Adjoint

ADjoint: An Approach for the Rapid Development of Discrete Adjoint Solvers. An automatic differentiation tool is used to develop the adjoint code for a three-dimensional computational fluid dynamics solver. Rather than using automatic differentiation to differentiate the entire source code of the computational fluid dynamics solver, we have applied it selectively to produce code that computes the flux Jacobian matrix and the other partial derivatives that are necessary to compute total derivatives using an adjoint method. The resulting linear discrete adjoint system is then solved using the portable, extensible toolkit for scientific computation. This selective application of automatic differentiation is the central idea behind the automatic differentiation adjoint (ADjoint) approach. This approach has the advantage that it is applicable to arbitrary sets of governing equations and cost functions, and that it is exactly consistent with the gradients that would be computed by exact numerical differentiation of the original solver. Furthermore, the approach is largely automatic, thus avoiding the lengthy development times usually required to develop adjoint solvers for partial differential equations. These significant advantages come at the cost of increased memory requirements for the adjoint solver. Derivatives of drag and lift coefficients are validated, and the low computational cost and ease of implementation of the method are shown


References in zbMATH (referenced in 11 articles )

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  1. Kambampati, Sandilya; Chung, Hayoung; Kim, H. Alicia: A discrete adjoint based level set topology optimization method for stress constraints (2021)
  2. Robert Falck; Justin S. Gray; Kaushik Ponnapalli; Ted Wright: dymos: A Python package for optimal control of multidisciplinary systems (2021) not zbMATH
  3. He, Ping; Mader, Charles A.; Martins, Joaquim R. R. A.; Maki, Kevin J.: An aerodynamic design optimization framework using a discrete adjoint approach with OpenFOAM (2018)
  4. James, Kai A.; Waisman, Haim: Layout design of a bi-stable cardiovascular stent using topology optimization (2016)
  5. Zahr, M. J.; Persson, P.-O.: An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems (2016)
  6. Cao, Danping; Liao, Wenyuan: A computational method for full waveform inversion of crosswell seismic data using automatic differentiation (2015)
  7. Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.: A practical discrete-adjoint method for high-fidelity compressible turbulence simulations (2015)
  8. Hicken, J. E.: Output error estimation for summation-by-parts finite-difference schemes (2012)
  9. Lee, Edmund; Martins, Joaquim R. R. A.: Structural topology optimization with design-dependent pressure loads (2012)
  10. Jones, Dominic; Müller, Jens-Dominik; Christakopoulos, Faidon: Preparation and assembly of discrete adjoint CFD codes (2011)
  11. Marta, A. C.; Mader, C. A.; Martins, J. R. R. A.; Van Der Weide, E.; Alonso, J. J.: A methodology for the development of discrete adjoint solvers using automatic differentiation tools (2007)