Aurelian Nicola

A general extending and constraining procedure for linear iterative methods

Algebraic reconstruction techniques (ARTs), on both their successive and simultaneous formulations, have been developed since the early 1970s as efficient ‘row-action methods’ for solving the image-reconstruction problem in computerized tomography. In this respect, two important development directions were concerned with, first, their extension to the inconsistent case of the reconstruction problem and, second, their combination with constraining strategies, imposed by the particularities of the reconstructed image. In the first part of this paper, we introduce extending and constraining procedures for a general iterative method of an ART type and we propose a set of sufficient assumptions that ensure the convergence of the corresponding algorithms. As an application of this approach, we prove that Cimminos simultaneous reflection method satisfies this set of assumptions, and we derive extended and constrained versions for it. Numerical experiments with all these versions are presented on a head phantom widely used in the image reconstruction literature. We also consider hard thresholding constraining used in sparse approximation problems and apply it successfully to a 3D particle image-reconstruction problem.

Preconditioned Conjugate Gradient and Multigrid Methods for Numerical Solution of Multicomponent Mass Transfer Equations II. Convection-Diffusion-Reaction Equations

This work continues our previous analysis concerning the performances of the nonlinear multigrid (the Full Approximation Storage algorithm) method and modified Picard preconditioned conjugate gradient methods for the numerical solution of the two-dimensional, steady-state, multicomponent mass transfer equations. The present test problems are steady-state, linear and nonlinear, convection-diffusion-reaction equations. The upwind finite difference method was used to discretize the mathematical model equations. The numerical results obtained show good numerical performances.

Splitting methods for the numerical solution of multi-component mass transfer problems

Abstract In a multi-component system the diffusion of a certain species is dictated not only by its own concentration gradient but also by the concentration gradient of the other species. In this case, the mathematical model is a system of strongly coupled second order elliptic/parabolic partial differential equations. In this paper, we adapt the splitting method for numerical solution of multi-component mass transfer equations, with emphasis on the linear ternary systems. We prove the positive definiteness assumptions for the discrete problem matrices which ensure the stability of the method. The numerical experiments performed confirmed the theoretical results, and the results obtained show good numerical performances.

Numerical solution of the parabolic multicomponent convection–diffusion mass transfer equations by a splitting method

ABSTRACT The splitting method used in a previous study for the numerical solution of mass transfer equations in ternary systems is generalized to mixtures with n-components. The diffusion coefficients are considered constant. Theoretical results about the stability of the method are presented, as well as numerical simulations for mixtures with n = 4, 5, and 6. The numerical experiments confirmed the theoretical results and show good numerical performances. Moreover, multicomponent diffusion effects without an imposed concentration gradient are investigated for mixtures with n = 4, 5, and 6 components.

Weaker hypotheses for the general projection algorithm with corrections

Abstract In an earlier paper [J. of Appl. Math. and Informatics, 29(3-4)(2011), 697-712] we proposed a general projection-type algorithm with corrections and proved its convergence under a set of special assumptions. In this paper we prove convergence of this algorithm under a much weaker set of assumptions. This new framework gives us the possibility to obtain as a particular case of our method the two-step algorithm analysed in [B I T, 38(2)(1998), 275-282].