Discrete adjoint gradient evaluations for linear stress and vibration analysis

  • Marc SchwalbachEmail author
  • Tom Verstraete
  • Nicolas R. Gauger
Original Article


This paper presents methods used to perform discrete adjoint gradient evaluations for linear stress and vibration analysis. The methods are implemented within the framework of a discrete adjoint structural solver being developed for multidisciplinary adjoint optimizations of turbomachinery components. The code is differentiated using the algorithmic differentiation tool CoDiPack in tandem with manual treatment of the iterative solvers. Stress analysis leads to a linear system of equations that is typically solved by an iterative solver (e.g. GMRES). To ensure accuracy, the adjoint problem is formulated as a new linear system of equations to be solved. Vibration analysis results in a generalized eigenvalue problem that is also typically solved by an interative solver. The adjoint problem takes out the generalized eigenvalue solve and replaces it by one outer product per eigenfrequency, leading to significantly cheap eigenfrequency gradients for vibration analysis.



This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 642959.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Marc Schwalbach
    • 1
    Email author
  • Tom Verstraete
    • 1
  • Nicolas R. Gauger
    • 2
  1. 1.von Karman Institute for Fluid DynamicsSint-Genesius-RodeBelgium
  2. 2.TU Kaiserslautern KaiserslauternGermany

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