Pubblicazioni

PUBLICATIONS

Here is a list of papers on electromagnetism 

• D. Funaro, A Full Review of the Theory of Electromagnetism, (2005). arXiv:0505068. Preliminary version of the book: Electromagnetism and the Structure of Matter.
• D. Funaro, Electromagnetism and the Structure of Matter, World-Scientific, Singapore, 2008. https://doi.org/10.1142/6853 
• D. Funaro, The Fractal Structure of Matter and the Casimir Effect, Preprint (2009). arXiv:0906.1874v1 .
• D. Funaro, Electromagnetic Radiations as a Fluid Flow, Preprint (2009). arXiv:0911.4848v1 .
• C. Chinosi, L. Della Croce, D. Funaro, Rotating Electromagnetic Waves in Toroid-Shaped Regions, International Journal of Modern Physics C, Vol. 21, n. 1 (2010), pp. 11-32. DOI: 10.1142/S0129183110014926, arXiv:1002.1206v1 .
• D. Funaro, Numerical Simulation of Electromagnetic Solitons and their Interaction with Matter, J. Sci. Comput., Vol. 45, 1 (2010), p. 259. DOI 10.1007/s10915-009-9338-5 , arXiv:0912.2639v1 .
• D. Funaro, A Lagrangian for Electromagnetic Solitary Waves in Vacuum, Preprint (2010). arXiv:1008.2103v1 .
•  D. Funaro, On the Near-field of an Antenna and the Development of New Devices, Preprint (2012). arXiv:1203.1229v1 .
• D. Funaro, From Photons to Atoms – The Electromagnetic Nature of Matter, Preprint (2012). arXiv:1206.3110v1 . Preliminary version of the book: From Photons to Atoms – The Electromagnetic Nature of Matter, DOI: 10.1142/11383 .
• D.Funaro, Charging Capacitors According to Maxwell’s Equations: Impossible, Les Annales de la Fondation Louis de Broglie, Vol. 39 (2014). ISSN 0182-4295 ,   arXiv:1412.6005v1  .
• D. Funaro, Trapping Electromagnetic Solitons in Cylinders, Mathematical Modelling and Analysis, Volume 1, Issue 19(2014). DOI10.3846/13926292.2014.892904, arXiv:1304.2287v1 .
• D. Funaro, E. Kashdan, Simulation of Electromagnetic Scattering with Stationary or Accelerating Targets, International Journal of Modern Physics C, Vol. 26, n. 7 (2015), pp. 1-16. DOI: 10.1142/S0129183115500758 , arXiv:1305.5116v1 .
• D. Funaro, A Model for Ball Lightning Derived from an Extension of the Electrodynamics Equations,  Proceedings of VI International Conference on Atmosphere, Ionosphere, safety, Kaliningrad 2018, Vol. I, p. 307, ISBN 978-5-9971-0491-7 , arXiv:1806.05555 .
• D. Funaro, High Frequency Electrical Oscillations in Cavities, Mathematical Modelling and Analysis, Vol. 23, n.3 (2018), pp. 345-358, DOI: 10.10386/mma.2018.021 , arXiv:1807.06421 .
• D. Funaro, From Photons to Atoms, The Electromagnetic Nature of Matter World-Scientific, Singapore, 2019. https://doi.org/10.1142/11383
• D. Funaro, Electromagnetic Waves in Annular Regions, Appl. Sci., Vol. 10, n.5 (2020), p. 1780, DOI: 10.3390/app10051780.
• A. Chiolerio, L. Diazzi, D. Funaro, Highly Directive Biconic Antennas Embedded in a Dielectric, Appl. Sci., Vol. 10, n.24 (2020), p. 8828, DOI: 10.3390/app10248828.
• D. Funaro,  A. Chiolerio, Tests on High-Directivity Unconventional Biconical Type Antennas,  arXiv:2202.01887 .
• D. Funaro, Ball Lightning as Plasma Vortexes: A Reinforcement of the Conjecture, Appl. Sci., Vol. 12, n.7 (2022), p. 3451, DOI: 10.3390/app12073451 .
• D. Funaro, The Space-Time Outside a Pulsating Charged Sphere, Appl. Sci., Vol. 12, n. 14 (2022), p. 7290, DOI: 10.3390/app12147290 .
• L. Fatone, D. Funaro, Electromagnetic Fields Simulating a Rotating Sphere and its Exterior with Implications to the Modeling of the Heliosphere, Math. Meth. Appl. Sci., 1-12 (2022),  DOI: 10.1002/mma8621 , arXiv:2106.05851 .
• D. Funaro, The Impact of a Pervasive Electrodynamical Background on Biological Interactions, Preprint (2022), hal.science/hal-03899223v1.
