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Here, a new approach called collocation coarse approximation (CCA) is introduced, which\u2014like GCA\u2014is algebraically defined and able to cater to difficult features such as discontinuous coefficients, but, unlike GCA, allows explicit control over the coarse-grid sparsity pattern (stencil) and therefore control over the computational complexity of the solver. CCA relies on certain basis functions for which the coarse approximation to the fine-grid problem is exact. Numerical experiments for two-dimensional diffusion problems including jumping coefficients demonstrate the potential of the resulting multigrid algorithms.<\/jats:p>","DOI":"10.1137\/08074461x","type":"journal-article","created":{"date-parts":[[2009,9,28]],"date-time":"2009-09-28T15:18:51Z","timestamp":1254151131000},"page":"3643-3660","source":"Crossref","is-referenced-by-count":7,"title":["Collocation Coarse Approximation in Multigrid"],"prefix":"10.1137","volume":"31","author":[{"given":"Roman","family":"Wienands","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Irad","family":"Yavneh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,9,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0902035"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.13182\/NSE96-A24230"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431719-X"},{"key":"R4","unstructured":"A. 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