This page has only limited features, please log in for full access.

Prof. Daniele Funaro
Dipartimento di Scienze Chimiche e Geologiche, University of Modena and Reggio Emilia, Via Campi 103, 41125 Modena, Italy

Basic Info


Research Keywords & Expertise

0 Computational methods for partial differential equations
0 High-order approximation techniques
0 Model equations in electromagnetism
0 Electromagnetic solitons
0 Waves in resonant cavities

Honors and Awards

The user has no records in this section


Career Timeline

The user has no records in this section.


Short Biography

The user biography is not available.
Following
Followers
Co Authors
The list of users this user is following is empty.
Following: 0 users

Feed

Article
Published: 12 June 2021 in Journal of Scientific Computing
Reads 0
Downloads 0

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electrostatic limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

ACS Style

Daniele Funaro; Gianmarco Manzini. Stability and Conservation Properties of Hermite-Based Approximations of the Vlasov-Poisson System. Journal of Scientific Computing 2021, 88, 1 -36.

AMA Style

Daniele Funaro, Gianmarco Manzini. Stability and Conservation Properties of Hermite-Based Approximations of the Vlasov-Poisson System. Journal of Scientific Computing. 2021; 88 (1):1-36.

Chicago/Turabian Style

Daniele Funaro; Gianmarco Manzini. 2021. "Stability and Conservation Properties of Hermite-Based Approximations of the Vlasov-Poisson System." Journal of Scientific Computing 88, no. 1: 1-36.

Journal article
Published: 10 December 2020 in Applied Sciences
Reads 0
Downloads 0

Designing antennas suitable for generating highly directive electromagnetic signals has become a fundamental task. This is particularly relevant for the development of efficient and sustainable point-to-point communication channels, and for energy transfer. Indeed, these are nowadays expanding areas of research. In order to deal with said particular wave phenomena, an extension of the electrodynamics equations is taken into account, where exact solitonic type solutions are admitted. These waves may have compact support and travel along a straight line, without dissipation, at the speed of light. The result suggests the design of biconic type antennas having specific properties that are numerically examined in this paper. The cones, supplied with an oscillating source, are embedded in a dielectric material of suitable shape, with the purpose of driving the signal in the proper direction. The computations based on the extended model are aimed toward simulating the possibility of generating peculiar wave behaviors, in view of practical implementations in the framework of point-to-point communications or wireless power transmission.

ACS Style

Alessandro Chiolerio; Lorenzo Diazzi; Daniele Funaro. Highly Directive Biconic Antennas Embedded in a Dielectric. Applied Sciences 2020, 10, 8828 .

AMA Style

Alessandro Chiolerio, Lorenzo Diazzi, Daniele Funaro. Highly Directive Biconic Antennas Embedded in a Dielectric. Applied Sciences. 2020; 10 (24):8828.

Chicago/Turabian Style

Alessandro Chiolerio; Lorenzo Diazzi; Daniele Funaro. 2020. "Highly Directive Biconic Antennas Embedded in a Dielectric." Applied Sciences 10, no. 24: 8828.

Journal article
Published: 05 March 2020 in Applied Sciences
Reads 0
Downloads 0

In suitable bounded regions immersed in vacuum, time periodic wave solutions solving a full set of electrodynamics equations can be explicitly computed. Analytical expressions are available in special cases, whereas numerical simulations are necessary in more complex situations. The attention here is given to selected three-dimensional geometries, which are topologically equivalent to a toroid, where the behavior of the waves is similar to that of fluid-dynamics vortex rings. The results show that the shape of the sections of these rings depends on the behavior of the eigenvalues of a certain elliptic differential operator. Time-periodic solutions are obtained when at least two of such eigenvalues attain the same value. The solutions obtained are discussed in view of possible applications in electromagnetic whispering galleries or plasma physics.

ACS Style

Daniele Funaro. Electromagnetic Waves in Annular Regions. Applied Sciences 2020, 10, 1780 .

AMA Style

Daniele Funaro. Electromagnetic Waves in Annular Regions. Applied Sciences. 2020; 10 (5):1780.

Chicago/Turabian Style

Daniele Funaro. 2020. "Electromagnetic Waves in Annular Regions." Applied Sciences 10, no. 5: 1780.

Original paper
Published: 22 May 2019 in Communications on Applied Mathematics and Computation
Reads 0
Downloads 0

In this work, we apply a semi-Lagrangian spectral method for the Vlasov–Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space–velocity domain with a BDF time-stepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.

ACS Style

Lorella Fatone; Daniele Funaro; Gianmarco Manzini. A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials. Communications on Applied Mathematics and Computation 2019, 1, 333 -360.

