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

Authors

  • Leonardo B. L. Santos Instituto Nacional de Pesquisas Espaciais
  • Leonardo D. Chiwiacoswsky Universidade do Vale do rio dos Sinos - UNISINOS
  • Haroldo F. Campos Velho Instituto Nacional de Pesquisas Espaciais

DOI:

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

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.

Author Biographies

Leonardo B. L. Santos, Instituto Nacional de Pesquisas Espaciais

Programa de Mestrado em Computação Aplicada

Leonardo D. Chiwiacoswsky, Universidade do Vale do rio dos Sinos - UNISINOS

Programa Interdisciplinar de Pós-graduação emComputação Aplicada - PIPCA

Haroldo F. Campos Velho, Instituto Nacional de Pesquisas Espaciais

Laboratório Associado de Computação e MatemáticaAplicada

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Published

2013-11-24

How to Cite

Santos, L. B. L., Chiwiacoswsky, L. D., & Campos Velho, H. F. (2013). Genetic Algorithm and Variational Method to Identify Initial Conditions: Worked Example in Hyperbolic Heat Transfer. Trends in Computational and Applied Mathematics, 14(2), 265–276. https://doi.org/10.1590/S2179-84512013005000012

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Original Article