Interface Reduction for CMS Methods and Alternative Model Order Reduction

Holzwarth, Philip; Eberhard, Peter

doi:10.1016/j.ifacol.2015.05.005

Cited by 21 publications

(4 citation statements)

References 9 publications

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“…Within the CMS approach this is realized by utilizing an eigenmode expansion [6,18,19,26], which has recently been combined with input-output-based model reduction in [20]. In [11] Eftang and Patera develop an empirical pairwise training procedure for port reduction within the scRBE context: Modes are selected from traces of snapshots generated by random boundary conditions.…”

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confidence: 99%

Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures

Smetana¹,

Patera²

2016

SIAM J. Sci. Comput.

111

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Abstract. In this paper we introduce local approximation spaces for component-based static condensation (sc) procedures that are optimal in the sense of Kolmogorov. To facilitate simulations for large structures such as aircraft or ships, it is crucial to decrease the number of degrees of freedom on the interfaces, or "ports," in order to reduce the size of the statically condensed system. To derive optimal port spaces we consider a (compact) transfer operator that acts on the space of harmonic extensions on a two-component system and maps the traces on the ports that lie on the boundary of these components to the trace of the shared port. Solving the eigenproblem for the composition of the transfer operator and its adjoint yields the optimal space. For a related work in the context of the generalized finite element method, we refer the reader to [I. Babuška and R. Lipton, Multiscale Model. Simul., 9 (2011), pp. 373-406]. We further introduce a spectral greedy algorithm to generalize the procedure to the parameter-dependent setting and to construct a quasi-optimal parameter-independent port space. Moreover, it is shown that, given a certain tolerance and an upper bound for the ports in the system, the spectral greedy constructs a port space that yields an sc approximation error on a system of arbitrary configuration which is smaller than this tolerance for all parameters in a rich train set. We present our approach for isotropic linear elasticity, although the idea may be readily applied to any linear coercive problem. Numerical experiments demonstrate the very rapid and exponential convergence both of the eigenvalues and of the sc approximation based on spectral modes for nonseparable and irregular geometries such as an I-beam with an internal crack. 1. Introduction. In the last decades numerical simulations based on partial differential equations (PDEs) have significantly gained importance in engineering applications. However, both the geometric complexity of the considered structures, such as ships, aircraft, and turbines, and the intricacy of the simulated physical phenomena often make a straightforward application of, say, the finite element (FE) method prohibitive. This is particularly true if multiple simulation requests or a real-time simulation response is desired, as in engineering design and optimization.One way to tackle such complex problems is to exploit the natural decomposition of the structures into components and apply static condensation (sc) to obtain a (Schur complement) system of the size of the degrees of freedom (DOFs) on all interfaces or ports in the system. To mitigate the computational costs for the required PDE solvers in the interior of the component, model order reduction procedures may be applied. One popular approach is component mode synthesis (CMS), introduced in [4,21], which uses an approximation based on the eigenmodes of local constrained eigenvalue problems. The static condensation reduced basis element (scRBE) method [22,23]

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confidence: 99%

Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures

Smetana¹,

Patera²

2016

SIAM J. Sci. Comput.

111

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“…Nevertheless, this local-level technique causes a considerable compromise in accuracy. Holzwarth et al [35] aimed to improve the accuracy of local-level CC modes computation by adopting the Legendre polynomials. However, accuracy compromising and synthesis cumbersome remain critical concerns.…”

Section: Introductionmentioning

confidence: 99%

An Enhanced Hybrid-Level Interface-Reduction Method Combined with an Interface Discrimination Algorithm

Cheon,

Lee

2023

Mathematics

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This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level.

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“…Using their approach, the modes used at every interface depend only on the adjacent substructures and can be quickly updated if substructures are added, removed, or changed. Holzwarth et al [11] recently demonstrated the use of Legendre Polynomials as basis functions for local interface reduction and compared the performance to S-CC interface reduction. The work by Balmès [3] explored a CMS basis that defined arbitrary interface deformations to describe a set of generalized DOF along an interface.…”

Section: Introductionmentioning

confidence: 99%

Interface reduction for Hurty/Craig-Bampton substructured models: Review and improvements

Krattiger

Zacharczuk

et al. 2019

Mechanical Systems and Signal Processing

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The Hurty/Craig-Bampton method in structural dynamics represents the interior dynamics of each subcomponent in a substructured system with a truncated set of normal modes and retains all of the physical degrees of freedom at the substructure interfaces. This makes the assembly of substructures into a reduced-order system model relatively simple, but means that the reduced-order assembly will have as many interface degrees of freedom as the full model. When the full-model mesh is highly refined, and/or when the system is divided into many subcomponents, this can lead to an unacceptably large system of equations of motion. To overcome this, interface reduction methods aim to reduce the size of the Hurty/Craig-Bampton model by reducing the number of interface degrees of freedom. This research presents a survey of interface reduction methods for Hurty/Craig-Bampton models, and proposes improvements and generalizations to some of the methods. Some of these interface reductions operate on the assembled system-level matrices while others perform reduction locally by considering the uncoupled substructures. The advantages and disadvantages of these methods are highlighted and assessed through comparisons of results obtained from a variety of representative linear FE models.

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Interface Reduction for CMS Methods and Alternative Model Order Reduction

Cited by 21 publications

References 9 publications

Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures

Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures

An Enhanced Hybrid-Level Interface-Reduction Method Combined with an Interface Discrimination Algorithm

Interface reduction for Hurty/Craig-Bampton substructured models: Review and improvements

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