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This feature turns out to be very important in terms of classical model order reduction methodologies. In fact, differently from time stepping integrators (like Runge\u2013Kutta methods), the use of the Laplace transform determines a significant reduction of the size of the reduced space. In this article we propose two reduction methods; the first one constructs a unique reduced space, based on the vectors representing the Laplace transform at the chosen quadrature points for different values of the parameters, and the second one instead constructs several reduced spaces, one at each quadrature node. This last approach is particularly well suited to a parallel computation approach, allowing a faster computation. We show the effectiveness of the method by some illustrative parabolic PDEs arising from finance.<\/jats:p>","DOI":"10.1137\/22m1520189","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T05:09:52Z","timestamp":1689052192000},"page":"A1711-A1740","source":"Crossref","is-referenced-by-count":8,"title":["Model Order Reduction in Contour Integral Methods for Parametric PDEs"],"prefix":"10.1137","volume":"45","author":[{"given":"Nicola","family":"Guglielmi","sequence":"first","affiliation":[{"name":"Division of Mathematics, Gran Sasso Science Institute, L\u2019Aquila, 67100 Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8294-4851","authenticated-orcid":true,"given":"Mattia","family":"Manucci","sequence":"additional","affiliation":[{"name":"Division of Mathematics, Gran Sasso Science Institute, L\u2019Aquila, 67100 Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.08.006"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/130932715"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/100795772"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1086\/260062"},{"key":"ref5","unstructured":"C. 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