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Comp."],"abstract":"<p>In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational efficiency: thanks to the proposed formulation and to the tensor-product construction of space-time splines, we can design a preconditioner whose application requires the solution of a Sylvester-like equation, which is performed efficiently by the fast diagonalization method. The preconditioner is robust w.r.t. spline degree and mesh size. The computational time required for its application, for a serial execution, is almost proportional to the number of degrees-of-freedom and independent of the polynomial degree. The proposed approach is also well-suited for parallelization.<\/p>","DOI":"10.1090\/mcom\/3471","type":"journal-article","created":{"date-parts":[[2019,6,26]],"date-time":"2019-06-26T09:27:55Z","timestamp":1561541275000},"page":"1193-1227","source":"Crossref","is-referenced-by-count":17,"title":["Space\u2013time least\u2013squares isogeometric method and efficient solver for parabolic problems"],"prefix":"10.1090","volume":"89","author":[{"given":"Monica","family":"Montardini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matteo","family":"Negri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giancarlo","family":"Sangalli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mattia","family":"Tani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"1","series-title":"Lectures in Mathematics ETH Z\\\"{u}rich","isbn-type":"print","volume-title":"Gradient flows in metric spaces and in the space of probability measures","author":"Ambrosio, Luigi","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9783764387211","edition":"2"},{"key":"2","isbn-type":"print","volume-title":"Applied functional analysis","author":"Aubin, Jean-Pierre","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/0471021490"},{"key":"3","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1017\/S096249291400004X","article-title":"Mathematical analysis of variational isogeometric methods","volume":"23","author":"Beir\u00e3o da Veiga, L.","year":"2014","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"},{"key":"4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cma.2011.10.016","article-title":"Anisotropic NURBS approximation in isogeometric analysis","volume":"209\/212","author":"Beir\u00e3o da Veiga, L.","year":"2012","journal-title":"Comput. 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