AMA Style

Lorella Fatone, Daniele Funaro, Gianmarco Manzini. A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials. Communications on Applied Mathematics and Computation. 2019; 1 (3):333-360.

Chicago/Turabian Style

Lorella Fatone; Daniele Funaro; Gianmarco Manzini. 2019. "A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials." Communications on Applied Mathematics and Computation 1, no. 3: 333-360.

Journal article
Published: 05 February 2019 in Journal of Computational Physics
Reads 0
Downloads 0

The Vlasov-Poisson system, modeling the evolution of non-collisional plasmas in the electrostatic limit, is approximated by a semi-Lagrangian technique. Spectral methods of periodic type are implemented through a collocation approach. Groups of particles are represented by the Fourier Lagrangian basis and evolve, for a single timestep, along an high-order accurate representation of the local characteristic lines. The time-advancing technique is based on truncated Taylor series that can be, in principle, of any order of accuracy. A variant is obtained by coupling the phase space discretization with high-order accurate Backward Differentiation Formulas (BDF). At each timestep, particle displacements are reinterpolated and expressed in the original basis to guarantee the order of accuracy in all the variables at relatively low costs. Thus, these techniques combine the excellent features of spectral approximations with high-order time integration. The resulting method has excellent conservation properties. Indeed, it can be proven that the total number of particles, proportional to the total mass and charge, is conserved up to the machine precision. Series of numerical experiments are performed in order to assess the real performance. In particular, comparisons with standard benchmarks are examined.

ACS Style

L. Fatone; D. Funaro; G. Manzini. Arbitrary-order time-accurate semi-Lagrangian spectral approximations of the Vlasov–Poisson system. Journal of Computational Physics 2019, 384, 349 -375.

AMA Style

L. Fatone, D. Funaro, G. Manzini. Arbitrary-order time-accurate semi-Lagrangian spectral approximations of the Vlasov–Poisson system. Journal of Computational Physics. 2019; 384 ():349-375.

Chicago/Turabian Style

L. Fatone; D. Funaro; G. Manzini. 2019. "Arbitrary-order time-accurate semi-Lagrangian spectral approximations of the Vlasov–Poisson system." Journal of Computational Physics 384, no. : 349-375.

Journal article
Published: 14 June 2018 in Mathematical Modelling and Analysis
Reads 0
Downloads 0

If the interior of a conducting cavity (such as a capacitor or a coaxial cable) is supplied with a very high-frequency electric signal, the information between the walls propagates with an appreciable delay, due to the _niteness of the speed of light. The con_guration is typical of cavities having size larger than the wavelength of the injected signal. Such a non rare situation, in practice, may cause a break down of the performances of the device. We show that the classical Coulomb's law and Maxwell's equations do not correctly predict this behavior. Therefore, we provide an extension of the modeling equations that allows for a more reliable determination of the electromagnetic _eld during the evolution process. The main issue is that, even in vacuum (no dielectric inside the device), the fast variation of the signal produces sinks and sources in the electric _eld, giving rise to zones where the divergence is not zero. These regions are well balanced, so that their average in the domain is zero. However, this behavior escapes the usual treatment with classical electromagnetism.

ACS Style

Daniele Funaro. HIGH FREQUENCY ELECTRICAL OSCILLATIONS IN CAVITIES. Mathematical Modelling and Analysis 2018, 23, 345 -358.

AMA Style

Daniele Funaro. HIGH FREQUENCY ELECTRICAL OSCILLATIONS IN CAVITIES. Mathematical Modelling and Analysis. 2018; 23 (3):345-358.

Chicago/Turabian Style

Daniele Funaro. 2018. "HIGH FREQUENCY ELECTRICAL OSCILLATIONS IN CAVITIES." Mathematical Modelling and Analysis 23, no. 3: 345-358.

Journal article
Published: 21 November 2009 in Journal of Scientific Computing
Reads 0
Downloads 0

A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on an explicit finite-difference technique. The experiments in two dimensions simulate travelling solitary electromagnetic waves, and show their interaction with conductive walls. In particular, the classical dispersion, exhibited by the passage of a photon through a small aperture, is examined.

ACS Style

Daniele Funaro. Numerical Simulation of Electromagnetic Solitons and Their Interaction with Matter. Journal of Scientific Computing 2009, 45, 259 -271.

AMA Style

Daniele Funaro. Numerical Simulation of Electromagnetic Solitons and Their Interaction with Matter. Journal of Scientific Computing. 2009; 45 (1):259-271.

Chicago/Turabian Style

Daniele Funaro. 2009. "Numerical Simulation of Electromagnetic Solitons and Their Interaction with Matter." Journal of Scientific Computing 45, no. 1: 259-271.