Convective Thermal Flow Problems

Moosmann, Christian; Greiner, Andreas

doi:10.1007/3-540-27909-1_16

Cited by 2 publications

(4 citation statements)

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“…In this section, we illustrate the effectiveness of OSA_lr in computing symmetric solutions to large-scale CDSEs (1) through practical examples [23,26,27,[30][31][32][33]. The algorithm OSA_lr was coded by MATLAB 2019a on a 64-bit PC running Windows 10.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems

Yu,

Dong,

2024

Axioms

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Consider a class of coupled Stein equations arising from jump control systems. An operator Smith algorithm is proposed for calculating the solution of the system. Convergence of the algorithm is established under certain conditions. For large-scale systems, the operator Smith algorithm is extended to a low-rank structured format, and the error of the algorithm is analyzed. Numerical experiments demonstrate that the operator Smith iteration outperforms existing linearly convergent iterative methods in terms of computation time and accuracy. The low-rank structured iterative format is highly effective in approximating the solutions of large-scale structured problems.

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Section: Numerical Examplesmentioning

confidence: 99%

“…Example 5. Consider the thermal convective flow control systems in [23,30,31]. These problems involve a flow region with a prescribed velocity profile, incorporating convective transport.…”

Section: Numerical Examplesmentioning

confidence: 99%

Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems

Yu,

Dong,

2024

Axioms

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“…The second numerical example evaluates the convection benchmark [42, Convection] 8 from the Oberwolfach Benchmark Collection [28]. This is a twodimensional computational fluid dynamics application of thermal flow modeled by a convection-diffusion partial differential equation:…”

Section: Convection Benchmarkmentioning

confidence: 99%

“…The model is discretized in space using the finite element method, yielding a generalized linear system (1) of order N = 9669 ≈ 10 4 , a single input M = 1, five outputs Q = 5 and E = I. For a more detailed description of this benchmark see [28] and references therein. This model is tested in two variants: First, in a symmetric setting with zero flow speed v = 0, and second, in a non-normal setting with a flow speed v = 0.5.…”

Section: Convection Benchmarkmentioning

confidence: 99%

Cross-Gramian-based dominant subspaces

Benner

2019

Adv Comput Math

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A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspaces projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.

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Convective Thermal Flow Problems

Cited by 2 publications

References 0 publications

Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems

Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems

Cross-Gramian-based dominant subspaces

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