leslie","family":"Greengard","sequence":"additional","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA."},{"name":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,12,4]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"T. 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