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Tempus: Implementation of HHT-Alpha method

James Willenbring requested to merge hillyuan:tempus_HHTAlpha into develop

Created by: hillyuan

@trilinos/tempus

Description

  1. HHT-Alpha method based upon ”Hilber, H.M, Hughes,T.J.R and Taylor, R.L. "Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics" Earthquake Engineering and Structural Dynamics, 5:282-292 , 1977" is implemented at Tempus::StepperHHTAlpha

  2. Before this modification, it semms like that Tempus::StepperHHTAlpha was implemeted as Newmark-beta method and planned to acomplish the algorithm according to G.M. Hulbert and J. Chung's paper in 1996, which is generally called "Generalized-Alpha method". In this modification, the former StepperHHTAlpha class is renamed as StepperGeneralizedAlpha, which I am going to implement later.

  3. To define HHT-alpha scheme, only the parameter allowed to input is "Alpha=...". Other parameters (beta & gamma) are calculated automaticcally to assure this algorithm second-order accurate. The accuracy is comfirmed by the test case in /package/tempus/test/HHTAlpha/Tempus_Newmark_Sincos_SecondOrder.xml

Checklist

  • My commit messages mention the appropriate GitHub issue numbers.
  • My code follows the code style of the affected package(s).
  • My change requires a change to the documentation.
  • I have updated the documentation accordingly.
  • I have read the code contribution guidelines for this project.
  • I have added tests to cover my changes.
  • All new and existing tests passed.
  • No new compiler warnings were introduced.
  • These changes break backwards compatibility.

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