1,959 research outputs found
Prehistoric archaeological research project in northern Zakynthos. The investigations in the ionian island and the provenance of the Zakinthos obsidian
No full textRICERCHE ARCHEOLOGICHE
Claudio Giardino Archaeological Prehistoric Research Project in Northern
Christina Merkouri Zakynthos. The investigations in the Ionian island
Giovanni Paternoster, Tiziana Zappatore University of Salento and Ephoria of Zakyntho
Buccione, R., Rizzo G., Paternoster M., Mongelli G., 2024. LucAS project: Evaluation of geochemical-mineralogical background in environmental matrices for the assessment of health risk Abstract. 2nd SOGEI Conference Perugia, 1 ǀ 4 July 2024.
No full textRizzo, G., Buccione, R., Paternoster, M., 2021. Natural sources of trace elements in the atmosphere and their influence on human health. Dust 2021, IV International Conference on Atmospheric Dust, Monopoli, Italy, 4-7 October 2021.
No full textBuccione, R., Paternoster, M., Rizzo, G., Mongelli, G., 2022. Trace elements in lake sediments: The case of the Pietra del Pertusillo reservoir (Basilicata region, Southern Italy). Clays application & valorisation – (CAV 2022) International Joint Conference, Hammamet, Tunisia December 17-21.
No full textNumerical solution of Hamiltonian problems by G-symplectic integrators
No full textIt is the purpose of this talk to analyze the employ of General Linear Methods (GLMs) for the numerical integration of Hamiltonian problems. Indeed, even if the numerical flow generated by a GLM cannot be symplectic, Butcher recently introduced in [1] a concept of near conservation, denoted as G-symplecticity, for such methods which, properly combined with other desirable features (such as symmetry and boundedness of parasitic components),
allows to achieve a very accurate long time conservation of the Hamiltonian. We also focus our attention on the connections between the order of convergence of a GLM and the observable Hamiltonian deviation, by employing the theory of B-series [3]. Moreover, we derive a semi-implicit GLM [2] which results competitive with respect to symplectic Runge-Kutta methods. Numerical results on a selection of Hamiltonian problems are presented, confirming the structure-preserving capability of G-symplectic integrators. References [1] J.C. Butcher, Numerical methods for Ordinary Differential Equations, Second Edition, Wiley, Chichester, 2008. [2] R. D’Ambrosio, G. De Martino and B. Paternoster, Construction of nearly conservative multivalue numerical methods for Hamiltonian problems, Comm. Appl. Ind. Math, doi: 10.1685/journal.caim.412 (2013). [3] R. D’Ambrosio, G. De Martino and B. Paternoster, Numerical integration of Hamiltonian problems by G-symplectic integrators, submitted
Exponentially-fitted quadrature methods for evolution problems with periodic solution
No full textThe interest for numerical solution of physical and biological problems with oscillating and/or periodic
behaviour requires the use of special-purpose methods. Examples include the electromagnetic scattering, the response of nonlinear circuits to a periodic input and the evolution of an age-structuredpopulation. These problems are characterized by either infinite integrals where the integrand function is oscillatory function, or by Volterra integral equations of type with periodic solution. By exploting the Exponential Fitting theory [1, 2, 3, 4,
5], a new class of quadrature rules, that are a generalization of the usual Gauss-Laguerre formulae, for
problem (1) and a new direct quadrature (DQ) method for problem (2) are derived, respectively. Two extra problems appear in the context of building the exponentially-fitted (ef ) DQ method. The first one is the construction of a two-nodes ef quadrature rule of Gaussian type, that is a generalization of the usual two-nodes Gauss-Legendre formula, on which the DQ method is based. The second problem is the building of a suitable ef interpolation technique on four points which preserves the order of
convergence of the overall method. These works are in collaboration with L. Gr. Ixaru (National Institute of Physics and Nuclear Engineering, Bucharest, Romania), B. Paternoster, A. Cardone and D. Conte (University of Salerno).
References
[1] Ixaru, L.Gr.; Vanden Berghe, G., Exponential fitting, Kluwer Academic Publishers, Dordrecht
(2004).
[2] A. Cardone, B. Paternoster, G. Santomauro, Exponential fitting quadrature rule for functional equations, AIP Conference Proceedings 1479 (2012) 1169-1172.
[3] A. Cardone, L. Gr. Ixaru, B. Paternoster, G. Santomauro, Ef-Gaussian direct quadrature methods
for Volterra integral equations with periodic solution, Mathematics and Computers in Simulation (submitted).
[4] D. Conte, B. Paternoster, G. Santomauro, An exponentially fitted quadrature rule over unbounded
intervals, AIP Conference Proceedings 1479 (2012) 1173-1176.
