{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:31:44Z","timestamp":1787337104223,"version":"3.56.0"},"reference-count":15,"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":[[2009,1]]},"abstract":"<jats:p>The correct numerical modeling of free-surface hydrodynamic problems often requires to have the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself. In doing so, one may fulfill relevant physical constraints. The existence, the uniqueness, and two constructive iterative methods to solve a piecewise linear system of the form $\\max[\\boldsymbol{l},\\min(\\boldsymbol{u},\\mathbf{x})]+T\\mathbf{x}=\\mathbf{b}$ are analyzed. The methods are shown to have a finite termination property; i.e., they converge to an exact solution in a finite number of steps and, actually, they converge very quickly, as confirmed by a few numerical tests, which are derived from the mathematical modeling of flows in porous media.<\/jats:p>","DOI":"10.1137\/08072749x","type":"journal-article","created":{"date-parts":[[2009,3,13]],"date-time":"2009-03-13T18:13:32Z","timestamp":1236968012000},"page":"1858-1873","source":"Crossref","is-referenced-by-count":58,"title":["Iterative Solution of Piecewise Linear Systems and Applications to Flows in Porous Media"],"prefix":"10.1137","volume":"31","author":[{"given":"Luigi","family":"Brugnano","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vincenzo","family":"Casulli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,3,13]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"J. Bear and A. Verruijt,\n                      Modeling Groundwater Flow and Pollution\n                      , D. Reidel, Dordrecht, Holland, 1987.","DOI":"10.1007\/978-94-009-3379-8"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(02)00170-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/070681867"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90091-E"},{"key":"R5","unstructured":"V. Casulli,\n                      A high resolution wetting and drying algorithm for free-surface hydrodynamics\n                      , Internat. J. Numer. Methods Fluids, to appear."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-6584.2006.00170.x"},{"key":"R7","unstructured":"C.W. Cryer,\n                      Successive overrelaxation methods for solving linear complementarity problems arising from free boundary value problems\n                      , in Proceedings of the Free Boundary Problems, Vol. I, Pavia, 1979 INdAM \u201cF. Severi\u201d, pp. 109\u2013131."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1145\/357456.2181"},{"key":"R9","unstructured":"G.H. Golub and C.F. van Loan,\n                      Matrix Computations\n                      , 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996."},{"key":"R10","doi-asserted-by":"crossref","unstructured":"R.A. Horn and C.R. Johnson,\n                      Topics in Matrix Analysis\n                      , Cambridge University Press, New York, 1991.","DOI":"10.1017\/CBO9780511840371"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-007-9029-9"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-1694(02)00318-9"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442196"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0803021"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"Y. Saad,\n                      Iterative Methods for Sparse Linear Systems\n                      , 2nd ed., SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/08072749X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:44:49Z","timestamp":1787334289000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/08072749X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/08072749X"],"URL":"https:\/\/doi.org\/10.1137\/08072749x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}