This paper presents an abstract analysis of bounded variation (BV) methods for ill-posed operator equations Au = z. Let T(u) def = kAu ? zk 2 + J(u); where the penalty, or \regularization", parameter > 0 and the functional J(u) is the BV norm or seminorm of u, also known as the total variation of u. Under mild restrictions on the operator A and the functional J(u), it is shown that the functional T(u) has a unique minimizer which is stable with respect to certain perturbations in the data z, the operator A, the parameter , and the functional J(u). In addition, convergence results are obtained which apply when these perturbations vanish and the regularization parameter is chosen appropriately.

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Abstract-A hybrid method to calculate mutual coupling of electric or magnetic current elements on a cylindrically layered structure using closed-form Green's functions is presented. When ρ = ρ and φ is not very close to φ , closed-form Green's functions are employed in the calculation of MoM matrix entries. When both ρ = ρ and φ = φ , series representation of the spectral domain Green's functions do not converge, therefore closed-form Green's functions can not be employed. In that case MoM matrix entries are evaluated using the proposed hybrid method. The technique is applied to both printed dipoles and slots placed on a layered cylindrical structures. The computational efficiency of the analysis of mutual coupling of printed elements on cylindrically layered geometries is increased with the use of proposed hybrid method which employs closed-form Green's functions.

This paper presents a multiscale fluid model based on mesoscale dynamics and viscous fluid equations as a generic tool for digital marbling purposes. The model uses an averaging technique on the adaptation of a stochastic mesoscale model to obtain the effect of fluctuations at different levels. It allows various user controls to simulate complex flow behaviors as in traditional marbling techniques, as well as laminar and turbulent flows. Material transport is based on an improved advection solution to be able to match the highly detailed, sharp fluid interfaces in marbling patterns. In the transport model, two reaction models are introduced to create different effects and to simulate density fluctuations.