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Extra resources for ANSYS 5.7 Thermal Analysis Guide. Решение задач теплообмена

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2. Nonlinear operator equations To formulate the nonlinear equations for the inverse boundary value problem, we introduce single-layer potential operators in terms of the fundamental solution *{x,y):=±H£\\x-y\), x^y, to the Helmholtz equation in IR2 with the Hankel function HQ of order zero and of the first kind. Denote by Sj : L 2 (r 0 ) - L2(Tj), j =0,1, the single-layer operators defined by (S;fc)(x):= / $>{x,y)h{y)ds{y), Jr0 xeTj. (8) 42 Further, in terms of the given data / and g onTi, we define the combined double- and single-layer potential zeUl2^.

F^-^xG(-,^||L2(r) 0 and

V. Lindell, Methods for Electromagnetic Field Analysis, 2nd ed, Oxford University Press, Oxford, (1995). N O N L I N E A R I N T E G R A L EQUATIONS IN I N V E R S E OBSTACLE SCATTERING 0 . I V A N Y S H Y N A N D R. K R E S S Institut E-mail: fur Numerische und Angewandte Mathematik Universitat Gottingen 37083 Gottingen, Germany kress@math. uni-goettingen. de, ivanyshy@math. uni-goettingen. de We present a novel solution method for inverse obstacle scattering problems for time-harmonic waves based on a pair of nonlinear and ill-posed integral equations for the unknown boundary that arises from the reciprocity gap principle.

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