Title

Explicit Calculation Of Smoothed Sensitivity Coefficients For Linear Problems

Keywords

Inverse problem; Sensitivity coefficient

Abstract

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. © 2003 John Wiley and Sons, Ltd.

Publication Date

5-14-2003

Publication Title

International Journal for Numerical Methods in Engineering

Volume

57

Issue

2

Number of Pages

143-167

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1002/nme.671

Socpus ID

17144461752 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/17144461752

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