Krylov-subspace methods for reduced-order modeling in circuit simulation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
Applied Numerical Mathematics
Piecewise polynomial nonlinear model reduction
Proceedings of the 40th annual Design Automation Conference
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Concepts and Applications of Finite Element Analysis
Concepts and Applications of Finite Element Analysis
Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme
Computers and Structures
Faster, parametric trajectory-based macromodels via localized linear reductions
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
On a composite implicit time integration procedure for nonlinear dynamics
Computers and Structures
Model order reduction of nonlinear dynamic systems using multiple projection bases and optimized state-space sampling
Model Order Reduction Techniques: with Applications in Finite Element Analysis
Model Order Reduction Techniques: with Applications in Finite Element Analysis
A Krylov enhanced proper orthogonal decomposition method for efficient nonlinear model reduction
Finite Elements in Analysis and Design
Insight into an implicit time integration scheme for structural dynamics
Computers and Structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Projection-based approaches for model reduction of weakly nonlinear, time-varying systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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The objective of the paper is to investigate the applicability of a model order reduction technique for dynamic simulation of beams with forcing and geometric nonlinearities. A cantilever and a doubly clamped beams actuated by an electrostatic force are considered in the paper. The governing partial differential equations for the two cases which account for the nonlinearities are presented. These equations are spatially discretized using the Galerkin finite element method (FEM). The resulting system of nonlinear ordinary differential equations is reduced using the trajectory piecewise linear model order reduction (TPWLMOR) method. Simulation indicates that the use of the original TPWLMOR method leads to the presence of a phase error in the long term dynamic simulation of the models. To improve the accuracy of the dynamic response, a modification to the original TPWLMOR based on minimization of residual at linearization point is proposed. Further, the parameters affecting the accuracy of the modified TPWLMOR are studied.