{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T10:53:40Z","timestamp":1775818420631,"version":"3.50.1"},"reference-count":35,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1522191"],"award-info":[{"award-number":["DMS 1522191"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>An efficient algorithm is proposed and studied for computing flow ensembles of incompressible magnetohydrodynamic (MHD)\nflows under uncertainties in initial or boundary data. The ensemble average of <jats:italic>J<\/jats:italic> realizations is approximated through a clever algorithm (adapted from a breakthrough idea of Jiang and Layton [23]) that,\nat each time step, uses the same matrix for each of the <jats:italic>J<\/jats:italic> systems solves. Hence, preconditioners need to be built only once per time step, and the algorithm can take advantage of block linear solvers. Additionally, an Els\u00e4sser variable formulation is used, which allows for a stable decoupling of each MHD system at each time step. We prove stability and convergence of the algorithm, and test it with two numerical experiments.<\/jats:p>","DOI":"10.1515\/cmam-2016-0033","type":"journal-article","created":{"date-parts":[[2016,10,25]],"date-time":"2016-10-25T10:01:30Z","timestamp":1477389690000},"page":"121-137","source":"Crossref","is-referenced-by-count":39,"title":["An Efficient Algorithm for Computation of MHD Flow Ensembles"],"prefix":"10.1515","volume":"17","author":[{"given":"Muhammad","family":"Mohebujjaman","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA"}]},{"given":"Leo G.","family":"Rebholz","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA"}]}],"member":"374","published-online":{"date-parts":[[2016,10,25]]},"reference":[{"key":"2023033115185145176_j_cmam-2016-0033_ref_001_w2aab3b7e2826b1b6b1ab2ab1Aa","unstructured":"Akbas M., Kaya S., Mohebujjaman M. and Rebholz L.,\nNumerical analysis and testing of a fully discrete, decoupled penalty-projection algorithm for MHD in Els\u00e4sser variable,\nInt. 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