We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically and exponential resolution in linear time is obtained. Global third-order convergence in space and time is shown and conservation properties are assessed. For benchmarking, we consider linear and nonlinear Landau damping and the two-stream instability. We compare the results with a Fourier pseudo-spectral method. The extreme fine-scale resolution features are illustrated showing the method's capabilities to efficiently treat filamentation in fusion plasma simulations.

翻译：我们提出了一种高效的半拉格朗日特征映射方法，用于在粗网格上高精度求解一维+一维Vlasov-Poisson方程。通过数值演化流映射，在线性时间内实现了指数级分辨率。该方法在空间和时间上均表现出全局三阶收敛性，并评估了其守恒性质。在基准测试中，我们考虑了线性和非线性朗道阻尼以及双流不稳定性，并将结果与傅里叶伪谱方法进行了对比。极细尺度分辨能力的展示揭示了该方法在聚变等离子体模拟中高效处理丝化现象的能力。