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Well‐scaled, a‐posteriori error estimation for model order reduction of large second‐order mechanical systems
Author(s) -
Grunert Dennis,
Fehr Jörg,
Haasdonk Bernard
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900186
Subject(s) - reduction (mathematics) , estimator , bottleneck , algorithm , a priori and a posteriori , computation , monotonic function , computer science , model order reduction , mathematical optimization , usable , computational complexity theory , polynomial , mathematics , statistics , projection (relational algebra) , mathematical analysis , philosophy , geometry , epistemology , world wide web , embedded system
Model Order Reduction is used to vastly speed up simulations but it also introduces an error to the simulation results, which needs to be controlled. The a‐posteriori error estimator of Ruiner et al. for second‐order systems, which is based on the residual, has the advantage of having provable upper bounds and being usable independently of the reduction method. Nevertheless a bottleneck is found in the offline phase, making it unusable for larger models. We use the spectral theorem, power series expansions, monotonicity properties, and self‐tailored algorithms to largely speed up the offline phase by one polynomial order both in terms of computation time as well as storage complexity. All properties are proven rigorously. This eliminates the aforementioned bottleneck. Hence, the error estimator of Ruiner et al. can finally be used for large, linear, second‐order mechanical systems reduced by any model reduction method based on Petrov–Galerkin reduction. The examples show speedups of up to 28.000 and the ability to compute much larger systems with a fixed amount of memory.