PhD Student in Numerical Analysis
Uppsala University · IT Department
Division of Scientific Computing
Uppsala, Sweden
PhD Student in Numerical Analysis
I'm Rafael, a PhD student in Scientific Computing with specialization in Numerical Analysis at Uppsala University, working under the supervision of Murtazo Nazarov and co-supervised by Ricardo Vinuesa and Mats Holmström.
My research project, Optimal Control of Fusion Processes, focuses on highly accurate magnetohydrodynamic (MHD) simulations using finite element methods. The goal is to solve optimization problems for plasma stabilization and to explore deep reinforcement learning for real-time control. This work has the potential to contribute to the development of feasible fusion energy reactors: a potentially limitless source of sustainable energy.
Before joining my current group, I completed my MSc in Computational Science at Uppsala University and my BSc in Theoretical Physics at University of Seville. Outside my research, I enjoy teaching, science communication, playing piano and bouldering.
Animated visualizations and numerical experiments from my research. Click to watch!
Hall Magnetohydrodynamics (Hall MHD) is an extension of the ideal MHD model that allows for rapid conversion of magnetic energy into kinetic energy, which gives rise to explosive plasma phenomena. We develop the first structure-preserving numerical method for Hall MHD, in collaboration with Ignacio Tomas
The Vlasov–Poisson equations describe plasma using the kinetic theory approach, capturing the evolution of the distribution function in phase space. These equations are extremely accurate for modeling plasma, but require a six-dimensional phase space for full resolution, making them challenging to solve numerically.
The Kuramoto–Sivashinsky (KS) equation is a fourth-order nonlinear PDE that models spatiotemporal chaos in dissipative systems. Its interplay between long-wave instability, short-wave dissipation, and nonlinear energy transfer produces persistent, turbulence-like chaos that never settles into a simple pattern.
Peer-reviewed papers, preprints, and theses. Authors are listed alphabetically. I publish under R. Rodriguez-Velasco.
Courses I have taught or assisted with.
I hold a certificate of completion for an academic teacher training course: [Certificate PDF]
| Course | Role | Institution | Year |
|---|---|---|---|
| Applied Finite Element Methods | Teaching Assistant | Uppsala University | 2026 |
| Applied Computational Fluid Dynamics | Teaching Assistant | Uppsala University | 2026 |
| Programming II | Teaching Assistant | Uppsala University | 2025 |
| Programming II | Teaching Assistant | Uppsala University | 2024 |
I am passionate about making math, physics and programming accessible to all students. I also worked part-time as a private mathematics tutor throughout my bachelor’s studies.
Questions about my research, collaborations, or teaching? Get in touch!