• D. Funaro, A. Chiolerio, An Efficient Ring-Shaped Electromagnetic Thruster, Inventions, Vol. 8, n. 2 (2023), p. 51, DOI: 10.3390/inventions8020051, hal.science/hal-03843874.
• D. Funaro, Spacetime Deformations of Electromagnetic Nature are Far from Negligible, Preprint (2023), This essay received an Honorable Mention in the 2023 Essay Competition of the Gravity Research Foundation, hal.science/hal-04095803v1.
• D. Funaro, A Dynamic Representation of mRNA Nucleotides Clarifies the Conundrum of Codon Redundancy, Biophysica, Vol. 3, n. 3 (2023), p. 548-557, DOI: 10.3390/biophysica3030037, hal.science/hal-04098442v1.
• L. Fatone, D. Funaro, Electromagnetic Displacements Rotating Inside an Annular Region, in Spectral and High Order Methods for Partial Differential Equations (ICOSAHOM Conference, Vienna, Austria, July 12-16, 2020+1), LNCSE, Springer, Vol. 137 (2023), p. 279-290. DOI: 10.1007/978-3-031-20432-6
• D. Funaro, Newtonian Forces Exerted by Electromagnetic Waves Traveling into Matter, International J. Theoretical Physics, Vol. 62, n. 231 (2023), DOI: 10.1007/s10773-023-05491-w, Nature Content Sharing View-only Version, hal.science/hal-03950038v1
• D. Funaro, Light and Matter, Two Sides of the Same Coin, Cambridge Scholars Publishing, Newcastle upon Tyne, 2024. ISBN13: 978-1-0364-0598-4 

Here is a list of old and recent papers on numerical analysis and related subjects

• D. Funaro, Error Estimates for Spectral Approximation of Linear Advection Equations over an Hypercube, Calcolo, vol. XX, fasc. III (1983), pp. 337-353.
• D. Funaro, Analysis of the Du Fort-Frankel Method for Linear Systems, Mathematical Modelling and Numerical Analysis, Vol. 19, n. 3 (1985), pp. 429-441.
• D. Funaro, A Multidomain Spectral approximation of Elliptic equations, Numerical Methods for P.D.E., n. 2 (1986), pp. 187-205.
• D. Funaro, A Preconditioning Matrix for the Chebyshev Differencing Operator, SIAM J. Numer. Anal., Vol. 24, n. 5 (1987), pp. 1024-1031.
• C. Canuto, D. Funaro, The Schwarz Algorithm for Spectral Methods, SIAM J. Numer. Anal., Vol. 25, n. 1 (1988), pp. 24-40.
• D. Funaro, Domain Decomposition Methods for Pseudo-Spectral Approximations. Part One: Second Order Equations in One Dimension, Numerische Mathematik, n. 52 (1988), pp. 329-344.
• D. Funaro, Computing the Inverse of the Chebyshev Collocation Derivative, SIAM J. Sci. Stat. Comp., Vol. 9, n. 6 (1988), pp. 1050-1057.
• D. Funaro, A. Quarteroni, P. Zanolli, An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods, SIAM J. Numer. Anal., Vol. 25, n. 6 (1988), pp. 1213-1236.
• D. Funaro, D.Gottlieb, A New Method of Imposing Boundary Conditions for Hyperbolic Equations, Mathematics of Computation, Vol. 51, n. 184 (1988), pp. 599-613.
• D. Funaro, E. Rothman, Preconditioning Matrices for the Pseudo-Spectral Approximation of First Order Operators, in Finite Element Analysis in Fluids (T. J. Chung & G. R. Karr Eds., UAH Press, Huntsville 1989), pp. 1458-1463.
• D. Funaro, Convergence Analysis for Pseudo Spectral Multidomain Approximations of Linear Advection Equations, IMA J. Numer. Anal., n. 10 (1990), pp. 63-74.
• D. Funaro, A Variational Formulation for the Chebyshev Pseudospectral Approximation of Neumann Problems, SIAM J. Numer. Anal., Vol. 27, n. 3 (1990), pp. 695-703.
• D. Funaro, Computational Aspects of Pseudospectral Laguerre Approximations, Applied Numerical Mathematics, n. 6 (1989/90), pp. 447-457.
• D. Funaro, Inverse Inequalities for Chebyshev Approximations in L-infinity Norms, Appl. Math. Letters, Vol. 3, n. 3 (1990), pp. 39-41.
• D. Funaro, W. Heinrichs, Some Results about the Pseudospectral Approximation of one-dimensional fourth-order Problems, Numer. Math., 58 (1990), pp. 399-418.
• D. Funaro, Pseudo Spectral Approximation of a P.D.E. defined on a Triangle, Applied Mathematics and Computations, Vol. 42, n. 2 (1991), pp. 121-138.
