Research

Research interests

• Numerical methods for stiff (dissipative and highly oscillatory) ordinary differential equations

• Time integrators for stiff partial differential equations

• Numerical schemes for stochastic differential equations

• Time integration of kinetic equations

Ph.D. Thesis

• Explicit stabilized methods for stiff stochastic differential equations and stiff optimal control problems, Ph.D. Thesis, University of Geneva (2020) No. 5511.

Publications

1. I. Almuslimani and N. Crouseilles. Conservative stabilized Runge-Kutta methods for the Vlasov- Fokker-Planck equation. Journal of Computational Physics, 488:112241, 2023. arXiv:2212.13943.

2. Almuslimani, I. A fully adaptive explicit stabilized integrator for advection–diffusion–reaction problems. Bit Numer Math 63, 3 (2023). arXiv:2201.10206.

3. I. Almuslimani, P. Chartier, M. Lemou, and F. Méhats. Uniformly accurate schemes for drift--oscillatory stochastic differential equations. Applied Numerical Mathematics, 181:468–482, 2022. arXiv:2108.06987.

4. I. Almuslimani and G. Vilmart. Explicit stabilized integrators for stiff optimal control problems. SIAM J. Sci. Comput. 43 (2021), no.2, A721-A743. arXiv:1910.10584.

5.  A. Abdulle, I. Almuslimani, and G. Vilmart. Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations. SIAM/ASA J. Uncertain. Quantif. 6 (2018), no. 2, 937–964. arXiv:1708.08145.

Posters

• Poster: Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations.

This poster was presented at SciCADE 2017 in Bath, and the Stepping stone symposium on theoretical and numerical analysis of PDEs in Geneva, and got the SIAM first prize for the best poster at SciCADE 2017.

• Poster: Explicit stabilized integrators for stiff optimal control problems.

This poster was presented at the Workshop on Multiscale Methods for Deterministic and Stochastic Dynamics, Geneva, January 2020.

Software

• Matlab codes for some numerical experiments in the paper: I. Almuslimani, N. Crouseilles. Conservative stabilized Runge--Kutta methods for the Vlasov--Fokker--Planck equation. Submitted. hal-03911417 : Section 5.1.3: RKC vs RK2, Section 5.2: Test 3 1dx-1dv, Section 5.3: 1dx-2dv.

• ARKC: Matlab code for the ARKC method with drivers. Paper: I. Almuslimani. A fully adaptive explicit stabilized integrator for advection-diffusion-reaction problems. Submitted (2022). hal-03542086.

• RKCOC: Matlab code for the RKC method and its double adjoint for optimal control problems. The method is introduced in the following paper: I. Almuslimani and G. Vilmart. Explicit stabilized integrators for stiff optimal control problems. SIAM J. Sci. Comput. 43 (2021), no.2, A721-A743.

• SK-ROCK method with driver for problem (55) of the paper: A. Abdulle, I. Almuslimani, G. Vilmart. Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations, SIAM/ASA J. Uncertain. Quantif. 6 (2018), no. 2, 937–964.