doi:10.1186/s40323-015-0050-8engAlfaro, IcíarGonzález, DavidZlotnik, SergioDíez, PedroCueto, ElíasChinesta, FranciscoAn error estimator for real-time simulators based on model order reductionART-2015-96917Model order reduction is one of the most appealing choices for real-time simulation of non-linear solids. In this work a method is presented in which real time performance is achieved by means of the off-line solution of a (high dimensional) parametric problem that provides a sort of response surface or computational vademecum. This solution is then evaluated in real-time at feedback rates compatible with haptic devices, for instance (i.e., more than 1 kHz). This high dimensional problem can be solved without the limitations imposed by the curse of dimensionality by employing proper generalized decomposition (PGD) methods. Essentially, PGD assumes a separated representation for the essential field of the problem. Here, an error estimator is proposed for this type of solutions that takes into account the non-linear character of the studied problems. This error estimator allows to compute the necessary number of modes employed to obtain an approximation to the solution within a prescribed error tolerance in a given quantity of interest.2015http://zaguan.unizar.es/record/5788810.1186/s40323-015-0050-8http://zaguan.unizar.es/record/57888oai:zaguan.unizar.es:57888info:eu-repo/grantAgreement/ES/MINECO/DPI2014-51844-C2-1-2-RAdvanced modeling and simulation in engineering sciences 2, 30 (2015), [16 pp.]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess