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
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Acceso en línea:https://doaj.org/article/37ec4c599e0f4f5fa70ec6b50697fafe
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Sumario: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.