On the treatment of high-frequency issues in numerical simulation for dynamic systems by model order reduction via the proper orthogonal decomposition

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Computer Methods in Applied Mechanics and Engineering, ISSN: 0045-7825, Vol: 325, Page: 139-154

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R. Deokar; M. Shimada; K. K. Tamma; C. Lin
Elsevier BV
Engineering; Physics and Astronomy; Computer Science
article description
A new numerical strategy to remedy high-frequency issues caused by finite element discretization in structural dynamic problems has been proposed. A noteworthy characteristic of this advocated approach is that it is based upon the use of the proper orthogonal decomposition (POD) incorporated in conjunction with implicit or explicit numerically non-dissipative time integration schemes to substantially improve or eliminate undesirable effects due to high-frequency instabilities. Original systems with high-frequency issues are reduced via POD based on an adequate choice of a numerically dissipative scheme so that the resulting reduced systems contain no high-frequency participation. This approach confers the inherent advantages that numerically non-dissipative mechanical integrators, e.g., energy–momentum conserving or variational integrators, can be used to solve the reduced systems, fulfilling the requisite conservation laws in the projected basis and therefore provides a robust simulation. Linear and nonlinear numerical applications are shown to demonstrate the benefits and feasibility of this technique.