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Explicit calculation of smoothed sensitivity coefficients for linear problems
Author(s) -
Białecki R. A.,
Divo E.,
Kassab A. J.,
Ait Maalem Lahcen R.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.671
Subject(s) - boundary value problem , sensitivity (control systems) , boundary (topology) , neumann boundary condition , mathematics , dirichlet boundary condition , mathematical analysis , robin boundary condition , inverse problem , boundary knot method , term (time) , inverse , function (biology) , finite element method , boundary element method , geometry , physics , quantum mechanics , electronic engineering , evolutionary biology , biology , engineering , thermodynamics
A technique of explicit calculation of sensitivity coefficients based on the approximation of the retrieved function by a linear combination of trial functions of compact support is presented. The method is applicable to steady state and transient linear inverse problems where unknown distributions of boundary fluxes, temperatures, initial conditions or source terms are retrieved. The sensitivity coefficients are obtained by solving a sequence of boundary value problems with boundary conditions and source term being homogeneous except for one term. This inhomogeneous term is taken as subsequent trial functions. Depending on the type of the retrieved function, it may appear on boundary conditions (Dirichlet or Neumann), initial conditions or the source term. Commercial software and analytic techniques can be used to solve this sequence of boundary value problems producing the required sensitivity coefficients. The choice of the approximating functions guarantees a filtration of the high frequency errors. Several numerical examples are included where the sensitivity coefficients are used to retrieve the unknown values of boundary fluxes in transient state and volumetric sources. Analytic, boundary‐element and finite‐element techniques are employed in the study. Copyright © 2003 John Wiley & Sons, Ltd.