{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:24:39Z","timestamp":1787336679066,"version":"build-2736575974"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>In this paper we propose a direct method for the solution of the Poisson equation in rectangular regions. It has an arbitrary order accuracy and low CPU requirements which makes it practical for treating large-scale problems.<\/jats:p>\n                  <jats:p>\n                    The method is based on a pseudospectral Fourier approximation and a polynomial subtraction technique. Fast convergence of the Fourier series is achieved by removing the discontinuities at the corner points using polynomial subtraction functions. These functions have the same discontinuities at the corner points as the sought solution. In addition to this, they satisfy the Laplace equation so that the subtraction procedure does not generate nonperiodic, nonhomogeneous terms. The solution of a boundary value problem is obtained in a series form in O(N log N) floating point operations, where N\n                    <jats:sup>2<\/jats:sup>\n                    is the number of grid nodes. Evaluating the solution at all N\n                    <jats:sup>2<\/jats:sup>\n                    interior points requires O(N\n                    <jats:sup>2<\/jats:sup>\n                    log N) operations.\n                  <\/jats:p>","DOI":"10.1137\/s1064827595288589","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"933-952","source":"Crossref","is-referenced-by-count":49,"title":["A Fast Poisson Solver of Arbitrary Order Accuracy in Rectangular Regions"],"prefix":"10.1137","volume":"19","author":[{"given":"A.","family":"Averbuch","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Israeli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Vozovoi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"M. 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Averbuch, High order fast elliptic solver in rectangular regions \u2010\n                      Technical report 846, Technion \u2010 Israel Institute of Technology\n                      , 1995."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01575035"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"Vozovoi L. Israeli M., Averbuch A. Application of the Multidomain Local Fourier method for CFD in complex geometries, in\n                      Computational Fluid Dynamics\n                      (selected topics), eds. D. Leutloff, R. C. Srivastava, Springer, 1995, p. 245\u2013256.","DOI":"10.1007\/978-3-642-79440-7_17"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"L. Vozovoi, M. Israeli, A. Averbuch, Multidomain local Fourier method for PDEs in complex geometries, Proceedings of the Sixth International Congress on Computational and Applied Mathematics (Leuven, 1994), Vol. 66, 1996, 543\u201355597b:65142","DOI":"10.1016\/0377-0427(95)00185-9"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827595288589","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:26:25Z","timestamp":1787333185000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827595288589"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S1064827595288589"],"URL":"https:\/\/doi.org\/10.1137\/s1064827595288589","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}