Semi-analytical sensitivity analysis for nonlinear transient problems

Felipe Fernandez, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; unfortunately, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

Original languageEnglish (US)
Pages (from-to)2387-2410
Number of pages24
JournalStructural and Multidisciplinary Optimization
Issue number6
StatePublished - Dec 1 2018


  • Adjoint
  • Direct
  • Dynamic
  • Non-linear
  • Semi-analytical
  • Sensitivity analysis

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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