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) accepted for publication in Mathematics of Computation.

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

Preprint

1. Generalized convolution quadrature based on the trapezoidal rule, (joint with L. Banjai), submitted.

2. 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) submitted.

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

4. T-coercivity of the Johnson-Nédélec coupling, submitted.

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).