Sentence examples for using the discrete adjoint from inspiring English sources

Once the nominal steady and unsteady flows have been computed, a sensitivity analysis is performed using the discrete adjoint equations of the computational fluid dynamics scheme used to discretize the Euler equations.

Sensitivity derivatives required for the optimization are computed using the discrete adjoint method.

This study introduces a new vortex finder shape optimized for minimum pressure drop using the discrete adjoint method.

We present a new approach for the computation of shape sensitivities using the discrete adjoint and flow-sensitivity methods on Cartesian meshes with general polyhedral cells (cut-cells) at the wall boundaries.

Automatic differentiation tools are selectively used to develop the discrete adjoint, which make for a much shorter implementation time and greatly reduce the probability of programming errors.

Error estimates are computed using an adjoint-weighted residual, where the discrete adjoint is computed on a finer space obtained by order enrichment of the primal space.

In the latter, at the first cycle, the exact gradients and Hessians are computed and used; during the subsequent optimization cycles, the discrete adjoint method provides the exact gradient whereas the Hessian is updated as in quasi-Newton methods.

Implementation of the discrete adjoint method is validated by comparing sensitivity derivatives obtained using the adjoint technique with results obtained using direct-differentiation and finite-difference methods.

An implicit algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier Stokes equations is presented.

To compute the Hessian, the direct differentiation of the viscous flow equations is used for the first-order sensitivities of the functional and the flow-related constraints, followed by the discrete adjoint method.

The discrete adjoint solver is obtained with the aid of an automatic differentiation tool, TAPENADE.