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2.Numericalproblemanalysis
Theequation(2.29)isnon-linearduetotheconductivityγ.Theexpansionintothe
Taylorseriesaroundthepointγ=γwilltaketheform
where:∆γ=γ-γk,F′′Hesse’smatrix.
Thismatrixhasbeenapproximatedbytheexpression
(2.31)
(2.32)
Aftersubstitutingtheequation(2.29)and(2.32)intotheequation(2.31)andequat-
ingtozeroandmultiplyingby[J′]T:
(2.33)
Inthek-thiterationforthecurrentestimation,γkmaydeterminethecorrection∆γk
andthevectorvaluesγforthenextiteration
(2.34)
where:αϵ〈0.1,1.0〉
Foragivenpairofpotentials,themeasurementdatais:
(2.35)
where:fj–calculatedvoltagevector,
T–transformationmatrix,
uej–thevectorofpotentialsintheboundarynodesofthenetworkinwhich
themeasuringelectrodesarelocated.
Afterdifferentiationofequation(2.35)
(2.36)
Sensitivityofnodepotentials,duetothechangeinthevalueofmaterialcoefficients,
maybethedeterminedbydifferentiationoftheequationofstate:
(2.37)
where~meansthatthevariableisaconstantvalueinthedifferentiationprocess.
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