Genetic Algorithm and Variational Method to Identify Initial Conditions: Worked Example in Hyperbolic Heat Transfer

Leonardo B. L. Santos, Leonardo D. Chiwiacoswsky, Haroldo F. Campos Velho

Abstract


The identification of initial condition from measurements at a giventime is a hard inverse problem, and it can be applied to evaluate the robustnessof inversion strategies. Relevant scientific issues are related with estimation of initialcondition: cosmology and data assimilation are good examples. Two differentinversion methods are employed to identify initial condition for parabolic and hyperbolicdifferential equations: Genetic Algorithm and Variational Method. Theheat transfer process was selected to be used in our tests. A harder inversion isverified on hyperbolic case. Both inverse methods were effective: the numericaldifference between the inverse solution was not significant, although the variationalmethod presented a smoother inversion. The inversion obtained with the variationalmethod presented lower processing time.

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DOI: https://doi.org/10.1590/S2179-84512013005000012

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