Research and Publications

My academic interests lie primarily in the efficient numerical solution of Ordinary Differential Equations and Partial Differential Equations. More in detail, my research focuses on the study, development, and implementation of exponential integrators for semidiscretized Partial Differential Equations, emphasizing applications and tensor structured problems.

I am also interested in developing efficient dynamical low-rank algorithms for plasma physics problems, particularly their effective implementation on GPUs.

You can find my Scopus record here.

You can find my Web of Science record here.

You can find my ORCID record here.

You can find my Google Scholar page here.

You can find my GitHub public page here.

Preprints

1. M. Caliari, F. Cassini, L. Einkemmer, and A. Ostermann. On the convergence of split exponential integrators for semilinear parabolic problems. arXiv preprint, arXiv:2503.16210, 2025. https://doi.org/10.48550/arXiv.2503.16210

2. F. Cassini and C. Segala. The turnpike control in stochastic multi-agent dynamics: a discrete-time approach with exponential integrators. arXiv preprint, arXiv:2503.09549, 2025.
   https://doi.org/10.48550/arXiv.2503.09549

3. ...

Papers

1. M. Caliari and F. Cassini. Exponential quadrature rules for problems with time-dependent fractional source. J. Comput. Appl. Math, 474:116993, 2026. Available online 7 August 2025.
   https://doi.org/10.1016/j.cam.2025.116993

2. F. Cassini. Efficient third-order tensor-oriented directional splitting for exponential integrators. Electron. Trans. Numer. Anal., 60:520--540, 2024.
   https://doi.org/10.1553/etna_vol60s520

3. M. Caliari, F. Cassini, and F. Zivcovich. A $\mu$-mode approach for exponential integrators: actions of $\varphi$-functions of Kronecker sums. Calcolo, 61:61, 2024.
   https://doi.org/10.1007/s10092-024-00610-3

4. G. Albi, M. Caliari, E. Calzola, and F. Cassini. Exponential integrators for a mean-field selective optimal control problem. J. Approx. Softw., 1(2):2, 2024.
   https://doi.org/10.13135/3103-1935/10973

5. M. Caliari and F. Cassini. Efficient simulation of complex Ginzburg--Landau equations using high-order exponential-type methods. Appl. Numer. Math., 206:340--357, 2024.
   https://doi.org/10.1016/j.apnum.2024.08.009

6. M. Caliari, F. Cassini, L. Einkemmer, and A. Ostermann. Accelerating exponential integrators to efficiently solve semilinear advection-diffusion-reaction equations. SIAM J. Sci. Comput., 46(2):A906--A928, 2024.
   https://doi.org/10.1137/23M1562056

7. M. Caliari and F. Cassini. A second order directional split exponential integrator for systems of advection--diffusion--reaction equations. J. Comput. Phys., 498:112640, 2024.
   https://doi.org/10.1016/j.jcp.2023.112640

8. M. Caliari and F. Cassini. Direction splitting of $\varphi$-functions for $d$-dimensional problems in Kronecker form. J. Approx. Softw., 1(1):1, 2024.
   https://doi.org/10.13135/3103-1935/10813

9. M. Caliari, F. Cassini, and F. Zivcovich. BAMPHI: matrix and transpose free action of linear combinations of $\varphi$-functions from exponential integrators. J. Comput. Appl. Math., 423:114973, 2023.
   https://doi.org/10.1016/j.cam.2022.114973

10. M. Caliari, F. Cassini, and F. Zivcovich. A $\mu$-mode BLAS approach for multidimensional tensor-structured problems. Numer. Algorithms, 92(4):2483--2508, 2023.
    https://doi.org/10.1007/s11075-022-01399-4

11. F. Cassini and L. Einkemmer. Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign. Comput. Phys. Commun., 280:108489, 2022.
    https://doi.org/10.1016/j.cpc.2022.108489

12. M. Caliari, F. Cassini, L. Einkemmer, A. Ostermann, and F. Zivcovich. A $\mu$-mode integrator for solving evolution equations in Kronecker form. J. Comput. Phys., 455:110989, 2022.
    https://doi.org/10.1016/j.jcp.2022.110989

13. M. Caliari, F. Cassini, and F. Zivcovich. Approximation of the matrix exponential for matrices with a skinny field of values. BIT Numer. Math., 60(4):1113--1131, 2020.
    https://doi.org/10.1007/s10543-020-00809-0

Miscellaneous

1. F. Cassini. Exponential integrators: tensor structured problems and applications. PhD thesis, 2023.
   https://doi.org/10.15168/11572_374707