Symplectic model reduction methods for the Vlasov equation
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Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to ordinary differential equations of a very high dimension. Solving such equations is computationally very expensive, especially when simulations for many different values of input parameters are desired. In this work we compare several model reduction techniques and demonstrate their applicability to numerical simulations of the Vlasov equation. The necessity of symplectic model reduction algorithms is illustrated with a simple numerical experiment.
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