[5] D. Conte, L. Gr. Ixaru, B. Paternoster, G. Santomauro, Gauss-Laguerre quadrature rule for oscillatory integrands, Computational and Applied Mathematics (submitted)
Adapted discretization of evolutionary problems by non-polynomially fitted numerical methods
No full textThe talk is devoted to the discretization of selected evolutionary problems generating periodic
wavefronts [5] and aims to explain the benefits gained by adapting the numerical scheme to the
problem. Such an adaptation is carried out by merging the a-priori known qualitative information
on the problem, as well as the structure of the vector field itself, into the numerical scheme.
53
Particular emphasis will be given to advection-reaction-diffusion problems, for which the adaptation
in space is developed by means of a finite difference scheme based on trigonometrical basis
functions [3], rather than on algebraic polynomials which could strongly reduce the stepsize in
order to accurately reproduce the prescribed oscillations of the exact solution. The adaptation
in time takes into account that the spatially discretized problem is characterized by a vector
field consisting in stiff and nonstiff terms, hence it makes sense to adopt an implicit-explicit
(IMEX) time integration, which implicitly integrate only the stiff constituents, while the nonstiff
part is computed explicitly. Clearly, the employ of non-polynomial basis functions makes
the coefficients of the numerical method dependent on unknown parameters (i.e. the frequency
of the oscillations), which need to be properly estimated [4]; the proposed estimation relies
on a minimization procedure of the local truncation error that is carried out a-priori, without
affecting the computational cost of the integration. A rigorous analysis on the stability and
accuracy properties of the overall method is presented, together with some numerical tests, in
order to highlight the effectiveness of the approach. The introduced technique also covers the
case of periodic dynamics generated by evolutionary problems with memory [1, 2], discretized
in terms of non-polynomially fitted quadrature methods able to accurately reproduce the oscillatory
behavior with a reduced computational cost with respect to their analogous polynomial
version, when a good estimate of the unknown frequency is provided. Stability issues for such
a discretization are also addressed. References
[1] Cardone, A., Ixaru, L.Gr. and Paternoster, B. Exponential fitting direct quadrature methods
for Volterra integral equations, Numer. Algorithms 55(4), 467–480 (2010).
[2] Cardone, A., Ixaru, L.Gr., Paternoster, B. and Santomauro, G. Ef-gaussian direct quadrature
methods for Volterra integral equations with periodic solution, Math. Comput. Simul.,
110, 125–143 (2015).
[3] D’Ambrosio, R., Moccaldi, M. and Paternoster, B. Adapted numerical methods for
advection-reaction-diffusion problems generating periodic wavefronts. Comput. Math. Appl.
74(5), 1029–1042 (2017).
[4] D’Ambrosio, R., Moccaldi, M. and Paternoster, B. Parameter estimation in IMEXtrigonometrically
fitted methods for the numerical solution of reaction-diffusion problems.,
Comput. Phys. Commun. 226, 55–66 (2018).
[5] Perumpanani, A.J., Sherratt, J.A. and Maini, P.K. Phase differences in reaction-diffusionadvection
systems and applications to morphogenesis, J. Appl. Math. 55, 19–33 (1995)
Buccione, R., Fortunato, E., Paternoster, M., Rizzo, G., Sinisi, R., Summa, V., Mongelli, G. 2020. Geochemistry and mineralogy of lacustrine and fluvio-lacustrine sediments: The case of the Pietra del Pertusillo fresh-water reservoir (Basilicata region, Southern Italy). EGU2020-9588 EGU General Assembly 2020, May 4-8.
No full textCisullo C., Zummo F., Buccione R., Paternoster M. & Mongelli G. 2023. Distribution of chemical and physical parameters of the water column of Lago Piccolo, Mount Vulture hydro-mineral basin (southern Italy). Congresso congiunto SIMP-SGI-SOGEI-AIV “The Geoscience paradigm: resources, risk and future perspectives”, 19-21 Settembre 2023, Potenza.
No full textHigh order exponentially fitted methods for periodic Volterra integral equations
No full textVolterra integral equations with periodic solution model a number of periodic phenomena with memory, e.g. the spread of seasonal epidemics. An efficient and accurate numerical solution of these equations may be found by means of special purpose methods, which exploit the a priori knowledge of the qualitative behavior of the solution. On this direction, we propose exponentially-fitted direct quadrature methods of high order. The coefficients of these methods depend on the frequency of the problem, to reduce the error when
periodic problems are treated and an estimate of the frequency is available. In this poster we present the construction and analysis of these methods, and illustrate their performances on some significant test problems.
REFERENCES
[1] A. Cardone, L.Gr. Ixaru and B. Paternoster. Exponential fitting direct quadrature methods for Volterra integral equations. Numer. Algorithms, 55 (4), 2010, 467 – 480.
[2] A. Cardone, L.Gr. Ixaru, B. Paternoster and G. Santomauro. Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution. Math. Comput. Simul., 110 2015, 125 – 143.
[3] L.Gr. Ixaru and G. Vanden Berghe. Exponential fitting. Kluwer Academic Publishers, Dordrecht, 2004
- …
