Download PDF by Robert Beauwens, Martin Berzins: Applied Numerical Mathematics 61 (January 2011)

By Robert Beauwens, Martin Berzins

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We will demonstrate the computational advantage of this simple idea in the following section. 5. Applications to electromagnetic scattering problems To evaluate the benefits of the techniques discussed in the above for problems of a more practical character, we consider electromagnetic scattering by a two-dimensional cylinder with holes where the size, the location, and ultimately, the number of holes, are considered as uncertain and described by continuous and discrete random variables. 32 M. Liu et al.

Wang / Applied Numerical Mathematics 61 (2011) 38–52 U = (u 1 , u 2 , . . , u N −1 )T , 41 V = ( v 1 , v 2 , . . , v N −1 )T , T G (U ) = g 1 (u 1 ), g 2 (u 2 ), . . , g N −1 (u N −1 ) , T T (U ) = T (u 1 ), T (u 2 ), . . , T (u N −1 ) , T H = T (α ) + h2 g (0, α ) − γ0 T (α ) /12, 0, . . , 0, T (β) + h2 g (1, β) − γ N T (β) /12 . 13) T (U ) = V . This is a coupled system of a nonlinear algebraic equation and a nonlinear functional equation. To analyze it and develop a linear monotone iterative algorithm for its solution, we review some well-known properties about the matrices J and B.

18) that V = V . This implies T (U ) − T (U ) = 0 which ensures U = U . This proves (U , V ) = (U , V ). 1. 1). 14) becomes the one in [46]. 3) provides a linear monotone iterative algorithm. 2. 10) that for each m, (U (m) , V (m) ) is an upper bound of the maximal solution (U , V ), while (U (m) , V (m) ) gives a lower bound of the minimal solution (U , V ). Moreover, these bounds are improved, step-by-step, as m increases. If (U , V ) = (U , V ) (≡ (U ∗ , V ∗ )) then they become improved upper and lower bounds of (U ∗ , V ∗ ).

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Applied Numerical Mathematics 61 (January 2011) by Robert Beauwens, Martin Berzins


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