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To demonstrate the parallel solution and gradient evaluation performance, we perform a structural analysis and gradient evaluation for a large transport aircraft wing with over 5.44 million unknowns.
Gradient evaluation of implicit functions is presented so that a gradient-based method can be used for optimization.
They require the likelihood function and its gradient evaluation (score), and might demand the Fisher information matrix (FIM) computation.
Therefore, there is a need for solution and gradient evaluation methods that scale well with the number of design variables, constraints, and processors.
This paper seeks to introduce and analyse the development of the Gradient Evaluation Framework (GEF) to facilitate evaluation of policy actions for their current or future use in terms of their 'gradient friendliness'.
The sequential quadratic programming algorithm was used for solving the constrained nonlinear optimization problem, and the modal sensitivity analysis was considered for the modal prediction of the modified design, as well as for the gradient evaluation of the objective function and system's constraints, throughout the optimization.
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The aim is to show in particular how to reduce the complexity of sensitivity evaluation using incomplete gradient evaluations.
The evaluation of the gradients is reduced to an integral around the boundary to circumvent hurdles posed by adjoint-based gradient evaluations on unstructured meshes.
The performance of the multigrid optimization technique is compared against the single-grid optimization method in terms of equivalent function and gradient evaluations.
The simplest variant of the algorithm, which requires 4 gradient evaluations per cycle, converges 2× 4× faster than the LBFGS algorithm, depending on the size of the system.
The reduced gradient evaluations provide major computational savings for unstructured grids and its accuracy and use for canonical and industrial problems is a major contribution of this study.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com