{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T02:40:27Z","timestamp":1768272027966,"version":"3.49.0"},"reference-count":26,"publisher":"Wiley","issue":"2-3","license":[{"start":{"date-parts":[[2010,3,5]],"date-time":"2010-03-05T00:00:00Z","timestamp":1267747200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"crossref","award":["DE-AC52-06NA25396"],"award-info":[{"award-number":["DE-AC52-06NA25396"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2010,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Black Box Multigrid (BoxMG) is a robust variational multigrid solver for diffusion equations on logically structured grids. BoxMG standardly uses coarsening by a factor of two. It handles cell\u2010centered discretizations on logically rectangular grids by treating the cell\u2010centers as the unknowns to be coarsened. Such a strategy does not preserve the cell structure. That is, coarse\u2010grid cells are not the union of fine\u2010grid cells. In some applications, such as local grid refinement, it is desirable that the cell structure be preserved. In this paper, we develop a method that employs coarsening by a factor of three. It is a natural generalization of standard BoxMG, using operator\u2010induced interpolation (which approximately preserves the continuity of the normal flux), restriction as the transpose of interpolation, and Galerkin coarsening. In addition, we introduce a new colored block Gauss\u2013Seidel scheme that is motivated by the form of the interpolation operator, dubbed \u2018pattern\u2019 relaxation. We present numerical results that demonstrate robustness of this method with respect to discontinuous diffusion coefficients, boundary conditions, and grid dimension. Published in 2010 by John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.705","type":"journal-article","created":{"date-parts":[[2010,3,5]],"date-time":"2010-03-05T19:35:35Z","timestamp":1267817735000},"page":"577-598","source":"Crossref","is-referenced-by-count":33,"title":["Black Box Multigrid with coarsening by a factor of three"],"prefix":"10.1002","volume":"17","author":[{"suffix":"Jr","family":"J. E. Dendy","sequence":"first","affiliation":[]},{"given":"J. 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