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Comput."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully implicit Runge\u2013Kutta methods with Radau nodes and that possess high stage order. We show that the new fully implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge\u2013Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge\u2013Kutta methods. For parallel (in space) finite element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge\u2013Kutta methods and\/or achieve a given accuracy several times times faster in terms of computational runtime.<\/jats:p>","DOI":"10.1137\/21m1446988","type":"journal-article","created":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T05:40:15Z","timestamp":1701236415000},"page":"A2945-A2972","source":"Crossref","is-referenced-by-count":2,"title":["Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods"],"prefix":"10.1137","volume":"45","author":[{"given":"Tommaso","family":"Buvoli","sequence":"first","affiliation":[{"name":"Department of Mathematics, Tulane University, New Orleans, LA 70118 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0283-4928","authenticated-orcid":true,"given":"Ben S.","family":"Southworth","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,11,29]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-002-0432-y"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2020.06.009"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/0719052"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384162"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(97)00056-1"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/0732037"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/060656929"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1002\/9781119121534"},{"key":"ref9","unstructured":"T. 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