• D.Funaro, D. Gottlieb, Convergence Results for Pseudospectral Approximations of Hyperbolic Systems by a Penalty-type Boundary Treatment, Mathematics of Computation, Vol. 57, n. 196 (1991), pp. 585-596.
• D. Funaro, O. Kavian, Approximation of Some Diffusion Evolution Equation in Unbounded Domains by Hermite Functions, Mathematics of Computation, Vol. 57, n. 196 (1991), pp. 597-619.
• D. Funaro, Polynomial Approximation of Differential Equations, Lecture Notes in Physics, Volume 8, Springer-Verlag, Heidelberg 1992.
• D. Funaro, Approximation by the Legendre Collocation Method of a Model Problem in Electrophysiology, Journal of Computational and Applied Math., 43 (1992), pp. 261-271.
• V. Comincioli, E. D’Angelo, D. Funaro, P. Rossi, A. Torelli, A Mathematical Model of Potential Spreading along Neuron Dendrites of Cerebellar Granule Cells, Applied Math. and Computation, Vol. 59, n. 1 (1993), pp. 73-87.
• D. Funaro, A new Scheme for the Approximation of Advection-Diffusion Equations by Collocation, SIAM J. Numer. Anal., Vol. 30, n. 6 (1993), pp. 1664-1676.
• C. De Veronico, D. Funaro, G. Reali, A novel Numerical Technique to investigate Nonlinear Guided Waves: Approximation of Nonlinear Schroedinger Equation by Nonperiodic Pseudospectral Methods, Numerical Methods for PDE, Vol. 10, n. 6 (1994), pp. 667-675.
• D. Boffi, D. Funaro, An Alternative Approach to the Analysis and the Approximation of the Navier-Stokes Equations, J. of Scientific Computing, Vol. 9, No. 1 (1994), pp. 1-16.
• D. Funaro, A Fast Solver for Elliptic Boundary-Value Problems in the Square, Computer Methods in Applied Mechanics and Engineering, 116 (1994), pp. 253-255.
• D. Funaro, Spectral Elements in the Approximation of Boundary-Value Problems in Complex Geometries, Applied Numerical Mathematics, Vol. 15, n. 2 (1994), pp. 201-205.
• D. Funaro, Some Remarks about the Collocation Method on a Modified Legendre Grid, Computers Math. Applic., Vol. 33, n. 1/2 (1997), pp. 95-103.
• D. Funaro, Improving the Performances of Implicit Schemes for Hyperbolic Equations, Journal of Scientific Computing, Vol. 12, n. 4 (1997), pp. 385-394.
• D. Funaro, Spectral Elements for Transport-Dominated Equations, Lecture Notes in Computational Science and Engineering, Volume 1, Springer-Verlag, New York 1997.
• D. Funaro, M. Giangi, D. Mansutti, A Splitting Method for Unsteady Incompressible Viscous Fluids Imposing no Boundary Conditions on Pressure, Journal of Scientific Computing, Vol. 13, n. 1 (1998), pp. 95-104.
• D. Funaro, A Note on Second-Order Finite-Difference Artificial-Viscosity Schemes on Uniform Meshes for Advection-Diffusion Equations, Numer. Methods Partial Differential Eq., Vol.15 (1999), pp. 581-588.
• D. Funaro, G. Pontrelli, Spline Approximation of Advection-Diffusion Problems Using Upwind Type Collocation Nodes, J. of Computational and Applied Math., 110 (1999), pp. 141-153.
• D. Funaro, About 3-D Spectral Element Computations, Recent Trends in Numerical Analysis (D. Trigiante Ed.), Advances in the Theory of Computational Mathematics, v. 3 (2000), Nova Science Pub., Huntington NY, pp. 163-173.
• D. Funaro, A Superconsistent Chebyshev Collocation Method for Second-Order Differential Operators, Numerical Algorithms, v. 28 (2001), pp.151-157.
• D. Funaro, Superconsistent Discretizations, J. Scientific Computing, v.17, n. 1-4 (2002), pp. 67-79.
• D. Funaro, Superconsistent Discretizations with Application to Hyperbolic Equation, Siberian Journal of Numer. Mathematics, v.6, n.1 (2003), pp.89-99.
• D. Funaro, Superconsistent Discretizations of Integral Type Equations, Applied Numerical Mathematics, v.48 (2004), pp.1-11.
• L. Fatone, D. Funaro, R. Giova, Finite-Difference Schemes for Transport-Dominated Equations Using Special Collocation Nodes, Numerical Methods for P.D.E., v.21 (2005), pp.649-671.
• D. Funaro, G. Pontrelli, A General Class of Finite-difference Methods for the Linear Transport Equation, Comm. Math. Sci., v.3, n.3 (2005), pp. 403-423.
