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Reconstruction of Geophysical Layers with Shape Optimization and Level Set Methods
Author(s) -
Papadopoulos Dimitrios,
Herty Michael,
Behr Marek,
Rath Volker
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010286
Subject(s) - level set (data structures) , level set method , shape optimization , boundary (topology) , initialization , function (biology) , computation , mathematical analysis , domain (mathematical analysis) , heat flux , mathematics , mathematical optimization , computer science , algorithm , heat transfer , physics , mechanics , finite element method , segmentation , artificial intelligence , evolutionary biology , biology , image segmentation , thermodynamics , programming language
A shape optimization method is used to reconstruct the unknown shape of geophysical layers from boundary heat flux measurements by the use of adjoint fields and level sets. The identification of the shape of the geophysical layers by boundary heat flux measurements is necessary for the efficient use of geothermal energy. The method of speed is used to calculate the shape sensitivities, and the continuous adjoint approach is followed for the computation of the shape derivatives. The unknown shape is described with the help of the level set function; the advantage of the shape function is that no mesh movement or remeshing is necessary, but an additional Hamilton‐Jacobi equation has to be solved. This equation is solved in an artificial time, where the velocity represents the movement in the direction of the normal vector of the interface. For large optimization steps, re‐initialization of the level set function is also necessary, in order to keep the magnitude of the level set function near unity and also to smooth the level set function. Numerical results are given for measured heat fluxes on the boundary of the domain for different time steps and conductivity ratios. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)