Fast & Flow-rious: A Hybrid Ride Through Phase Space
Date(s) : 02/12/2025 iCal
11h00 - 12h00
This talk presents a hybrid semi-Lagrangian scheme for the Vlasov–Poisson equation that combines high-speed accuracy with efficient structure preservation by merging the Characteristic Mapping Method [1] (CMM) and the Numerical Flow Iteration[2] (NuFi) approach. Both methods leverage the semigroup property of the underlying diffeomorphic flow, allowing the solution to be reconstructed by tracing characteristics back to their origins via a flow map.
NuFi constructs this map iteratively, preserving symplectic structure, but with computational cost growing quadratically in time. Its strength lies in a compact, low-dimensional representation tied to the electric field. In contrast, CMM explicitly composes the flow map from stored submaps, achieving linear time complexity at the expense of higher memory usage.
The proposed hybrid method uses NuFi for accurate, structure-preserving local updates and CMM for efficient composition of the global flow map. This combination enables fast and flexible navigation through phase space, while reducing storage demands and maintaining precision. I will discuss the trade-offs involved, the design choices behind the coupling, and demonstrate the effectiveness of the approach through numerical results.
Authors: P. Krah (CEA), Zetao Lin (AMU), Paul Wilhelm (KUL), Fabio Bacchini (KUL), Virginie Grandgirard (CEA), Kai Schneider (AMU)
References:
[1] Krah, P., Yin, X. Y., Bergmann, J., Nave, J. C., & Schneider, K. (2024). A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties. _Communications in Computational Physics_, _35_(4), 905-937.
[2] Kirchhart, Matthias, and R. Paul Wilhelm. « The Numerical Flow Iteration for the Vlasov–Poisson Equation. » _SIAM Journal on Scientific Computing_ 46.3 (2024): A1972-A1997.
Emplacement
I2M Saint-Charles - Salle de séminaire
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