High-order generalized-alpha method

The generalized-α method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation. Additionally, the numerical dissipation can be controlled by the user by setting a single parameter, ρ∞. The method is unconditi...

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Autores principales:	Pouria Behnoudfar, Quanling Deng, Victor M. Calo
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2020
Materias:	Generalized-α method High-order Spectral analysis Time integrator Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/37ec4c599e0f4f5fa70ec6b50697fafe
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id	oai:doaj.org-article:37ec4c599e0f4f5fa70ec6b50697fafe
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spelling	oai:doaj.org-article:37ec4c599e0f4f5fa70ec6b50697fafe2021-12-01T05:05:39ZHigh-order generalized-alpha method2666-496810.1016/j.apples.2020.100021https://doaj.org/article/37ec4c599e0f4f5fa70ec6b50697fafe2020-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496820300212https://doaj.org/toc/2666-4968The generalized-α method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation. Additionally, the numerical dissipation can be controlled by the user by setting a single parameter, ρ∞. The method is unconditionally stable and has second-order accuracy in time. We extend the second-order generalized-α method to third-order in time while the numerical dissipation can be controlled by a single parameter. In each time step, the scheme only requires inverting one matrix on acceleration and update the displacement and velocity explicitly. We establish that the third-order method is unconditionally stable. We discuss a possible path to the generalization to higher order schemes. All these high-order schemes can be easily implemented into programs that already contain the second-order generalized-α method.Pouria BehnoudfarQuanling DengVictor M. CaloElsevierarticleGeneralized-α methodHigh-orderSpectral analysisTime integratorEngineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 4, Iss , Pp 100021- (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Generalized-α method High-order Spectral analysis Time integrator Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Generalized-α method High-order Spectral analysis Time integrator Engineering (General). Civil engineering (General) TA1-2040 Pouria Behnoudfar Quanling Deng Victor M. Calo High-order generalized-alpha method
description	The generalized-α method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation. Additionally, the numerical dissipation can be controlled by the user by setting a single parameter, ρ∞. The method is unconditionally stable and has second-order accuracy in time. We extend the second-order generalized-α method to third-order in time while the numerical dissipation can be controlled by a single parameter. In each time step, the scheme only requires inverting one matrix on acceleration and update the displacement and velocity explicitly. We establish that the third-order method is unconditionally stable. We discuss a possible path to the generalization to higher order schemes. All these high-order schemes can be easily implemented into programs that already contain the second-order generalized-α method.
format	article
author	Pouria Behnoudfar Quanling Deng Victor M. Calo
author_facet	Pouria Behnoudfar Quanling Deng Victor M. Calo
author_sort	Pouria Behnoudfar
title	High-order generalized-alpha method
title_short	High-order generalized-alpha method
title_full	High-order generalized-alpha method
title_fullStr	High-order generalized-alpha method
title_full_unstemmed	High-order generalized-alpha method
title_sort	high-order generalized-alpha method
publisher	Elsevier
publishDate	2020
url	https://doaj.org/article/37ec4c599e0f4f5fa70ec6b50697fafe
work_keys_str_mv	AT pouriabehnoudfar highordergeneralizedalphamethod AT quanlingdeng highordergeneralizedalphamethod AT victormcalo highordergeneralizedalphamethod
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High-order generalized-alpha method

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