%0 Book %1 wirtz2013aposteriori %A Wirtz, Daniel %A Sorensen, D. C. %A Haasdonk, Bernard %B Preprint Series / Stuttgart Research Centre for Simulation Technology (SRC SimTech) %D 2013 %I SimTech - Cluster of Excellence %K ians liste unibibliografie %T A-posteriori error estimation for DEIM reduced nonlinear dynamical systems %X In this work an effcient approach for a-posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameter-affne linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system's nonlinearity by the DEIM method Chaturantabut & Sorensen (2010). The proposed a-posteriori error estimator can be effciently decomposed in an offine/online fashion and is obtained by a one dimensional auxiliary ODE during reduced simulations. Key elements for effcient online computation are partial similarity transformations and matrix DEIM approximations of the nonlinearity Jacobians. The theoretical results are illustrated by application to an unsteady Burgers equation and a cell apoptosis model.

@book{wirtz2013aposteriori, abstract = {In this work an effcient approach for a-posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameter-affne linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system's nonlinearity by the DEIM method [Chaturantabut & Sorensen (2010)]. The proposed a-posteriori error estimator can be effciently decomposed in an offine/online fashion and is obtained by a one dimensional auxiliary ODE during reduced simulations. Key elements for effcient online computation are partial similarity transformations and matrix DEIM approximations of the nonlinearity Jacobians. The theoretical results are illustrated by application to an unsteady Burgers equation and a cell apoptosis model.}, added-at = {2019-06-17T14:25:24.000+0200}, author = {Wirtz, Daniel and Sorensen, D. C. and Haasdonk, Bernard}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2363b533a0ad948aae43199b6a057125b/britsteiner}, interhash = {f0eba34d7ef4487f846b3b9b42aef554}, intrahash = {363b533a0ad948aae43199b6a057125b}, keywords = {ians liste unibibliografie}, language = {eng}, location = {Stuttgart}, pagetotal = {24}, publisher = {SimTech - Cluster of Excellence}, series = {Preprint Series / Stuttgart Research Centre for Simulation Technology (SRC SimTech)}, timestamp = {2019-06-17T12:34:15.000+0200}, title = {A-posteriori error estimation for DEIM reduced nonlinear dynamical systems}, year = 2013 }