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Main papers

Here is a list of recent papers on electromagnetism: 

 

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.
  • 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. 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.
  • 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, 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, (2017), pp. 1-22. 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, arXiv:1803.09305 .
  • D.Funaro, High Frequency Electrical Oscillations in Cavities, Mathematical Modelling and Analysis, n. 23 (2018).
  • D.Funaro, Understanding the Meaning of Understanding, arXiv:1806.05234 .