Quanling Deng: Thursday 6 June at 11:00, A415 Inria Paris.
The well-known generalized-alpha method is an unconditionally stable and second-order accurate time-integrator which has a feature of user-control on numerical dissipation. The method encompasses a wide range of time-integrators, such as the Newmark method, the HHT-alpha method by Hilber, Hughes, and Taylor, and the WBZ-alpha method by Wood, Bossak, and Zienkiewicz. The talk starts with the simplest time-integrator, forward/backward Euler schemes, then introduces Newmark’s idea followed by the ideas of Chung and Hulbert on the generalized-alpha method. For parabolic equations, we show that the generalized-alpha method also includes the BDF-2 and the second-order dG time-integration scheme. The focus of the talk is to introduce two ideas to generalize the method further to higher orders while maintaining the features of unconditional stability and dissipation control. We will show third-order (for parabolic equations) and 2n-order (for hyperbolic equations) accurate schemes with numerical validations. The talk closes with the introduction of a variational-splitting framework for these time-integrators. As a consequence, the splitting schemes reduce the computational costs significantly (to linear cost) for multi-dimensional problems.