Preconditioned fully implicit PDE solvers for monument conservation - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: Mathematical models for the description, in a quantitative way, of thedamages induced on the monuments by the action of specific pollutants are oftensystems of nonlinear, possibly degenerate, parabolic equations. Although somethe asymptotic properties of the solutions are known, for a short window oftime, one needs a numerical approximation scheme in order to have aquantitative forecast at any time of interest. In this paper a fully implicitnumerical method is proposed, analyzed and numerically tested for parabolicequations of porous media type and on a systems of two PDEs that models thesulfation of marble in monuments. Due to the nonlinear nature of the underlyingmathematical model, the use of a fixed point scheme is required and every stepimplies the solution of large, locally structured, linear systems. A specialeffort is devoted to the spectral analysis of the relevant matrices and to thedesign of appropriate iterative or multi-iterative solvers, with specialattention to preconditioned Krylov methods and to multigrid procedures.Numerical experiments for the validation of the analysis complement thiscontribution.



Author: Matteo Semplice

Source: https://arxiv.org/







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