• L. Fatone, D. Funaro, V. Scannavini, Finite-Differences Preconditioners for Superconsistent Pseudospectral Approximations, Math. Modelling and Num. Anal., v.41, n.6 (2007), pp.1021-1039.
• L. Fatone, D. Funaro, G. J. Yoon, A Convergence Analysis for the Superconsistent Chebyshev Method, Applied and Num. Math., v.58, n.1 (2008), pp. 88-100.
• D. Funaro, Exact Solutions on Twisted Rings for the 3D Navier-Stokes Equations, Preprint (2011), arXiv:1112.0881v1.
• L. Fatone, D. Funaro, Optimal Collocation Nodes for Fractional Derivative Operators, SIAM J. Scientific Computing, Vol. 37, n. 3 (2015), pp. A1504-A1524. DOI: 10.1137/140993697  , arXiv:1407.0552.
• G. Manzini, D. Funaro, G.L. Delzanno, Convergence of Spectral Discretizations of the Vlasov-Poisson System, SIAM J. Numer. Anal, Vol. 55, n. 5 (2017), pp. 2312-2335. DOI: 10.1137/16M1076848 , arXiv:1612.08013.
• L. Fatone, D. Funaro, Isospectral Domains for Discrete Elliptic Operators, J. of Scientific Computing, (2018),  75, pp. 405-426. DOI: 10.1007/s10915-017-0541-5 , Print ISSN: 0885-7474, Online ISSN: 1573-7691, arXiv:1803.11108 .
• L. Fatone, D. Funaro, G. Manzini, Arbitrary-order Time-accurate Semi-Lagrangian Spectral Approximations of the Vlasov-Poisson System, Journal of Computational Physics, Vol. 384 (2019), pp. 349-375, DOI: 10.1016/j.jcp.2019.01.020, arXiv:1803.09305 .
• L. Fatone, D. Funaro, G. Manzini, A Semi-Lagrangian Spectral Method for the Vlasov-Poisson System based on Fourier, Legendre and Hermite Polynomials, Communications on Applied Mathematics and Computation, Vol. 1, n.3 (2019), pp. 333-360, DOI: 10.1007/s42967-019-00027-8, arXiv:1807.02418.
• L. Fatone, D. Funaro, G. Manzini, On the Use of Hermite Functions for the Vlasov–Poisson System, in Spectral and High Order Methods for Partial Differential Equations (ICOSAHOM Conference, London, UK, July 9-13, 2018), LNCSE, Springer,  Vol. 134 (2020), pp. 143-153, DOI: 10.1007/978-3-030-39647-3 .
• D. Funaro,  G. Manzini, Stability and Conservation Properties of Hermite-based Approximations of the Vlasov-Poisson System, J. of Scientific Computing, Vol. 88, n. 29 (2021), DOI: 10.1007/s10915-021-01537-5, arXiv:2103.00691 .
• L. Fatone, D. Funaro, G. Manzini, A Decision-Making Machine Learning Approach in Hermite Spectral Approximations of Partial Differential Equations, Journal of Scientific Computing, Vol. 92, n.3 (2022),  10.1007/s10915-022-01853-4, arXiv:2104.02181.
• L. Fatone, D. Funaro, High-Order Discretization of Backward Anisotropic Diffusion and Application to Image Processing, Annali dell’Università di Ferrara, Vol. 68 (2022), pp. 295-310, DOI: 10.1007/s11565-022-00419-4, arXiv:2204.13475 .
• D. Funaro, How and why non smooth solutions of the 3D Navier–Stokes equations could possibly develop, Numerische Mathematik, Vol.152 (2022), pp. 789-817, DOI: 10.1007/s00211-022-01333-9, arXiv:2004.04262
• D. Funaro, Understanding the Meaning of Understanding: a Possible Way to Self-Consciousness, Preprint (2023), hal.science/hal-04055975v1 (previous version: arXiv:1806.05234 ).
• L. Fatone, D. Funaro, An Anisotropic Diffusion Algorithm for Image Deblurring, AIP Conference Proceedings, Vol. 3094 (2024), 1, 370004, DOI: 10.1063/5.0210637.
• L. Fatone, D. Funaro, Low-Cost Denoising and Deblurring Using a Novel Nonlinear Diffusion Technique, Journal of Computational and Applied Mathematics, Vol. 461 (2025), 116423, DOI:10.1016/j.cam.2024.116423 .
• L. Fatone, D. Funaro, An Alternative Nonlinear Diffusion Algorithm for Image Denoising and Deblurring, Sergeyev Y.D., Kvasov D.E., Astorino A. (Eds.), Numerical Computations: Theory and Algorithms, Lecture Notes in Computer Science, NUMTA 2023, Springer, Switzerland (2024), in press.