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Sensitivity computations in higher order continuation methods. (English) Zbl 07159256
Summary: Sensitivity analysis is a key tool in the study of the relationships between the input parameters of a model and the output solution. Although sensitivity analysis is extensively addressed in the literature, little attention has been brought to the methodological aspects of the sensitivity of nonlinear parametric solutions computed through a continuation technique. This paper proposes four combinations of sensitivity analysis with continuation and homotopy methods, including sensitivity analysis along solution branches or at a particular point. Theoretical aspects are discussed in the higher order continuation framework Diamant. The sensitivity methods are applied to a thermal ignition problem and some free vibration problems. Remarkable eigenvalue maps are produced for the complex nonlinear eigenvalue problems.
MSC:
65 Numerical analysis
74 Mechanics of deformable solids
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