{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:51:47Z","timestamp":1776721907529,"version":"3.51.2"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"215","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We develop an efficient iterative method for computing the steady linearized potential flow around a submerged body moving in a liquid of finite constant depth. In this paper we restrict the presentation to the two-dimensional problem, but the method is readily generalizable to the three-dimensional case, i.e., the flow in a canal. The problem is indefinite, which makes the convergence of most iterative methods unstable. To circumvent this difficulty, we decompose the problem into two more easily solvable subproblems and form a Schwarz\u2013type iteration to solve the original problem. The first subproblem is definite and can therefore be solved by standard iterative methods. The second subproblem is indefinite but has no body. It is therefore easily and efficiently solvable by separation of variables. We prove that the iteration converges for sufficiently small Froude numbers. In addition, we present numerical results for a second-order accurate discretization of the problem. We demonstrate that the iterative method converges rapidly, and that the convergence rate improves when the Froude number decreases. We also verify numerically that the convergence rate is essentially independent of the grid size.<\/p>","DOI":"10.1090\/s0025-5718-96-00715-6","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"1067-1083","source":"Crossref","is-referenced-by-count":3,"title":["A fast iterative method to compute the flow around a submerged body"],"prefix":"10.1090","volume":"65","author":[{"given":"Johan","family":"Malmliden","sequence":"first","affiliation":[]},{"given":"N.","family":"Petersson","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","unstructured":"D. L. Brown, G. Chesshire, and W. D. Henshaw, Getting started with CMPGRD. Introductory user\u2019s guide and reference manual. LA\u2013UR 90-3729, Los Alamos National Laboratory, 1989."},{"key":"2","unstructured":"D. L. Brown, G. Chesshire, and W. D. Henshaw, An explanation of the CMPGRD composite grid data structure. IBM Research Report RC 14354, IBM Research Division, Yorktown Heights, NY, 1990."},{"issue":"12","key":"3","first-page":"819","article-title":"R\u00e9solution num\u00e9rique du probl\u00e8me non lin\u00e9aire de la r\u00e9sistance de vagues bidimensionnelle","volume":"297","author":"Cahouet, Jacques","year":"1983","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. II M\\'{e}c. Phys. Chim. Sci. Univers Sci. Terre","ISSN":"https:\/\/id.crossref.org\/issn\/0249-6305","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0021-9991(90)90196-8","article-title":"Composite overlapping meshes for the solution of partial differential equations","volume":"90","author":"Chesshire, G.","year":"1990","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"key":"5","volume-title":"Methods of mathematical physics. Vol. II: Partial differential equations","author":"Courant, R.","year":"1962"},{"key":"6","unstructured":"C. W. Dawson, A practical computer method for solving ship wave problems. In Proceedings of the Second International Conference on Numerical Ship Hydrodynamics, pages 30\u201338. University of California, Berkeley, 1977."},{"key":"7","doi-asserted-by":"crossref","unstructured":"L. J. Doctors and R. F. Beck, Convergence properties of the Neumann\u2013Kelvin problem for a submerged body. J. Ship Res., 31:227\u2013234, 1987.","DOI":"10.5957\/jsr.1987.31.4.227"},{"key":"8","doi-asserted-by":"crossref","unstructured":"S. Eisenstat, M. Gursky, M. H. Schultz, and A. H. Sherman, The Yale matrix package II: The non\u2013symmetric case. Report 114, Dept. of Computer Science, Yale University, 1977.","DOI":"10.21236\/ADA047725"},{"key":"9","doi-asserted-by":"crossref","unstructured":"P. S. Jensen, On the numerical radiation condition in the steady state ship wave problem. J. 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Eng., 10:1153\u20131175, 1976.","DOI":"10.1002\/nme.1620100514"},{"key":"14","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1017\/S0022112090002646","article-title":"On steady and unsteady ship wave patterns","volume":"215","author":"Nakos, D. E.","year":"1990","journal-title":"J. Fluid Mech.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-1120","issn-type":"print"},{"key":"15","doi-asserted-by":"crossref","unstructured":"J. N. Newman, Evaluation of the wave-resistance Green function: Part 2. The single integral on the centerplane. J. Ship Res., 31(3):145\u2013150, 1987.","DOI":"10.5957\/jsr.1987.31.3.145"},{"issue":"1","key":"16","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1137\/0729002","article-title":"A numerical method to calculate the two-dimensional flow around an underwater obstacle","volume":"29","author":"Petersson, N. Anders","year":"1992","journal-title":"SIAM J. Numer. 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