Numerical Analysis

Published

1.  On the coupling of the Curved Virtual Element Method with the one-equation Boundary Element Method for 2D exterior Helmholtz problems, (joint with L. Desiderio, S. Falletta and L. Scuderi), SIAM Journal of Numerical Analysis, 60 (4), 2099-2124 (2022).

2. CVEM-BEM coupling with decoupled orders for 2D exterior Poisson problems, (joint with L. Desiderio, S. Falletta and L. Scuderi), Journal of Scientific Computing, 92 (2022) Paper No. 96.

3. CVEM-BEM coupling for the simulation of time-domain wave fields scattered by obstacles with complex geometries,  (joint with L. Desiderio, S. Falletta and L. Scuderi), Computational Method in Applied Mathematics, 23, 353-372 (2023).

4. Developments on the stability of the non-symmetric coupling of finite and boundary elements,Computational Method in Applied Mathematics. 23, 372-388 (2023).

5. A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials, (joint with S. Falletta and L. Scuderi), Journal of Computational and Applied Mathematics, 441, 115625 (2024).

6. Some properties of a modified Hilbert transform, Comptes Rendus. Mathématique, 362, 799-806 (2024).

7. Runge-Kutta convolution quadrature based on Gauss methods, (joint with L. Banjai), Numerische Mathematik, 156, 1719-1750 (2024).

8. Unconditionally stable space-time isogeometric discretization of the wave equation in Hamiltonian formulation, (joint with S. Fraschini, G. Loli and I. Perugia), ESAIM: Mathematical Modeling and Numerical Analysis 59, 2447-2490 (2025).

9. Stability of conforming space-time isogeometric methods for the wave equation, (joint with S. Fraschini) Mathematics of Computation 95, 683-719 (2026).

10. Intrinsic unconditional stability in space-time isogeometric approximation of the acoustic wave equation in second-order formulation, (joint with I. Perugia) Mathematical Models and Methods in Applied Sciences 36 (3), 561-599, (2026).

11. Generalized convolution quadrature based on the trapezoidal rule, (joint with L. Banjai), accepted for publication in IMA Journal of Numerical Analysis.

12. Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation, (joint with I. Perugia and E. Zampa) accepted for publication in Journal of Scientific Computing.

13. Stability, convergence, and geometric properties of second-order-in-time space-time discretizations for linear and semilinear wave equations, (joint with I. Perugia and E. Zampa) accepted for publication in ESAIM: Mathematical Modeling and Numerical Analysis.

Preprint

1. Unconditionally stable space-time isogeometric method for the linear Schrödinger equation, (joint with S. Gómez)

2. T-coercivity of the Johnson-Nédélec coupling

3. A space-time sparse-grid method for the wave equation, (joint with A. Moiola, C. Perinati, and I. Perugia)

4. Convolution quadrature based on a truncated trapezoidal rule

Number Theory

Published

1. Binary recurrences with prime powers as fixed points of their discriminator, INTEGERS (21) A116, (2021).

2. On a basic mean value Theorem with explicit exponents, International Journal of Number Theory, 18, (3), 673-690 (2022).

3. On the minimal number of solutions of the equation ϕ(n+k)=Mϕ(n), M=1, 2, (joint with L. Sillari), Journal of Integers Sequences 26 (2023) Paper No. 26.1.3.

Preprint

1. On the discriminator of Lucas sequences II (joint with L. Florian and P. Moree).